Claude Opus 5 · Claude Code · effort: max
A short film about category theory, and the generative art it makes.
Claude Opus 5 · effort max · Claude Code 2.1.239 · 2026-08-22 · timestamps UTC
Every human turn and every word Claude wrote to the user appears verbatim, in order. Tool calls are listed with their command or target; their outputs are not reproduced — the raw session log is 23 MB, most of it rendered PNGs, ffmpeg logs and multi-megabyte command output. Where a result mattered, Claude's next message says what it showed.
Two kinds of entry are not the user speaking, and are marked as such:
🖼 image returned to Claude — Claude read a PNG it had just rendered. The
harness returns image attachments on the user channel; these are Claude
looking at its own output, which is how most of the visual iteration happened.📎 skill loaded — a bundled skill was pulled into the turn.There is no visible reasoning to include. The session ran with thinking
display: "omitted", so all 423 assistant turns carried empty thinking blocks;
the raw chain of thought is never returned by the API. Nothing has been cut from
the visible conversation.
Session shape: 4 human turns, 1 question asked back, 96 assistant messages, 218 tool calls.
03:34:33(slash command) /effort — set the session's effort level to max.
03:38:03You're in an empty git repository. Use mise, python, uv, and whatever dependencies you like to create a short film about category theory. Explain it to the layman, and creative a generative art project to give a visual demonstration of the power and beauty of category theory.
03:38:05I'll build this. Let me start by understanding the environment and setting up the project.
03:38:06
Bash — Check environment and tooling
pwd && ls -la && echo "---MISE---" && which mise && mise --version && echo "---UV---" && which uv && uv --version && echo "---PY---" && which python3 && python3 --version && echo "---FFMPEG---" && which ffmpeg && ffmpeg -version 2>&1 | head -3
03:38:08
Bash — Check git state and system resources
echo "---git---" && git status --short && git log --oneline -5 2>&1 | head -5; echo "---cpu---" && sysctl -n hw.ncpu && sysctl -n hw.memsize; echo "---fonts---" && ls /System/Library/Fonts/ 2>/dev/null | head -30
03:38:50
Bash — List macOS TTS voices
echo "---SAY VOICES (en)---" && say -v '?' 2>/dev/null | grep -E 'en_|en-' | head -40; echo "---count---" && say -v '?' 2>/dev/null | wc -l
03:38:53
Bash — Check available fonts for typography
ls ~/Library/Fonts/ 2>/dev/null | head -40; echo "---system---"; ls /System/Library/Fonts/Supplemental/ 2>/dev/null | grep -iE 'times|georgia|garamond|baskerv|didot|optima|futura|helvet|charter|palatino|iowan' | head -20; echo "---mono---"; ls /System/Library/Fonts/ | grep -iE 'mono|menlo|sf' | head
03:39:01
Bash — Look for premium TTS voices
say -v '?' 2>/dev/null | grep -iE 'ava|allison|tom |serena|zoe|jamie|nathan|evan|susan|isha|noelle|joelle' | head -20; echo "=== check quality tags ==="; say -v '?' 2>/dev/null | awk '{print $1}' | sort -u | head -60
03:39:03
Bash — Create project directory structure
mkdir -p src/catfilm/{render,scenes,audio} out assets && ls -R . | head -20
03:39:08Environment is good. Setting up the project scaffold:
03:39:14
Bash — Write mise tool and task config
cat > mise.toml <<'EOF'
# Tool + task definitions for the "Functor" short film.
# Everything the project needs, pinned in one place.
[tools]
python = "3.13"
uv = "latest"
ffmpeg = "latest"
[env]
_.python.venv = { path = ".venv", create = true }
PYTHONPATH = "{{config_root}}/src"
[tasks.install]
description = "Sync the Python environment with uv"
run = "uv sync"
[tasks.render]
description = "Render every frame of the film"
run = "uv run catfilm render"
[tasks.audio]
description = "Generate narration and the functorial score"
run = "uv run catfilm audio"
[tasks.film]
description = "Full pipeline: audio -> frames -> muxed film"
run = "uv run catfilm build"
[tasks.stills]
description = "Render the generative-art gallery as high-res stills"
run = "uv run catfilm gallery"
[tasks.preview]
description = "Render one scene quickly for iteration (mise run preview -- <scene>)"
run = "uv run catfilm render --preview"
[tasks.clean]
description = "Remove build output"
run = "rm -rf out/frames out/audio out/film.mp4"
EOF
cat > .python-version <<'EOF'
3.13
EOF
echo "wrote mise.toml"
03:39:18
Bash — Write pyproject and sync dependencies
cat > pyproject.toml <<'EOF'
[project]
name = "catfilm"
version = "1.0.0"
description = "Functor — a short film about category theory, and the generative art it makes"
readme = "README.md"
requires-python = ">=3.13"
dependencies = [
"numpy>=2.1",
"pycairo>=1.27",
"pillow>=11.0",
"scipy>=1.14",
]
[project.scripts]
catfilm = "catfilm.cli:main"
[build-system]
requires = ["hatchling"]
build-backend = "hatchling.build"
[tool.hatch.build.targets.wheel]
packages = ["src/catfilm"]
[tool.uv]
package = true
[tool.ruff]
line-length = 100
target-version = "py313"
EOF
cat > .gitignore <<'EOF'
.venv/
__pycache__/
*.pyc
out/frames/
out/audio/
out/*.mp4
out/*.wav
out/*.aiff
.uv-cache/
.DS_Store
EOF
uv sync 2>&1 | tail -20
03:39:24
Bash — Add README and stub modules, then sync
printf '# Functor\n\nA short film about category theory.\n' > README.md && touch src/catfilm/__init__.py src/catfilm/render/__init__.py src/catfilm/scenes/__init__.py src/catfilm/audio/__init__.py && printf 'def main():\n print("catfilm")\n' > src/catfilm/cli.py && uv sync 2>&1 | tail -20
03:39:31
Bash — Check for cairo and pkg-config via homebrew
brew list 2>/dev/null | grep -iE '^(cairo|pkg-config|pkgconf|pango|freetype)$'; echo "---"; ls /opt/homebrew/lib/libcairo* 2>/dev/null; echo "---pkgconfig---"; which pkg-config pkgconf 2>/dev/null; ls /opt/homebrew/lib/pkgconfig/cairo.pc 2>/dev/null
03:39:42
Bash — Test if skia-python installs from wheels
cd /tmp && uv pip download --help >/dev/null 2>&1; uv run --no-project --python 3.13 --with skia-python python -c "import skia; print('skia OK', skia.__file__)" 2>&1 | tail -5
03:39:43
Bash — Test aggdraw as antialiased 2D fallback
cd /tmp && uv run --no-project --python 3.13 --with aggdraw python -c "import aggdraw; print('aggdraw OK')" 2>&1 | tail -3
03:39:51skia-python installs from wheels — that's a better renderer than cairo (GPU-grade AA, blurs, gradients, blend modes). Switching to it:
03:39:52
Bash — Swap pycairo for skia-python and sync
sed -i '' 's|"pycairo>=1.27",|"skia-python>=87.0",|' pyproject.toml && cat pyproject.toml | head -16 && uv sync 2>&1 | tail -8
03:39:59
Bash — Probe skia API surface
uv run python - <<'PY'
import skia, numpy as np
print("skia", skia.__version__ if hasattr(skia,'__version__') else '?')
surf = skia.Surface(64, 64)
with surf as c:
c.clear(skia.Color4f(0,0,0,1))
p = skia.Paint(AntiAlias=True, Color=skia.ColorRED)
c.drawCircle(32,32,20,p)
img = surf.makeImageSnapshot()
arr = img.toarray()
print("array", arr.shape, arr.dtype, arr[32,32])
# feature probes
for name in ["MaskFilter","ImageFilters","BlurStyle","Font","Typeface","TextBlob","PathMeasure",
"GradientShader","Shaders","BlendMode","RuntimeEffect","Path","FontMgr","kSrcOver"]:
print(name, hasattr(skia, name))
PY
03:41:12Skia 144 with full feature set. Now let me write the actual mathematics — the category theory has to be real, not decorative.
03:41:21
Bash — Write config module
cat > src/catfilm/config.py <<'PY'
"""Global constants: canvas, palette, timing, paths."""
from __future__ import annotations
from pathlib import Path
ROOT = Path(__file__).resolve().parents[2]
OUT = ROOT / "out"
FRAMES = OUT / "frames"
AUDIO = OUT / "audio"
CACHE = OUT / "cache"
GALLERY = OUT / "gallery"
# --- Canvas -----------------------------------------------------------------
W, H = 1920, 1080
FPS = 30
SS = 1 # supersample factor (skia is already analytically antialiased)
# --- Palette ----------------------------------------------------------------
# A dark observatory: near-black ground, warm paper-white ink, three accents
# that carry meaning throughout the film (they are the three generators a,b,c).
BG = (0x06, 0x07, 0x0B)
BG_LIFT = (0x0D, 0x10, 0x18)
INK = (0xEC, 0xE7, 0xDA) # warm paper white — text
INK_DIM = (0x8A, 0x8B, 0x92) # secondary text
RULE = (0x2A, 0x2E, 0x38) # hairlines
A_BLUE = (0x6E, 0xC5, 0xFF) # generator 'a'
A_AMBER = (0xFF, 0xB2, 0x6B) # generator 'b'
A_VIOLET = (0xC4, 0x9B, 0xFF) # generator 'c'
A_MINT = (0x7C, 0xE0, 0xB0) # composites / identity
A_ROSE = (0xFF, 0x8F, 0xA8) # emphasis
GENERATORS = (A_BLUE, A_AMBER, A_VIOLET)
# --- Typography -------------------------------------------------------------
FONT_SERIF = "/System/Library/Fonts/Supplemental/Iowan Old Style.ttc"
FONT_SERIF_2 = "/System/Library/Fonts/Supplemental/Charter.ttc"
FONT_MONO = "/System/Library/Fonts/Menlo.ttc"
FONT_SANS = "/System/Library/Fonts/Supplemental/Futura.ttc"
# --- Audio ------------------------------------------------------------------
SAMPLE_RATE = 44100
NARRATOR_VOICE = "Daniel"
NARRATOR_WPM = 172
for _d in (OUT, FRAMES, AUDIO, CACHE, GALLERY):
_d.mkdir(parents=True, exist_ok=True)
PY
echo ok
03:41:56
Bash — Write and test the category theory core
cat > src/catfilm/core.py <<'PY'
"""The actual category theory.
This module is not decoration for the film — it is the engine that drives it.
Every picture later in the project is produced by *evaluating a functor*, and
the functor laws are checked here, in code, at build time.
A category is:
* a collection of objects,
* for each ordered pair (X, Y) a set of arrows X -> Y,
* an associative composition,
* an identity arrow on every object.
Nothing about what the objects *are*. That absence is the whole point.
"""
from __future__ import annotations
from dataclasses import dataclass, field
from itertools import product
from typing import Callable, Generic, Hashable, Iterable, Iterator, Sequence, TypeVar
Obj = TypeVar("Obj", bound=Hashable)
Arr = TypeVar("Arr")
# ---------------------------------------------------------------------------
# Finite categories, given by generators and relations on a graph.
# ---------------------------------------------------------------------------
@dataclass(frozen=True)
class Arrow:
"""An arrow is a *word*: a formal composite of generating edges.
``Arrow(src, dst, ())`` is the identity on ``src``. Composition is
concatenation, which is associative for free — that is exactly why the
associativity axiom of a category feels like it costs nothing.
"""
src: str
dst: str
word: tuple[str, ...] = ()
@property
def is_identity(self) -> bool:
return not self.word
def __len__(self) -> int:
return len(self.word)
def __repr__(self) -> str:
return f"id_{self.src}" if self.is_identity else "∘".join(reversed(self.word))
class Category:
"""A small category presented by a directed graph (its free category).
Objects are vertices; arrows are directed paths. Every finite directed
graph generates a category this way, and every diagram in the film is a
picture of one of them.
"""
def __init__(self, objects: Sequence[str], edges: dict[str, tuple[str, str]]):
self.objects = tuple(objects)
self.edges = dict(edges) # name -> (src, dst)
for name, (s, d) in self.edges.items():
if s not in self.objects or d not in self.objects:
raise ValueError(f"edge {name}: endpoint not an object")
# -- the three pieces of structure --------------------------------------
def identity(self, x: str) -> Arrow:
return Arrow(x, x, ())
def compose(self, g: Arrow, f: Arrow) -> Arrow:
"""``g ∘ f``: do *f* first, then *g*. Reads right-to-left, as always."""
if f.dst != g.src:
raise ValueError(f"cannot compose {g!r} ∘ {f!r}: {f.dst} != {g.src}")
return Arrow(f.src, g.dst, f.word + g.word)
def source_of(self, word: tuple[str, ...], start: str) -> Arrow:
cur = start
for e in word:
s, d = self.edges[e]
if s != cur:
raise ValueError(f"edge {e} does not start at {cur}")
cur = d
return Arrow(start, cur, word)
# -- enumeration ---------------------------------------------------------
def arrows(self, x: str, y: str, max_len: int = 3) -> list[Arrow]:
"""All arrows x -> y of length <= max_len. ``Hom(x, y)``, truncated."""
found: list[Arrow] = []
frontier: list[tuple[str, tuple[str, ...]]] = [(x, ())]
for _ in range(max_len + 1):
nxt = []
for cur, w in frontier:
if cur == y:
found.append(Arrow(x, y, w))
for name, (s, d) in self.edges.items():
if s == cur:
nxt.append((d, w + (name,)))
frontier = nxt
return found
def all_arrows(self, max_len: int = 3) -> list[Arrow]:
return [a for x, y in product(self.objects, repeat=2)
for a in self.arrows(x, y, max_len)]
# -- law checks ----------------------------------------------------------
def check_laws(self, max_len: int = 3) -> None:
"""Associativity and unit laws. They hold; we assert it anyway."""
arrs = self.all_arrows(max_len)
for f in arrs:
assert self.compose(self.identity(f.dst), f) == f, "left unit"
assert self.compose(f, self.identity(f.src)) == f, "right unit"
for f, g, h in product(arrs, repeat=3):
if f.dst == g.src and g.dst == h.src:
left = self.compose(self.compose(h, g), f)
right = self.compose(h, self.compose(g, f))
assert left == right, f"associativity failed on {f},{g},{h}"
# ---------------------------------------------------------------------------
# The one-object category: a monoid. This is the seed of every image.
# ---------------------------------------------------------------------------
def free_monoid(letters: Sequence[str], name: str = "•") -> Category:
"""One object, one loop per letter. Its arrows are exactly the words."""
return Category([name], {ell: (name, name) for ell in letters})
def words(letters: Sequence[str], length: int) -> Iterator[tuple[str, ...]]:
yield from product(letters, repeat=length)
def words_upto(letters: Sequence[str], length: int) -> Iterator[tuple[str, ...]]:
for n in range(length + 1):
yield from words(letters, n)
# ---------------------------------------------------------------------------
# Functors.
# ---------------------------------------------------------------------------
class Functor(Generic[Obj, Arr]):
"""A structure-preserving translation between categories.
Objects go to objects, arrows to arrows, and one law must hold::
F(g ∘ f) == F(g) ∘ F(f) and F(id) == id
"Translate, then combine" equals "combine, then translate". Everything
the film shows is a consequence of that single equation.
"""
def __init__(
self,
source: Category,
on_objects: Callable[[str], Obj],
on_generators: Callable[[str], Arr],
compose: Callable[[Arr, Arr], Arr],
identity: Callable[[Obj], Arr],
name: str = "F",
):
self.source = source
self.on_objects = on_objects
self.on_generators = on_generators
self._compose = compose
self._identity = identity
self.name = name
def __call__(self, a: Arrow) -> Arr:
"""Evaluate the functor on an arrow, by composing its image letters."""
out = self._identity(self.on_objects(a.src))
for e in a.word: # word is in application order: leftmost applied first
out = self._compose(self.on_generators(e), out)
return out
def check_functoriality(self, max_len: int = 3, eq=None) -> None:
eq = eq or (lambda p, q: p == q)
C = self.source
for f in C.all_arrows(max_len):
for g in C.all_arrows(max_len):
if f.dst != g.src:
continue
if len(f) + len(g) > max_len:
continue
lhs = self(C.compose(g, f))
rhs = self._compose(self(g), self(f))
assert eq(lhs, rhs), f"functoriality failed at {g!r} ∘ {f!r}"
for x in C.objects:
assert eq(self(C.identity(x)), self._identity(self.on_objects(x))), "unit"
# ---------------------------------------------------------------------------
# Natural transformations.
# ---------------------------------------------------------------------------
@dataclass
class NaturalTransformation(Generic[Obj, Arr]):
"""A map between functors that respects every arrow at once.
For functors ``F, G : C -> D`` a natural transformation ``alpha`` gives one
arrow ``alpha_X : F(X) -> G(X)`` per object, such that for every arrow
``f : X -> Y`` the *naturality square* commutes::
F(X) --F(f)--> F(Y)
| |
alpha_X alpha_Y
| |
v v
G(X) --G(f)--> G(Y)
Both ways round the square give the same arrow. Eilenberg and Mac Lane
invented categories in 1945 for the sole purpose of being able to write
this square down.
"""
F: Functor
G: Functor
component: Callable[[str], Arr]
name: str = "α"
def check_naturality(self, max_len: int = 4, eq=None) -> None:
eq = eq or (lambda p, q: p == q)
C = self.F.source
comp = self.F._compose
for f in C.all_arrows(max_len):
down_then_across = comp(self.G(f), self.component(f.src))
across_then_down = comp(self.component(f.dst), self.F(f))
assert eq(down_then_across, across_then_down), (
f"naturality square failed for {f!r}"
)
__all__ = [
"Arrow", "Category", "Functor", "NaturalTransformation",
"free_monoid", "words", "words_upto",
]
PY
uv run python -c "
from catfilm.core import *
C = Category(['A','B','C'], {'f':('A','B'),'g':('B','C'),'h':('A','C')})
C.check_laws(3); print('category laws OK')
M = free_monoid(list('abc')); M.check_laws(3); print('free monoid OK')
print('Hom(A,C) len<=2:', C.arrows('A','C',2))
"
03:42:19Now the generative engine — functors from the free monoid into affine plane maps:
03:43:14
Bash — Write IFS functor engine and verify laws
cat > src/catfilm/ifs.py <<'PY'
"""Functors from a free monoid into the category of affine maps of the plane.
The source category is fixed for the whole film: **one object, three arrows**
called ``a``, ``b``, ``c``. Its arrows are exactly the finite words in those
letters — there is no geometry in it whatsoever.
A functor out of it into the plane is determined by nothing more than a choice
of three affine maps. Functoriality then does all the work: the image of the
word ``abc`` *has* to be the composite of the images of ``a``, ``b`` and ``c``.
Every picture in this project is the attractor of such a functor.
"""
from __future__ import annotations
from dataclasses import dataclass
from typing import Sequence
import numpy as np
from .core import Category, Functor, NaturalTransformation, free_monoid
LETTERS = ("a", "b", "c")
MONOID = free_monoid(LETTERS)
# ---------------------------------------------------------------------------
# The target category: affine maps of the plane, one object, composition = @
# ---------------------------------------------------------------------------
@dataclass(frozen=True)
class Aff:
"""An affine map of the plane, as a 3x3 homogeneous matrix."""
m: tuple # 9 floats, row-major — hashable so Aff can live in sets
@staticmethod
def of(mat: np.ndarray) -> "Aff":
return Aff(tuple(np.asarray(mat, dtype=np.float64).reshape(9)))
@property
def mat(self) -> np.ndarray:
return np.asarray(self.m, dtype=np.float64).reshape(3, 3)
# -- category structure --------------------------------------------------
@staticmethod
def identity() -> "Aff":
return Aff.of(np.eye(3))
def then(self, other: "Aff") -> "Aff":
"""``self`` first, then ``other``. (= ``other ∘ self``)"""
return Aff.of(other.mat @ self.mat)
def inverse(self) -> "Aff":
return Aff.of(np.linalg.inv(self.mat))
# -- action --------------------------------------------------------------
def apply(self, pts: np.ndarray) -> np.ndarray:
"""Apply to an (N, 2) array of points."""
m = self.mat
return pts @ m[:2, :2].T + m[:2, 2]
@property
def contraction(self) -> float:
return float(np.max(np.linalg.svd(self.mat[:2, :2], compute_uv=False)))
def __eq__(self, other) -> bool: # numeric equality, for law checking
return isinstance(other, Aff) and bool(
np.allclose(self.mat, other.mat, atol=1e-9)
)
def __hash__(self) -> int:
return hash(tuple(np.round(self.m, 9)))
def compose_aff(g: Aff, f: Aff) -> Aff:
"""``g ∘ f`` — f first."""
return f.then(g)
def _mk(sx: float, sy: float, theta: float, shear: float, tx: float, ty: float) -> Aff:
ct, st = np.cos(theta), np.sin(theta)
rot = np.array([[ct, -st], [st, ct]])
scl = np.array([[sx, shear], [0.0, sy]])
lin = rot @ scl
m = np.eye(3)
m[:2, :2] = lin
m[:2, 2] = (tx, ty)
return Aff.of(m)
# ---------------------------------------------------------------------------
# Systems: a name, three affine maps, weights, and a framing box.
# ---------------------------------------------------------------------------
@dataclass
class System:
name: str
subtitle: str
maps: tuple[Aff, Aff, Aff]
weights: tuple[float, float, float] = (1 / 3, 1 / 3, 1 / 3)
def functor(self) -> Functor:
table = dict(zip(LETTERS, self.maps))
return Functor(
source=MONOID,
on_objects=lambda _o: "plane",
on_generators=lambda e: table[e],
compose=compose_aff,
identity=lambda _o: Aff.identity(),
name=self.name,
)
def conjugate(self, alpha: Aff, name: str | None = None) -> "System":
"""``alpha ∘ - ∘ alpha⁻¹``.
The result is a genuinely *naturally isomorphic* functor: ``alpha`` is
a natural transformation from this system to the conjugated one, and
its attractor is exactly ``alpha`` applied to this one's.
"""
ai = alpha.inverse()
return System(
name=name or f"{alpha!s}·{self.name}",
subtitle=self.subtitle,
maps=tuple(compose_aff(alpha, compose_aff(f, ai)) for f in self.maps),
weights=self.weights,
)
def naturality(src: System, alpha: Aff, dst: System) -> NaturalTransformation:
"""The natural transformation ``alpha : F => G`` between two IFS functors."""
return NaturalTransformation(
F=src.functor(), G=dst.functor(), component=lambda _x: alpha, name="α"
)
# ---------------------------------------------------------------------------
# The cast. Every one of these is a functor out of the *same* free monoid on
# {a, b, c}; only the three chosen matrices differ.
# ---------------------------------------------------------------------------
TAU = 2 * np.pi
def _sierpinski() -> System:
h = 0.5
corners = [(-0.5, -0.43), (0.5, -0.43), (0.0, 0.43)]
maps = []
for cx, cy in corners:
m = np.eye(3)
m[:2, :2] = np.eye(2) * h
m[:2, 2] = (cx * h * 2 * 0.5 + cx * 0.5, cy * h * 2 * 0.5 + cy * 0.5)
m[:2, 2] = (cx * 0.5, cy * 0.5)
maps.append(Aff.of(m))
return System("Sierpiński", "three corners, halved", tuple(maps))
SYSTEMS: dict[str, System] = {
# the canonical first reveal: the plainest possible choice of three maps
"sierpinski": _sierpinski(),
# a whirl: same three corners, but each map also turns
"pinwheel": System(
"Pinwheel", "corners, halved, and turned",
(
_mk(0.52, 0.52, 0.42, 0.0, -0.26, -0.20),
_mk(0.52, 0.52, 0.42, 0.0, 0.26, -0.20),
_mk(0.52, 0.52, 0.42, 0.0, 0.00, 0.36),
),
),
# a fern-like frond built from only three maps
"frond": System(
"Frond", "a stem and two leaves",
(
_mk(0.10, 0.72, 0.00, 0.00, 0.00, -0.28),
_mk(0.62, 0.62, -0.42, 0.00, 0.13, 0.18),
_mk(0.60, 0.60, 0.48, 0.00, -0.14, 0.16),
),
weights=(0.16, 0.42, 0.42),
),
# a dragon-ish fold
"fold": System(
"Fold", "two folds and a pivot",
(
_mk(0.62, 0.62, TAU / 8, 0.00, -0.18, 0.06),
_mk(0.62, 0.62, -TAU / 8, 0.00, 0.18, 0.06),
_mk(0.36, 0.36, TAU / 2, 0.00, 0.00, -0.40),
),
weights=(0.40, 0.40, 0.20),
),
# a spiral galaxy: contraction plus rotation about three centres
"spiral": System(
"Spiral", "shrink, turn, repeat",
(
_mk(0.74, 0.74, 0.52, 0.10, 0.10, 0.06),
_mk(0.44, 0.44, -1.05, 0.00, -0.34, -0.14),
_mk(0.40, 0.40, 2.30, 0.00, 0.22, -0.34),
),
weights=(0.62, 0.21, 0.17),
),
# a fivefold-looking lattice from a sheared trio
"lattice": System(
"Lattice", "sheared thirds",
(
_mk(0.50, 0.50, 0.00, 0.28, -0.25, -0.22),
_mk(0.50, 0.50, TAU / 3, 0.00, 0.26, -0.20),
_mk(0.50, 0.50, -TAU / 3, 0.00, 0.00, 0.34),
),
),
# a crown / cathedral window
"crown": System(
"Crown", "an arch that arches",
(
_mk(0.46, 0.46, 0.00, 0.00, -0.34, -0.26),
_mk(0.46, 0.46, 0.00, 0.00, 0.34, -0.26),
_mk(0.66, 0.66, 0.00, -0.36, 0.00, 0.22),
),
weights=(0.30, 0.30, 0.40),
),
}
# ---------------------------------------------------------------------------
# Evaluating a functor: the chaos game, carrying the word that made each point.
# ---------------------------------------------------------------------------
def chaos_game(
system: System,
n: int = 400_000,
seed: int = 7,
burn: int = 24,
colors: Sequence[tuple[int, int, int]] | None = None,
memory: float = 0.42,
) -> tuple[np.ndarray, np.ndarray]:
"""Sample the attractor of ``system``.
Returns ``(xy, rgb)``. The colour of a point is a running blend of the
letters most recently applied to it, so the image is literally *coloured by
the word that produced it*: blue where ``a`` has just acted, amber for
``b``, violet for ``c``, and mixtures in between.
"""
from .config import GENERATORS
cols = np.array(colors if colors is not None else GENERATORS, dtype=np.float32) / 255.0
rng = np.random.default_rng(seed)
mats = np.stack([f.mat[:2, :2] for f in system.maps]).astype(np.float64)
offs = np.stack([f.mat[:2, 2] for f in system.maps]).astype(np.float64)
w = np.array(system.weights, dtype=np.float64)
w = w / w.sum()
# Run many independent chains at once — vectorised over an ensemble.
chains = 4096
steps = max(1, int(np.ceil(n / chains)))
p = rng.normal(scale=0.25, size=(chains, 2))
c = np.full((chains, 3), 0.5, dtype=np.float32)
xy = np.empty((steps * chains, 2), dtype=np.float32)
rgb = np.empty((steps * chains, 3), dtype=np.float32)
total = burn + steps
draws = rng.choice(3, size=(total, chains), p=w)
k = 0
for i in range(total):
d = draws[i]
p = np.einsum("nij,nj->ni", mats[d], p) + offs[d]
c = c * memory + cols[d] * (1.0 - memory)
if i >= burn:
xy[k * chains:(k + 1) * chains] = p
rgb[k * chains:(k + 1) * chains] = c
k += 1
return xy[: k * chains], rgb[: k * chains]
def word_images(system: System, depth: int, unit: np.ndarray) -> list[tuple[tuple[str, ...], np.ndarray]]:
"""The image of a seed shape under *every word* of a given length.
This is the deterministic face of the same fact: at depth ``k`` there are
``3**k`` words, and the attractor is the limit of their images.
"""
from .core import words
F = system.functor()
out = []
for w in words(LETTERS, depth):
arrow = MONOID.source_of(w, "•")
out.append((w, F(arrow).apply(unit)))
return out
def blend_systems(s0: System, s1: System, t: float, name: str = "morph") -> System:
"""Interpolate two functors matrix-wise.
Each intermediate ``t`` is itself a perfectly good functor — three matrices
are three matrices — so the whole slide is a continuous path through the
space of translations.
"""
maps = tuple(
Aff.of((1 - t) * f.mat + t * g.mat) for f, g in zip(s0.maps, s1.maps)
)
wt = tuple((1 - t) * a + t * b for a, b in zip(s0.weights, s1.weights))
return System(name, "", maps, wt)
UNIT_TRIANGLE = np.array(
[[-0.5, -0.43], [0.5, -0.43], [0.0, 0.43], [-0.5, -0.43]], dtype=np.float64
)
UNIT_SQUARE = np.array(
[[-0.5, -0.5], [0.5, -0.5], [0.5, 0.5], [-0.5, 0.5], [-0.5, -0.5]], dtype=np.float64
)
PY
uv run python - <<'PY'
import numpy as np, time
from catfilm.ifs import *
# 1. verify the functor laws actually hold for every system
for key, s in SYSTEMS.items():
s.functor().check_functoriality(max_len=3)
print("functoriality OK for", len(SYSTEMS), "systems")
# 2. verify a real natural transformation
alpha = _mk(1.0, 1.0, 0.6, 0.35, 0.12, -0.05)
src = SYSTEMS["sierpinski"]; dst = src.conjugate(alpha, "sheared")
naturality(src, alpha, dst).check_naturality(max_len=4)
print("naturality square commutes ✓")
# 3. speed of the chaos game
t=time.time(); xy,rgb = chaos_game(SYSTEMS["spiral"], 600_000); print(f"chaos {len(xy)} pts in {time.time()-t:.2f}s", xy.min(0), xy.max(0))
for k,s in SYSTEMS.items():
xy,_=chaos_game(s, 60_000)
print(f"{k:12s} bbox x[{xy[:,0].min():+.2f},{xy[:,0].max():+.2f}] y[{xy[:,1].min():+.2f},{xy[:,1].max():+.2f}] contr {[round(m.contraction,2) for m in s.maps]}")
PY
03:43:21
Bash — Verify naturality and profile chaos game
uv run python - <<'PY'
import numpy as np, time
from catfilm.ifs import *
from catfilm.ifs import _mk
alpha = _mk(1.0, 1.0, 0.6, 0.35, 0.12, -0.05)
src = SYSTEMS["sierpinski"]; dst = src.conjugate(alpha, "sheared")
naturality(src, alpha, dst).check_naturality(max_len=4)
print("naturality square commutes ✓")
t=time.time(); xy,rgb = chaos_game(SYSTEMS["spiral"], 600_000); print(f"chaos {len(xy)} pts in {time.time()-t:.2f}s")
for k,s in SYSTEMS.items():
xy,_=chaos_game(s, 60_000)
print(f"{k:12s} bbox x[{xy[:,0].min():+.2f},{xy[:,0].max():+.2f}] y[{xy[:,1].min():+.2f},{xy[:,1].max():+.2f}] contr {[round(m.contraction,2) for m in s.maps]}")
PY
03:43:36Chaos game is fast and all attractors are well-defined. Now the glow renderer — the biggest aesthetic risk, so I'll validate it immediately:
03:44:01
Bash — Write glow renderer and produce a test contact sheet
cat > src/catfilm/render/glow.py <<'PY'
"""Density-accumulation renderer.
Points from the chaos game are histogrammed into a buffer that records, per
pixel, how *often* the attractor visits it and in what colour. A logarithmic
tone curve then turns visit-count into light. Regions the functor returns to
again and again glow; regions it barely touches stay as embers.
This is how the picture gets its depth: brightness is a direct readout of how
many words of the free monoid land on that pixel.
"""
from __future__ import annotations
import numpy as np
def accumulate(
xy: np.ndarray,
rgb: np.ndarray,
size: tuple[int, int],
center: tuple[float, float] = (0.0, 0.0),
scale: float = 1.0,
ss: int = 2,
) -> tuple[np.ndarray, np.ndarray]:
"""Histogram points into (count, colour-sum) buffers at ``ss`` supersample."""
w, h = size
W, H = w * ss, h * ss
px = (xy[:, 0] - center[0]) * scale * ss + W * 0.5
py = H * 0.5 - (xy[:, 1] - center[1]) * scale * ss
ix = px.astype(np.int32)
iy = py.astype(np.int32)
ok = (ix >= 0) & (ix < W) & (iy >= 0) & (iy < H)
idx = (iy[ok].astype(np.int64) * W + ix[ok].astype(np.int64))
n = W * H
cnt = np.bincount(idx, minlength=n).astype(np.float32)
col = np.empty((n, 3), dtype=np.float32)
r = rgb[ok]
for k in range(3):
col[:, k] = np.bincount(idx, weights=r[:, k].astype(np.float64), minlength=n)
return cnt.reshape(H, W), col.reshape(H, W, 3)
def _box_down(a: np.ndarray, ss: int) -> np.ndarray:
if ss == 1:
return a
H, W = a.shape[:2]
tail = a.shape[2:]
return a.reshape(H // ss, ss, W // ss, ss, *tail).sum(axis=(1, 3))
def tone_map(
cnt: np.ndarray,
col: np.ndarray,
ss: int = 2,
gamma: float = 2.1,
exposure: float = 1.0,
saturation: float = 1.18,
knee: float = 0.985,
) -> np.ndarray:
"""Log-density tone curve -> premultiplied linear RGB in [0, 1]."""
cnt = _box_down(cnt, ss)
col = _box_down(col, ss)
hot = cnt > 0
mean = np.zeros_like(col)
mean[hot] = col[hot] / cnt[hot, None]
dens = np.log1p(cnt * exposure)
hi = np.quantile(dens[hot], knee) if hot.any() else 1.0
lum = np.clip(dens / max(hi, 1e-6), 0.0, 1.0) ** (1.0 / gamma)
grey = mean.mean(axis=2, keepdims=True)
mean = np.clip(grey + (mean - grey) * saturation, 0.0, 1.0)
# hottest cores bleach toward white, the way real light does
core = np.clip((lum - 0.72) / 0.28, 0.0, 1.0)[..., None] ** 2
mean = mean + (1.0 - mean) * core * 0.85
return np.clip(mean * lum[..., None], 0.0, 1.0)
def _gauss1d(sigma: float) -> np.ndarray:
r = max(1, int(sigma * 3))
x = np.arange(-r, r + 1, dtype=np.float32)
k = np.exp(-(x**2) / (2 * sigma * sigma))
return k / k.sum()
def blur(img: np.ndarray, sigma: float) -> np.ndarray:
from scipy.ndimage import convolve1d
k = _gauss1d(sigma)
out = convolve1d(img, k, axis=0, mode="constant")
return convolve1d(out, k, axis=1, mode="constant")
def bloom(img: np.ndarray, strength: float = 0.55, sigmas=(3.0, 10.0, 34.0)) -> np.ndarray:
"""Multi-scale halo. Cheap, and it is what makes the light feel physical."""
if strength <= 0:
return img
acc = np.zeros_like(img)
wsum = 0.0
for i, s in enumerate(sigmas):
w = 1.0 / (i + 1)
acc += blur(img, s) * w
wsum += w
return np.clip(img + acc / wsum * strength, 0.0, 1.0)
def render_points(
xy: np.ndarray,
rgb: np.ndarray,
size: tuple[int, int],
center=(0.0, 0.0),
scale: float = 1.0,
ss: int = 2,
gamma: float = 2.1,
exposure: float = 1.0,
bloom_strength: float = 0.5,
saturation: float = 1.18,
) -> np.ndarray:
cnt, col = accumulate(xy, rgb, size, center, scale, ss)
img = tone_map(cnt, col, ss, gamma, exposure, saturation)
return bloom(img, bloom_strength)
def fit_scale(xy: np.ndarray, size: tuple[int, int], margin: float = 0.86) -> tuple[tuple[float, float], float]:
"""Centre and scale so the attractor fills the frame handsomely."""
lo = np.quantile(xy, 0.0008, axis=0)
hi = np.quantile(xy, 0.9992, axis=0)
c = (lo + hi) / 2
span = np.maximum(hi - lo, 1e-6)
s = min(size[0] / span[0], size[1] / span[1]) * margin
return (float(c[0]), float(c[1])), float(s)
PY
uv run python - <<'PY'
import time, numpy as np
from PIL import Image
from catfilm.ifs import SYSTEMS, chaos_game
from catfilm.render.glow import render_points, fit_scale
from catfilm.config import BG, GALLERY
size=(960,540)
tiles=[]
for k in ["sierpinski","pinwheel","frond","fold","spiral","lattice"]:
t=time.time(); xy,rgb=chaos_game(SYSTEMS[k], 1_200_000, seed=11)
c,s = fit_scale(xy,size)
img = render_points(xy,rgb,size,c,s,exposure=1.4,bloom_strength=0.6)
bg = np.array(BG,dtype=np.float32)/255.0
out = np.clip(bg + img*(1.0), 0,1)
tiles.append((k,(out*255).astype(np.uint8), time.time()-t))
print(f"{k:11s} {time.time()-t:.2f}s")
rows=[np.concatenate([tiles[i][1] for i in r],axis=1) for r in [(0,1,2),(3,4,5)]]
Image.fromarray(np.concatenate(rows,axis=0)).save(GALLERY/"probe.png")
print("saved", GALLERY/"probe.png")
PY
03:44:10
Read ← ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code/out/gallery/probe.png
03:44:10 · 🖼 image returned to Claude — [Image: original 2880x1080, displayed at 2000x750. Multiply coordinates by 1.44 to map to original image.]
03:44:26The math and the palette-by-word coloring both work. Now the vector/typography layer:
03:44:31
Bash — Probe skia typography and path APIs
uv run python - <<'PY'
import skia, numpy as np, inspect
tf = skia.Typeface.MakeFromFile("/System/Library/Fonts/Supplemental/Iowan Old Style.ttc")
print("typeface:", tf, tf.getFamilyName() if tf else None)
f = skia.Font(tf, 40)
print("measure:", f.measureText("Functor ∘ id"))
print("has Image.fromarray:", hasattr(skia.Image,'fromarray'))
pm = skia.PathMeasure()
print("PathMeasure methods:", [m for m in dir(pm) if not m.startswith('_')][:20])
p = skia.Path(); p.moveTo(0,0); p.lineTo(100,0)
pm2 = skia.PathMeasure(p, False)
print("length", pm2.getLength())
seg = skia.Path()
print("getSegment sig ok:", pm2.getSegment(0, 50, seg, True), seg.countPoints())
print("Font glyph for ring:", f.textToGlyphs("∘"), f.textToGlyphs("⇒"), f.textToGlyphs("×"))
print("drawTextBlob?", hasattr(skia.Canvas,'drawString'), hasattr(skia.Canvas,'drawTextBlob'))
print("ImageFilters:", [m for m in dir(skia.ImageFilters) if not m.startswith('_')])
PY
03:44:46
Bash — Find fonts containing math symbols
uv run python - <<'PY'
import skia, glob
syms = "∘⇒→≅⟶∀∈×·⟼↦≃⊗"
cands = ["/System/Library/Fonts/Menlo.ttc","/System/Library/Fonts/Supplemental/Charter.ttc",
"/System/Library/Fonts/Supplemental/Times New Roman.ttf","/System/Library/Fonts/Supplemental/Georgia.ttf",
"/System/Library/Fonts/Apple Symbols.ttf","/System/Library/Fonts/Supplemental/Arial Unicode.ttf",
"/System/Library/Fonts/SFNSMono.ttf","/System/Library/Fonts/Supplemental/Baskerville.ttc",
"/System/Library/Fonts/Supplemental/Iowan Old Style.ttc","/System/Library/Fonts/Supplemental/Palatino.ttc",
"/System/Library/Fonts/Supplemental/Optima.ttc","/System/Library/Fonts/Geneva.ttf",
"/System/Library/Fonts/Supplemental/STIXGeneral.otf","/System/Library/Fonts/Supplemental/Zapfino.ttf"]
import os
for p in cands:
if not os.path.exists(p): print("MISSING", p); continue
tf = skia.Typeface.MakeFromFile(p)
if tf is None: print("nil", p); continue
f = skia.Font(tf, 30)
got = "".join(s if f.textToGlyphs(s)[0] else "·" for s in syms)
print(f"{os.path.basename(p):32s} {got} [{tf.getFamilyName()}]")
print("--- search all for ring operator ---")
for p in sorted(glob.glob("/System/Library/Fonts/**/*.tt*", recursive=True)+glob.glob("/System/Library/Fonts/**/*.otf", recursive=True)):
tf = skia.Typeface.MakeFromFile(p)
if tf is None: continue
f = skia.Font(tf, 30)
if f.textToGlyphs("∘")[0] and f.textToGlyphs("⇒")[0]:
print(" HAS BOTH:", os.path.basename(p), tf.getFamilyName())
PY
03:45:05STIX Two Math is available — professional math typography. Building the canvas layer with font fallback:
03:45:57
Bash — Write canvas module and test typography
cat > src/catfilm/render/canvas.py <<'PY'
"""Drawing surface: typography, vector layers, and float compositing.
Every frame is assembled the same way: a float32 RGB buffer is created, glow
layers are *added* into it, vector layers (text, arrows, dots) are composited
*over* it, and the result is graded, vignetted and grained on the way out.
"""
from __future__ import annotations
import math
from dataclasses import dataclass
from functools import lru_cache
import numpy as np
import skia
from ..config import (BG, FONT_MONO, FONT_SERIF, H, INK, W)
MATH_FONT = "/System/Library/Fonts/Supplemental/STIXTwoMath.otf"
MATH_FONT_ALT = "/System/Library/Fonts/Supplemental/STIXGeneral.otf"
ITALIC_FONT = "/System/Library/Fonts/Supplemental/Iowan Old Style.ttc"
# ---------------------------------------------------------------------------
# Colour
# ---------------------------------------------------------------------------
def rgba(c, a: float = 1.0) -> int:
r, g, b = c[:3]
return skia.Color4f(r / 255.0, g / 255.0, b / 255.0, a).toColor()
def mix(c0, c1, t: float):
t = float(np.clip(t, 0, 1))
return tuple(int(round(a + (b - a) * t)) for a, b in zip(c0[:3], c1[:3]))
# ---------------------------------------------------------------------------
# Easing
# ---------------------------------------------------------------------------
def clamp01(x: float) -> float:
return 0.0 if x < 0 else (1.0 if x > 1 else float(x))
def ease_out(t, p=3.0): return 1 - (1 - clamp01(t)) ** p
def ease_in(t, p=3.0): return clamp01(t) ** p
def ease(t, p=3.0):
t = clamp01(t)
return 4 ** (p - 1) * t**p if t < 0.5 else 1 - (-2 * t + 2) ** p / 2
def smooth(t): return (lambda u: u * u * (3 - 2 * u))(clamp01(t))
def smoother(t): return (lambda u: u**3 * (u * (u * 6 - 15) + 10))(clamp01(t))
def overshoot(t, s=1.34):
t = clamp01(t) - 1
return t * t * ((s + 1) * t + s) + 1
def pulse(t, a, b, fade=0.25):
"""1 inside [a,b] with soft shoulders, 0 outside."""
if t <= a - fade or t >= b + fade: return 0.0
if t < a: return smooth((t - a + fade) / fade)
if t > b: return 1 - smooth((t - b) / fade)
return 1.0
def seg(t, a, b):
"""Normalise t from the window [a, b] to [0, 1]."""
return clamp01((t - a) / max(b - a, 1e-9))
# ---------------------------------------------------------------------------
# Fonts, with automatic fallback for mathematical glyphs
# ---------------------------------------------------------------------------
@lru_cache(maxsize=64)
def _typeface(path: str, index: int = 0):
tf = skia.Typeface.MakeFromFile(path, index)
if tf is None:
raise FileNotFoundError(path)
return tf
@lru_cache(maxsize=512)
def font(kind: str = "serif", size: float = 40.0, weight: str = "regular"):
path = {"serif": FONT_SERIF, "mono": FONT_MONO, "math": MATH_FONT}[kind]
idx = {"serif": {"regular": 0, "bold": 1, "italic": 2}.get(weight, 0),
"mono": {"regular": 0, "bold": 1, "italic": 2}.get(weight, 0),
"math": 0}[kind]
f = skia.Font(_typeface(path, idx), size)
f.setSubpixel(True)
f.setEdging(skia.Font.Edging.kSubpixelAntiAlias)
f.setHinting(skia.FontHinting.kNone)
return f
@lru_cache(maxsize=8192)
def _runs(text: str, kind: str, size: float, weight: str) -> tuple:
"""Split text into (font, substring) runs, falling back for missing glyphs."""
primary = font(kind, size, weight)
fb = skia.Font(_typeface(MATH_FONT), size)
fb.setSubpixel(True); fb.setEdging(skia.Font.Edging.kSubpixelAntiAlias)
out, cur, cur_f = [], "", None
for ch in text:
f = primary if (ch == " " or primary.textToGlyphs(ch)[0]) else fb
if f is not cur_f and cur:
out.append((cur_f, cur)); cur = ""
cur_f, cur = f, cur + ch
if cur:
out.append((cur_f, cur))
return tuple(out)
def measure(text: str, kind="serif", size=40.0, weight="regular", tracking=0.0) -> float:
w = sum(f.measureText(s) for f, s in _runs(text, kind, size, weight))
return w + tracking * size * max(0, len(text) - 1)
# ---------------------------------------------------------------------------
# Frame: the float compositing buffer
# ---------------------------------------------------------------------------
class Frame:
def __init__(self, w: int = W, h: int = H, bg=BG):
self.w, self.h = w, h
self.buf = np.tile(
(np.array(bg, dtype=np.float32) / 255.0)[None, None, :], (h, w, 1)
)
# -- glow ---------------------------------------------------------------
def add(self, img: np.ndarray, alpha: float = 1.0):
"""Additive light."""
if alpha <= 0:
return
self.buf += img.astype(np.float32) * float(alpha)
def over(self, rgb: np.ndarray, a: np.ndarray):
a = a[..., None] if a.ndim == 2 else a
self.buf = self.buf * (1 - a) + rgb * a
# -- vector -------------------------------------------------------------
def vector(self, draw, blend: str = "over", alpha: float = 1.0):
"""Run ``draw(canvas)`` on a transparent skia surface, composite in."""
if alpha <= 0:
return
surf = skia.Surface(self.w, self.h)
with surf as c:
c.clear(skia.Color4f(0, 0, 0, 0))
draw(c)
arr = surf.makeImageSnapshot().toarray(
colorType=skia.kRGBA_8888_ColorType, alphaType=skia.kUnpremul_AlphaType
).astype(np.float32) / 255.0
rgb, a = arr[..., :3], arr[..., 3:4] * float(alpha)
if blend == "add":
self.buf += rgb * a
else:
self.buf = self.buf * (1 - a) + rgb * a
# -- output -------------------------------------------------------------
def finish(self, vignette: float = 0.42, grain: float = 0.010,
lift: float = 0.0, seed: int = 0) -> np.ndarray:
img = self.buf
if vignette > 0:
img = img * _vignette(self.w, self.h, vignette)[..., None]
img = np.clip(img + lift, 0.0, 1.0)
# gentle filmic shoulder so highlights roll off instead of clipping flat
img = img * (1.0 + 0.09 * img) / (1.0 + 0.09)
img = np.clip(img, 0, 1)
if grain > 0:
rng = np.random.default_rng(seed * 2654435761 % (2**32))
n = rng.standard_normal((self.h, self.w, 1)).astype(np.float32)
img = np.clip(img + n * grain * (0.30 + 0.70 * (1 - img)), 0, 1)
return (img * 255.0 + 0.5).astype(np.uint8)
@lru_cache(maxsize=8)
def _vignette(w: int, h: int, strength: float) -> np.ndarray:
y, x = np.mgrid[0:h, 0:w].astype(np.float32)
dx = (x / w - 0.5) * 2.0
dy = (y / h - 0.5) * 2.0 * (h / w) * 1.7
r = np.sqrt(dx * dx + dy * dy)
return np.clip(1.0 - strength * np.clip(r - 0.42, 0, None) ** 1.7, 0, 1)
# ---------------------------------------------------------------------------
# Text drawing
# ---------------------------------------------------------------------------
def draw_text(
c, text: str, x: float, y: float, *, size=40.0, kind="serif", weight="regular",
color=INK, alpha=1.0, align="left", tracking=0.0, reveal: float = 1.0,
rise: float = 0.0, glow: float = 0.0,
):
"""Draw a line of text.
``reveal`` in [0,1] fades the line in glyph by glyph, with each glyph also
rising by ``rise`` pixels as it arrives — the whole film's text behaviour.
"""
if alpha <= 0 or reveal <= 0 or not text:
return
runs = _runs(text, kind, size, weight)
total = measure(text, kind, size, weight, tracking)
if align == "center": x -= total / 2
elif align == "right": x -= total
n = max(1, len(text))
# glyph i fades across a window; the last glyph finishes exactly at reveal=1
span = 0.55
i = 0
for f, s in runs:
widths = f.getWidths(f.textToGlyphs(s))
for ch, wd in zip(s, widths):
if ch != " ":
t0 = (i / n) * (1 - span)
a = alpha * smooth((reveal - t0) / max(span, 1e-6))
if a > 0.003:
dy = rise * (1 - smoother((reveal - t0) / max(span, 1e-6)))
p = skia.Paint(AntiAlias=True, Color=rgba(color, a))
if glow > 0:
gp = skia.Paint(
AntiAlias=True, Color=rgba(color, a * glow),
MaskFilter=skia.MaskFilter.MakeBlur(
skia.kNormal_BlurStyle, size * 0.16),
)
c.drawString(ch, x, y + dy, f, gp)
c.drawString(ch, x, y + dy, f, p)
x += wd + tracking * size
i += 1
def wrap(text: str, max_w: float, kind="serif", size=40.0, weight="regular",
tracking=0.0) -> list[str]:
out, line = [], ""
for word in text.split():
trial = f"{line} {word}".strip()
if measure(trial, kind, size, weight, tracking) > max_w and line:
out.append(line); line = word
else:
line = trial
if line:
out.append(line)
return out
def draw_paragraph(
c, text: str, x: float, y: float, max_w: float, *, size=40.0, kind="serif",
weight="regular", color=INK, alpha=1.0, align="left", leading=1.5,
tracking=0.0, reveal=1.0, rise=0.0, glow=0.0,
) -> float:
lines = wrap(text, max_w, kind, size, weight, tracking)
lh = size * leading
# reveal marches through the whole paragraph, line by line
for i, ln in enumerate(lines):
lo, hi = i / len(lines), (i + 1) / len(lines)
r = clamp01((reveal - lo * 0.8) / max(hi - lo * 0.8, 1e-6))
draw_text(c, ln, x, y + i * lh, size=size, kind=kind, weight=weight,
color=color, alpha=alpha, align=align, tracking=tracking,
reveal=r, rise=rise, glow=glow)
return y + len(lines) * lh
# ---------------------------------------------------------------------------
# Small helpers used all over the scenes
# ---------------------------------------------------------------------------
def paint(color=INK, alpha=1.0, width=0.0, blur=0.0, cap="round"):
p = skia.Paint(AntiAlias=True, Color=rgba(color, alpha))
if width > 0:
p.setStyle(skia.Paint.kStroke_Style)
p.setStrokeWidth(width)
p.setStrokeCap({"round": skia.Paint.kRound_Cap,
"butt": skia.Paint.kButt_Cap,
"square": skia.Paint.kSquare_Cap}[cap])
p.setStrokeJoin(skia.Paint.kRound_Join)
if blur > 0:
p.setMaskFilter(skia.MaskFilter.MakeBlur(skia.kNormal_BlurStyle, blur))
return p
def rule(c, x0, y0, x1, y1, color, alpha=1.0, width=1.0):
c.drawLine(x0, y0, x1, y1, paint(color, alpha, width))
def np_to_image(arr: np.ndarray) -> "skia.Image":
a = np.clip(arr, 0, 1)
if a.shape[2] == 3:
a = np.concatenate([a, np.ones_like(a[..., :1])], axis=2)
return skia.Image.fromarray((a * 255).astype(np.uint8),
colorType=skia.kRGBA_8888_ColorType)
PY
uv run python - <<'PY'
from PIL import Image
import numpy as np, skia
from catfilm.render.canvas import *
from catfilm.config import *
fr = Frame(1200, 500)
def d(c):
draw_text(c,"Functor", 60, 120, size=76, color=INK, tracking=0.06)
draw_text(c,"F(g ∘ f) = F(g) ∘ F(f)", 60, 210, size=54, kind="math", color=A_BLUE)
draw_text(c,"a thing is determined by its relationships", 60, 290, size=34, color=INK_DIM)
draw_paragraph(c,"Objects and arrows — that is all a category is, and the arrows compose.", 60, 350, 1080, size=30, color=INK, reveal=0.6, rise=14)
draw_text(c,"words = ('a','b','c')", 60, 460, size=26, kind="mono", color=A_MINT)
fr.vector(d)
Image.fromarray(fr.finish(grain=0.006)).save(GALLERY/"type.png")
print("ok")
PY
03:46:02
Read ← ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code/out/gallery/type.png
03:46:10Typography and math-font fallback both work. Now the diagram grammar — objects, arrows, self-loops, commuting squares:
03:46:59
Bash — Write diagram module and test visual grammar
cat > src/catfilm/render/diagram.py <<'PY'
"""The visual grammar of category theory: dots, arrows, and squares.
Objects are dots. Morphisms are arrows. Everything in the film is built from
these two marks, because everything in category theory is.
"""
from __future__ import annotations
import math
import numpy as np
import skia
from ..config import A_MINT, INK, INK_DIM, RULE
from .canvas import clamp01, draw_text, ease_out, mix, paint, rgba, smooth, smoother
# ---------------------------------------------------------------------------
# Objects
# ---------------------------------------------------------------------------
def node(c, x, y, *, r=11.0, color=INK, alpha=1.0, label=None, label_size=34,
label_dy=-30.0, label_dx=0.0, label_color=None, reveal=1.0, halo=1.0,
ring=0.0, kind="serif"):
"""An object: a dot of light, optionally named."""
if alpha <= 0 or reveal <= 0:
return
a = alpha * smooth(reveal)
s = 0.35 + 0.65 * smoother(reveal)
if halo > 0:
for k, (m, w) in enumerate(((3.2, 0.22), (1.9, 0.30))):
c.drawCircle(x, y, r * s * m, paint(color, a * w * halo, blur=r * m * 0.55))
c.drawCircle(x, y, r * s, paint(color, a))
if ring > 0:
c.drawCircle(x, y, r * s * 2.6, paint(color, a * ring, width=1.6))
if label:
draw_text(c, label, x + label_dx, y + label_dy, size=label_size,
kind=kind, color=label_color or color, alpha=a, align="center",
reveal=reveal)
# ---------------------------------------------------------------------------
# Arrows
# ---------------------------------------------------------------------------
def _bezier(p0, p1, bend: float) -> skia.Path:
(x0, y0), (x1, y1) = p0, p1
mx, my = (x0 + x1) / 2, (y0 + y1) / 2
dx, dy = x1 - x0, y1 - y0
L = math.hypot(dx, dy) or 1.0
cx, cy = mx - dy / L * bend * L, my + dx / L * bend * L
p = skia.Path()
p.moveTo(x0, y0)
p.quadTo(cx, cy, x1, y1)
return p
def _trim(path: skia.Path, t0: float, t1: float) -> tuple[skia.Path, tuple, tuple]:
pm = skia.PathMeasure(path, False)
L = pm.getLength()
out = skia.Path()
pm.getSegment(L * clamp01(t0), L * clamp01(t1), out, True)
pos, tan = pm.getPosTan(L * clamp01(t1))
return out, (pos.x(), pos.y()), (tan.x(), tan.y())
def _shorten(p0, p1, a: float, b: float):
dx, dy = p1[0] - p0[0], p1[1] - p0[1]
L = math.hypot(dx, dy) or 1.0
ux, uy = dx / L, dy / L
return (p0[0] + ux * a, p0[1] + uy * a), (p1[0] - ux * b, p1[1] - uy * b)
def arrowhead(c, pos, tan, size, color, alpha, filled=True):
if alpha <= 0 or size <= 0:
return
ang = math.atan2(tan[1], tan[0])
spread = 0.42
p = skia.Path()
p.moveTo(pos[0], pos[1])
for s in (+1, -1):
p.lineTo(pos[0] - size * math.cos(ang - s * spread),
pos[1] - size * math.sin(ang - s * spread))
p.close()
if filled:
c.drawPath(p, paint(color, alpha))
c.drawPath(p, paint(color, alpha, width=size * 0.16))
def arrow(c, p0, p1, *, bend=0.0, color=INK, alpha=1.0, width=2.4, t=1.0,
gap=(16.0, 20.0), head=15.0, label=None, label_size=30, label_off=-24.0,
label_color=None, dash=None, glow=0.35, label_kind="serif",
label_reveal=None, head_at_start=False):
"""A morphism.
``t`` animates the arrow drawing itself from source to target — the arrow
growing is the visual verb of this whole film.
"""
if alpha <= 0 or t <= 0:
return
q0, q1 = _shorten(p0, p1, gap[0], gap[1])
path = _bezier(q0, q1, bend)
body_t = clamp01(t / 0.82)
seg, pos, tan = _trim(path, 0.0, body_t)
pen = paint(color, alpha, width=width)
if dash:
pen.setPathEffect(skia.DashPathEffect.Make(list(dash), 0.0))
if glow > 0:
gp = paint(color, alpha * glow, width=width * 3.4, blur=width * 2.6)
c.drawPath(seg, gp)
c.drawPath(seg, pen)
hs = head * smooth((t - 0.72) / 0.28)
arrowhead(c, pos, tan, hs, color, alpha)
if head_at_start:
_, spos, stan = _trim(path, 0.0, 0.001)
arrowhead(c, spos, (-stan[0], -stan[1]), hs, color, alpha)
if label:
pm = skia.PathMeasure(path, False)
L = pm.getLength()
mp, mt = pm.getPosTan(L * 0.5)
nx, ny = -mt.y(), mt.x()
lr = t if label_reveal is None else label_reveal
draw_text(c, label, mp.x() + nx * label_off, mp.y() + ny * label_off + 10,
size=label_size, kind=label_kind, color=label_color or color,
alpha=alpha, align="center", reveal=clamp01((lr - 0.45) / 0.45))
def self_loop(c, x, y, *, r=64.0, angle=-math.pi / 2, spread=0.62, color=INK,
alpha=1.0, width=2.4, t=1.0, node_r=13.0, head=14.0, label=None,
label_size=30, label_off=1.42, glow=0.35):
"""An arrow from an object to itself — the only kind a monoid has."""
if alpha <= 0 or t <= 0:
return
a0, a1 = angle - spread, angle + spread
p0 = (x + node_r * math.cos(a0), y + node_r * math.sin(a0))
p1 = (x + node_r * math.cos(a1), y + node_r * math.sin(a1))
c0 = (x + r * 1.9 * math.cos(a0 - 0.30), y + r * 1.9 * math.sin(a0 - 0.30))
c1 = (x + r * 1.9 * math.cos(a1 + 0.30), y + r * 1.9 * math.sin(a1 + 0.30))
path = skia.Path()
path.moveTo(*p0)
path.cubicTo(*c0, *c1, *p1)
seg, pos, tan = _trim(path, 0.0, clamp01(t / 0.85))
if glow > 0:
c.drawPath(seg, paint(color, alpha * glow, width=width * 3.4, blur=width * 2.6))
c.drawPath(seg, paint(color, alpha, width=width))
arrowhead(c, pos, tan, head * smooth((t - 0.7) / 0.3), color, alpha)
if label:
lx = x + r * label_off * math.cos(angle)
ly = y + r * label_off * math.sin(angle)
draw_text(c, label, lx, ly + 11, size=label_size, color=color, alpha=alpha,
align="center", reveal=clamp01((t - 0.5) / 0.4))
# ---------------------------------------------------------------------------
# Composite figures
# ---------------------------------------------------------------------------
def commuting_mark(c, x, y, r=17.0, color=A_MINT, alpha=1.0, t=1.0):
"""The little turning arrow that says: both ways round agree."""
if alpha <= 0 or t <= 0:
return
a = alpha * smooth(t)
path = skia.Path()
path.addArc(skia.Rect.MakeLTRB(x - r, y - r, x + r, y + r), -60, 300 * smoother(t))
c.drawPath(path, paint(color, a * 0.9, width=2.0))
pm = skia.PathMeasure(path, False)
pos, tan = pm.getPosTan(pm.getLength())
arrowhead(c, (pos.x(), pos.y()), (tan.x(), tan.y()), 9.0 * smooth((t - .5) / .5),
color, a)
def square(c, corners, labels, *, color=INK, alpha=1.0, t=1.0, arrow_color=None,
obj_color=None, label_size=30, obj_size=34, commute=0.0, bends=(0, 0, 0, 0),
order=(0, 1, 2, 3), node_r=11.0, kinds=("serif",) * 4):
"""A naturality square: four objects, four arrows, two ways round.
``corners`` are (tl, tr, bl, br); ``labels`` is (objects[4], arrows[4]) with
arrows in the order top, left, right, bottom.
"""
objs, arrs = labels
tl, tr, bl, br = corners
ac = arrow_color or color
oc = obj_color or color
pairs = [(tl, tr), (tl, bl), (tr, br), (bl, br)]
for i, ((p, q), lab, bend) in enumerate(zip(pairs, arrs, bends)):
k = order[i]
tt = clamp01((t - 0.10 * k) / 0.72)
off = -26.0 if i in (0, 3) else -30.0
if i == 3:
off = 30.0
if i == 2:
off = 34.0
arrow(c, p, q, bend=bend, color=ac, alpha=alpha, t=tt, label=lab,
label_size=label_size, label_off=off, label_kind=kinds[i])
for i, (pt, lab) in enumerate(zip(corners, objs)):
dy = -34.0 if i < 2 else 46.0
node(c, *pt, r=node_r, color=oc, alpha=alpha, label=lab, label_size=obj_size,
label_dy=dy, reveal=clamp01((t - 0.04 * i) / 0.4))
if commute > 0:
cx = (tl[0] + br[0]) / 2
cy = (tl[1] + br[1]) / 2
commuting_mark(c, cx, cy, alpha=alpha, t=commute)
def grid_dots(c, rect, nx, ny, color=RULE, alpha=0.5, r=1.6):
x0, y0, x1, y1 = rect
for i in range(nx):
for j in range(ny):
x = x0 + (x1 - x0) * i / max(nx - 1, 1)
y = y0 + (y1 - y0) * j / max(ny - 1, 1)
c.drawCircle(x, y, r, paint(color, alpha))
def polyline(c, pts, *, color=INK, alpha=1.0, width=2.0, t=1.0, close=False,
glow=0.0, dash=None):
if len(pts) < 2 or alpha <= 0 or t <= 0:
return
p = skia.Path()
p.moveTo(*pts[0])
for q in pts[1:]:
p.lineTo(*q)
if close:
p.close()
if t < 1:
p, _, _ = _trim(p, 0, t)
if glow > 0:
c.drawPath(p, paint(color, alpha * glow, width=width * 3.2, blur=width * 2.4))
pen = paint(color, alpha, width=width)
if dash:
pen.setPathEffect(skia.DashPathEffect.Make(list(dash), 0.0))
c.drawPath(p, pen)
PY
uv run python - <<'PY'
from PIL import Image
import numpy as np, math, skia
from catfilm.render.canvas import Frame, draw_text
from catfilm.render.diagram import *
from catfilm.config import *
fr = Frame(1400, 620)
def d(c):
node(c, 200, 200, label="A", color=INK); node(c, 560, 200, label="B", color=INK); node(c, 920, 200, label="C", color=INK)
arrow(c, (200,200),(560,200), color=A_BLUE, label="f")
arrow(c, (560,200),(920,200), color=A_AMBER, label="g")
arrow(c, (200,200),(920,200), bend=0.20, color=A_MINT, label="g ∘ f", label_off=30, t=0.85)
# monoid: one object, three loops
for i,(ang,col,lab) in enumerate(zip([-math.pi/2, math.pi/6, math.pi*5/6],[A_BLUE,A_AMBER,A_VIOLET],["a","b","c"])):
self_loop(c, 300, 470, angle=ang, color=col, label=lab, r=58)
node(c, 300, 470, color=INK, r=13)
square(c, ((760,400),(1120,400),(760,560),(1120,560)),
(["F(X)","F(Y)","G(X)","G(Y)"],["F(f)","α","α","G(f)"]),
color=INK, arrow_color=A_BLUE, obj_color=INK, commute=0.9, t=1.0)
fr.vector(d)
Image.fromarray(fr.finish(grain=0.005)).save(GALLERY/"diag.png"); print("ok")
PY
03:47:03
Read ← ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code/out/gallery/diag.png
03:47:53Self-loops need bigger geometry. Let me fix that and write the script — narration durations will drive the entire timeline:
03:47:58
Bash — Fix self-loop geometry and test TTS voices
python3 - <<'PY'
import re,io,sys
p='src/catfilm/render/diagram.py'
s=open(p).read()
s=s.replace(""" c0 = (x + r * 1.9 * math.cos(a0 - 0.30), y + r * 1.9 * math.sin(a0 - 0.30))
c1 = (x + r * 1.9 * math.cos(a1 + 0.30), y + r * 1.9 * math.sin(a1 + 0.30))""",
""" c0 = (x + r * 3.05 * math.cos(a0 - 0.34), y + r * 3.05 * math.sin(a0 - 0.34))
c1 = (x + r * 3.05 * math.cos(a1 + 0.34), y + r * 3.05 * math.sin(a1 + 0.34))""")
s=s.replace("label_size=30, label_off=1.42, glow=0.35)","label_size=30, label_off=1.72, glow=0.35)")
open(p,'w').write(s)
print("patched")
PY
say -v '?' 2>/dev/null | grep -iE 'siri|premium|enhanced|neural' | head; echo "--- timing test ---"
for V in Daniel Samantha Tessa Moira; do
say -v "$V" -r 170 -o /tmp/t.aiff "A category is made of three things, and nothing else. Objects, arrows between them, and a rule for chaining arrows together." 2>/dev/null
D=$(ffprobe -v error -show_entries format=duration -of csv=p=0 /tmp/t.aiff 2>/dev/null)
echo "$V -> ${D}s"
done
03:48:13Now the script — the writing is the soul of this, so let me get it right:
03:48:57
Bash — Write the screenplay and estimate runtime
cat > src/catfilm/script.py <<'PY'
"""The screenplay.
Each ``Beat`` is one spoken line. Its duration is measured from the generated
narration audio, and the whole film's timing is derived from those measurements
— so the pictures are cut to the voice, never the other way round.
"""
from __future__ import annotations
from dataclasses import dataclass, field
@dataclass
class Beat:
key: str
text: str | None = None # None = a silent beat of length `hold`
hold: float = 0.55 # silence after the line
lead: float = 0.0 # silence before the line
@dataclass
class Act:
name: str
scene: str # module in catfilm.scenes
beats: list[Beat] = field(default_factory=list)
def B(key, text=None, hold=0.55, lead=0.0):
return Beat(key, text, hold, lead)
SCRIPT: list[Act] = [
# ---------------------------------------------------------------- open --
Act("Cold open", "opening", [
B("o1", "This is a thing.", hold=1.0, lead=1.6),
B("o2", "It doesn't matter what it is. That isn't a limitation. That is the point.", hold=1.0),
B("o3", "Here is another thing.", hold=0.9),
B("o4", "And this is an arrow — a way of getting from the first one to the second.", hold=1.1),
B("o5", "Add a third. Add a second arrow.", hold=1.0),
B("o6", "And now something happens that you already know how to do, "
"and have probably never been asked to notice.", hold=0.8),
B("o7", "If you can get from here to here, and from here to here, "
"then you can get from here to here. You simply do both.", hold=1.3),
B("o8", "That is called composition. And it is enough — right there — "
"to build an entire branch of mathematics.", hold=1.5),
]),
Act("Title", "title", [
B("t1", None, hold=4.4),
]),
# ------------------------------------------------------------ category --
Act("What a category is", "category", [
B("c1", "A category is made of three things, and nothing else.", hold=0.9, lead=0.5),
B("c2", "Objects — dots. Arrows between them. And a way of chaining arrows together.", hold=1.0),
B("c3", "Two rules. Every object has a do-nothing arrow, "
"which leaves it exactly where it was.", hold=1.0),
B("c4", "And when you chain three arrows, the grouping doesn't matter. "
"First two, then the last; or the first, then the last two. Same journey.", hold=1.3),
B("c5", "That is the whole definition. Now read it again, "
"and notice what is missing.", hold=1.2),
B("c6", "We never said what the dots are. We never said what the arrows do.", hold=1.1),
B("c7", "Category theory is the study of the shape of relationships, "
"with the things themselves deliberately left out.", hold=1.5),
]),
# ------------------------------------------------------------ examples --
Act("Everything is a category", "examples", [
B("e1", "Which sounds like a theory about nothing at all. "
"It is the exact opposite.", hold=0.9, lead=0.4),
B("e2", "Let the dots be sets, and the arrows be functions between them. "
"That's a category.", hold=0.9),
B("e3", "Let the dots be numbers, and draw an arrow from x to y whenever x "
"is at most y. Composition is just: if x is at most y, and y is at most z, "
"then x is at most z. That's a category.", hold=1.0),
B("e4", "Let them be cities and flights. Let them be the types in a computer "
"program and the functions between them. Let them be ingredients, "
"and the steps of a recipe.", hold=1.0),
B("e5", "Each one is a category — and so every theorem about categories "
"is a theorem about all of them at once.", hold=1.6),
]),
# -------------------------------------------------------------- monoid --
Act("The smallest interesting category", "monoid", [
B("m1", "Here is the smallest interesting one.", hold=0.9, lead=0.5),
B("m2", "Take a single dot. Give it three arrows, "
"each one going from that dot back to itself. Call them a, b and c.", hold=1.2),
B("m3", "There is nowhere to go. All you can do is compose.", hold=1.0),
B("m4", "So every arrow in this category is nothing but a word. "
"a then b then c. Or c, c, a. Or b, b, b, b.", hold=1.2),
B("m5", "This category has no shape. It has no picture. It is a bag of words.", hold=1.2),
B("m6", "Remember it. We are going to come back to it, "
"and it is going to do something that should not be possible.", hold=1.6),
]),
# ------------------------------------------------------------- functor --
Act("Functors", "functor", [
B("f1", "If a category is a world, a functor is a way of translating "
"one world into another.", hold=1.0, lead=0.5),
B("f2", "It sends objects to objects, and arrows to arrows. "
"And it obeys exactly one law.", hold=1.1),
B("f3", "F of g-after-f equals F of g, after F of f.", hold=1.4),
B("f4", "Translate, then combine. Or combine, then translate. "
"Always the same answer.", hold=1.2),
B("f5", "That is what preserving structure means. Not that every detail "
"survives the journey — but that the shape does.", hold=1.4),
B("f6", "Which brings us back to our bag of words.", hold=1.2),
]),
# ---------------------------------------------------------- first bloom --
Act("The first functor", "bloom", [
B("b1", "We are going to build a functor out of that one-dot category. "
"There is only one object, so it goes to the only place we have: "
"the flat plane.", hold=1.0, lead=0.4),
B("b2", "And then we choose. Three choices, and only three. "
"What does a do? What does b do? What does c do?", hold=1.1),
B("b3", "Let a shrink the plane by half, toward this corner. "
"b, toward this one. c, toward the top.", hold=1.2),
B("b4", "That is every decision we are allowed to make. "
"Everything after this is forced by the functor law.", hold=1.2),
B("b5", "Because now the word a-then-b has no choice about what it means. "
"Shrink toward here; then shrink toward there. "
"Every word in the bag becomes a place on the plane.", hold=1.2),
B("b6", "So let us ask where the words go.", hold=1.4),
B("b7", None, hold=3.6),
B("b8", "Nobody drew that.", hold=1.5),
B("b9", "There is no triangle anywhere in the definition. "
"There are three matrices and a rule about composition. "
"What you are looking at is a picture of the words.", hold=1.5),
B("b10", "Even the colour is grammar. Blue where a acted last. "
"Amber for b. Violet for c. The image is painted by its own sentences.", hold=1.8),
]),
# ------------------------------------------------------------- variants --
Act("Change the functor", "variants", [
B("v1", "Now watch what happens if we keep every word and change "
"only the translation.", hold=1.0, lead=0.4),
B("v2", "Same single object. Same three letters. Same composition. "
"Three different matrices.", hold=2.2),
B("v3", "And again.", hold=2.4),
B("v4", "And again.", hold=2.6),
B("v5", "Every one of these is the same abstract thing, "
"seen through a different functor. The skeleton never moved.", hold=1.6),
B("v6", "This is what mathematicians mean when they call abstraction powerful. "
"Not that it is vague — that it is load-bearing.", hold=1.2),
B("v7", "Prove something upstairs, in the world with no pictures in it, "
"and it becomes true in every world downstairs at once.", hold=1.8),
]),
# ------------------------------------------------------------- natural --
Act("Natural transformations", "natural", [
B("n1", "So we have many translations of one story. "
"Which raises the obvious question: when are two translations "
"really the same translation?", hold=1.2, lead=0.4),
B("n2", "That question is the reason this entire subject exists.", hold=1.4),
B("n3", "In nineteen forty-five, Samuel Eilenberg and Saunders Mac Lane "
"were trying to pin down a word that mathematicians used constantly "
"and could not define. The word was: naturally.", hold=1.3),
B("n4", "As in: this construction works naturally — without anyone "
"having to make an arbitrary choice.", hold=1.2),
B("n5", "To define natural, they had to invent the functor. "
"To define the functor, they had to invent the category. "
"The whole subject was built backwards, to justify one adjective.", hold=1.6),
B("n6", "Here is what they found. A natural transformation hands you "
"one arrow for every object — and then demands that this square commutes.", hold=1.3),
B("n7", "Across, then down. Or down, then across. "
"If those two always agree, the translations are genuinely versions "
"of one another.", hold=1.4),
B("n8", "Let me show you one.", hold=1.2),
B("n9", "Here is our triangle again. And here is a single map of the plane: "
"a turn and a lean. Nothing to do with fractals.", hold=1.2),
B("n10", "Apply that one map on both sides of every arrow, "
"and you get a new functor — three completely different matrices.", hold=1.2),
B("n11", "And its picture is this.", hold=2.6),
B("n12", "The same triangle, standing differently. Every square commutes.", hold=1.2),
B("n13", "Different in every number. Identical in every relationship.", hold=1.8),
]),
# -------------------------------------------------------------- yoneda --
Act("Yoneda", "yoneda", [
B("y1", "Which brings us to the strangest result in the subject.", hold=1.2, lead=0.5),
B("y2", "The Yoneda lemma. Written out properly it takes a page. "
"Written honestly, it says this.", hold=1.4),
B("y3", "A thing is completely determined by its relationships "
"to everything else.", hold=2.0),
B("y4", "Not approximately. Completely.", hold=1.4),
B("y5", "If you know every arrow into an object, from every other object "
"in the category, then you know that object exactly. Anything with "
"the same arrows is the same thing.", hold=1.6),
B("y6", "You never have to open the box. The box was never the point.", hold=1.8),
B("y7", "It is the most abstract theorem in mathematics, "
"and it says something you could tell a child.", hold=1.2),
B("y8", "You are not what you are made of. You are how you connect.", hold=2.4),
]),
# -------------------------------------------------------------- finale --
Act("Finale", "finale", [
B("z1", "Three letters. One rule about chaining them.", hold=1.0, lead=0.6),
B("z2", "And out of that —", hold=5.0),
B("z3", "None of this was drawn. It was composed.", hold=2.2),
B("z4", "Objects, and arrows. Arrows all the way down.", hold=3.4),
]),
Act("Credits", "credits", [
B("cr", None, hold=13.0),
]),
]
def all_beats() -> list[Beat]:
return [b for a in SCRIPT for b in a.beats]
def word_count() -> int:
return sum(len(b.text.split()) for b in all_beats() if b.text)
PY
uv run python -c "
from catfilm.script import SCRIPT, all_beats, word_count
print('acts', len(SCRIPT), 'beats', len(all_beats()), 'words', word_count())
print('est speech min', round(word_count()/167,2))
print('est holds', round(sum(b.hold+b.lead for b in all_beats()),1),'s')
print('est total min', round((word_count()/167*60 + sum(b.hold+b.lead for b in all_beats()))/60,2))
"
03:49:07
Bash — Test say wav output format
say -v Daniel -r 168 --data-format=LEI16@44100 -o /tmp/t2.wav "Testing the narration pipeline." 2>&1 && ffprobe -v error -show_entries stream=codec_name,sample_rate,channels -show_entries format=duration -of default=nw=1 /tmp/t2.wav
03:49:29
Bash — Generate all narration and measure durations
cat > src/catfilm/audio/narration.py <<'PY'
"""Narration: synthesise every line, then let its measured length set the cut.
The film is edited to the voice. Each beat is rendered to its own wav once,
its true duration is measured and cached, and the timeline is rebuilt from
that cache — so a change to the script re-times the pictures automatically.
"""
from __future__ import annotations
import json
import subprocess
import wave
from pathlib import Path
import numpy as np
from ..config import AUDIO, NARRATOR_VOICE, NARRATOR_WPM, SAMPLE_RATE
from ..script import all_beats
VOICE_DIR = AUDIO / "voice"
DURATIONS = AUDIO / "durations.json"
def _say(text: str, out: Path) -> None:
subprocess.run(
["say", "-v", NARRATOR_VOICE, "-r", str(NARRATOR_WPM),
"--data-format=LEI16@%d" % SAMPLE_RATE, "-o", str(out), text],
check=True, capture_output=True,
)
def read_wav(p: Path) -> np.ndarray:
with wave.open(str(p), "rb") as w:
n = w.getnframes()
raw = w.readframes(n)
a = np.frombuffer(raw, dtype=np.int16).astype(np.float32) / 32768.0
if w.getnchannels() == 2:
a = a.reshape(-1, 2).mean(axis=1)
return a
def write_wav(p: Path, mono_or_stereo: np.ndarray, rate: int = SAMPLE_RATE) -> None:
a = np.clip(mono_or_stereo, -1.0, 1.0)
ch = 1 if a.ndim == 1 else a.shape[1]
with wave.open(str(p), "wb") as w:
w.setnchannels(ch)
w.setsampwidth(2)
w.setframerate(rate)
w.writeframes((a * 32767).astype("<i2").tobytes())
def _trim_tail(a: np.ndarray, thresh: float = 2.5e-3, keep: float = 0.10) -> np.ndarray:
"""`say` pads a little dead air; trim it so `hold` values mean what they say."""
loud = np.abs(a) > thresh
if not loud.any():
return a[: int(0.1 * SAMPLE_RATE)]
last = int(np.nonzero(loud)[0][-1])
first = int(np.nonzero(loud)[0][0])
start = max(0, first - int(0.04 * SAMPLE_RATE))
return a[start: min(len(a), last + int(keep * SAMPLE_RATE))]
def synthesize(force: bool = False) -> dict[str, float]:
VOICE_DIR.mkdir(parents=True, exist_ok=True)
cache = json.loads(DURATIONS.read_text()) if DURATIONS.exists() and not force else {}
out: dict[str, float] = {}
for b in all_beats():
if b.text is None:
out[b.key] = 0.0
continue
wav = VOICE_DIR / f"{b.key}.wav"
stamp = f"{NARRATOR_VOICE}|{NARRATOR_WPM}|{b.text}"
if not force and wav.exists() and cache.get(b.key + ".stamp") == stamp:
out[b.key] = cache[b.key]
continue
raw = VOICE_DIR / f"{b.key}.raw.wav"
_say(b.text, raw)
a = _trim_tail(read_wav(raw))
write_wav(wav, a)
raw.unlink(missing_ok=True)
out[b.key] = len(a) / SAMPLE_RATE
cache[b.key + ".stamp"] = stamp
print(f" voice {b.key:5s} {out[b.key]:6.2f}s {b.text[:56]}")
merged = {**cache, **out}
DURATIONS.write_text(json.dumps(merged, indent=1))
return out
def durations() -> dict[str, float]:
if not DURATIONS.exists():
raise SystemExit("run `catfilm audio` first — narration timings are missing")
d = json.loads(DURATIONS.read_text())
return {k: v for k, v in d.items() if not k.endswith(".stamp")}
def voice_track(schedule: dict[str, float], total: float) -> np.ndarray:
"""Lay every line onto one track at the times the timeline assigned."""
buf = np.zeros(int(total * SAMPLE_RATE) + SAMPLE_RATE, dtype=np.float32)
for key, t0 in schedule.items():
p = VOICE_DIR / f"{key}.wav"
if not p.exists():
continue
a = read_wav(p)
i = int(t0 * SAMPLE_RATE)
buf[i:i + len(a)] += a
return buf
PY
uv run python -c "
from catfilm.audio.narration import synthesize
import time; t=time.time()
d = synthesize()
print(f'{len(d)} beats in {time.time()-t:.1f}s, speech total {sum(d.values())/60:.2f} min')
" 2>&1 | tail -25
03:50:35Narration done — 6.2 min of speech. Now the timeline and render plumbing:
03:50:52
Bash — Write timeline module and print the schedule
cat > src/catfilm/timeline.py <<'PY'
"""Cutting the picture to the voice.
Beat durations come from the measured narration; this module turns them into
absolute times and hands every scene a small query object so animation can be
written as "one and a half seconds after the line about matrices".
"""
from __future__ import annotations
from dataclasses import dataclass, field
from .config import FPS
from .script import SCRIPT, Act, Beat
@dataclass
class Slot:
key: str
start: float
speech_end: float
end: float
act: str
@property
def dur(self) -> float:
return self.end - self.start
@dataclass
class ActSpan:
act: Act
start: float
end: float
slots: dict[str, Slot] = field(default_factory=dict)
@property
def dur(self) -> float:
return self.end - self.start
class Timeline:
def __init__(self, durations: dict[str, float]):
self.acts: list[ActSpan] = []
self.slots: dict[str, Slot] = {}
t = 0.0
for act in SCRIPT:
a0 = t
span = ActSpan(act, a0, a0)
for b in act.beats:
t += b.lead
d = durations.get(b.key, 0.0)
s = Slot(b.key, t, t + d, t + d + b.hold, act.name)
span.slots[b.key] = s
self.slots[b.key] = s
t = s.end
span.end = t
self.acts.append(span)
self.total = t
@property
def frames(self) -> int:
return int(round(self.total * FPS))
def at(self, t: float) -> ActSpan:
for a in self.acts:
if t < a.end:
return a
return self.acts[-1]
def schedule(self) -> dict[str, float]:
return {k: s.start for k, s in self.slots.items()}
def summary(self) -> str:
out = []
for a in self.acts:
out.append(f" {a.start/60:5.2f} {a.act.name:34s} {a.dur:6.1f}s"
f" [{a.act.scene}]")
out.append(f" total {self.total/60:.2f} min · {self.frames} frames")
return "\n".join(out)
class Ctx:
"""What a scene is given for one frame."""
def __init__(self, tl: Timeline, span: ActSpan, t: float, frame: int):
self.timeline = tl
self.span = span
self.t = t # absolute seconds into the film
self.tl = t - span.start # seconds into this act
self.dur = span.dur
self.frame = frame
self.slots = span.slots
# -- beat queries --------------------------------------------------------
def since(self, key: str) -> float:
"""Seconds since that line began speaking (negative before it)."""
return self.t - self.timeline.slots[key].start
def after(self, key: str) -> float:
"""Seconds since that line finished speaking."""
return self.t - self.timeline.slots[key].speech_end
def until(self, key: str) -> float:
return self.timeline.slots[key].start - self.t
def spoken(self, key: str) -> float:
"""0 -> 1 across the spoken part of a beat."""
s = self.timeline.slots[key]
return _c01((self.t - s.start) / max(s.speech_end - s.start, 1e-6))
def held(self, key: str) -> float:
"""0 -> 1 across the whole beat, speech plus its trailing silence."""
s = self.timeline.slots[key]
return _c01((self.t - s.start) / max(s.dur, 1e-6))
def live(self, key: str) -> bool:
s = self.timeline.slots[key]
return s.start <= self.t < s.end
def window(self, k0: str, k1: str) -> float:
"""0 -> 1 from the start of beat k0 to the end of beat k1."""
a = self.timeline.slots[k0].start
b = self.timeline.slots[k1].end
return _c01((self.t - a) / max(b - a, 1e-6))
# -- act-level -----------------------------------------------------------
@property
def progress(self) -> float:
return _c01(self.tl / max(self.dur, 1e-6))
def fade_in(self, d: float = 0.7) -> float:
return _c01(self.tl / d)
def fade_out(self, d: float = 0.7) -> float:
return _c01((self.dur - self.tl) / d)
@property
def envelope(self) -> float:
"""Act-level fade at both ends, so cuts never snap."""
return min(self.fade_in(), self.fade_out())
def _c01(x: float) -> float:
return 0.0 if x < 0 else (1.0 if x > 1 else float(x))
def build() -> Timeline:
from .audio.narration import durations
return Timeline(durations())
PY
uv run python -c "
from catfilm.timeline import build
tl = build(); print(tl.summary())"
03:51:08Now the render pipeline — parallel chunked encoding straight to ffmpeg, no intermediate frame files:
03:51:49
Bash — Write build pipeline, CLI, and contact sheets
cat > src/catfilm/build.py <<'PY'
"""Rendering and encoding.
Frames are never written to disk. The film is split into contiguous chunks,
one per core; each worker pipes raw frames into its own ffmpeg, and the chunks
are concatenated at the end. A nine-minute film costs a few hundred megabytes
of temporary video instead of thirty gigabytes of PNGs.
"""
from __future__ import annotations
import importlib
import multiprocessing as mp
import os
import shutil
import subprocess
import sys
import time
from pathlib import Path
import numpy as np
from .config import AUDIO, FPS, H, OUT, W
from .timeline import Ctx, Timeline, build as build_timeline
CHUNKS = OUT / "chunks"
_SCENES: dict[str, object] = {}
def scene_module(name: str):
if name not in _SCENES:
try:
_SCENES[name] = importlib.import_module(f".scenes.{name}", __package__)
except ModuleNotFoundError:
_SCENES[name] = importlib.import_module(".scenes.placeholder", __package__)
return _SCENES[name]
def render_frame(tl: Timeline, i: int, size=(W, H)) -> np.ndarray:
t = i / FPS
span = tl.at(t)
ctx = Ctx(tl, span, t, i)
mod = scene_module(span.act.scene)
return mod.render(ctx, size)
# ---------------------------------------------------------------------------
# Parallel chunk encoding
# ---------------------------------------------------------------------------
def _ffmpeg_writer(path: Path, size, fps=FPS, crf=16, preset="medium"):
w, h = size
return subprocess.Popen(
["ffmpeg", "-hide_banner", "-loglevel", "error", "-y",
"-f", "rawvideo", "-pix_fmt", "rgb24", "-s", f"{w}x{h}", "-r", str(fps),
"-i", "-", "-an",
"-c:v", "libx264", "-preset", preset, "-crf", str(crf),
"-pix_fmt", "yuv420p", "-g", "60", "-x264-params", "keyint=60:min-keyint=60:scenecut=0",
"-movflags", "+faststart", str(path)],
stdin=subprocess.PIPE,
)
_TL = None
def _init():
global _TL
_TL = build_timeline()
np.seterr(all="ignore")
def _work(job):
idx, f0, f1, size, crf, preset = job
path = CHUNKS / f"part{idx:03d}.mp4"
proc = _ffmpeg_writer(path, size, crf=crf, preset=preset)
t0 = time.time()
for i in range(f0, f1):
frame = render_frame(_TL, i, size)
proc.stdin.write(frame.tobytes())
proc.stdin.close()
proc.wait()
return idx, f1 - f0, time.time() - t0
def render_film(size=(W, H), crf=16, preset="medium", workers: int | None = None,
frame_range: tuple[int, int] | None = None) -> Path:
tl = build_timeline()
n = tl.frames
f0, f1 = frame_range or (0, n)
workers = workers or max(1, min(mp.cpu_count(), 10))
shutil.rmtree(CHUNKS, ignore_errors=True)
CHUNKS.mkdir(parents=True, exist_ok=True)
total = f1 - f0
# more chunks than workers keeps the tail from being dominated by one core
nchunks = workers * 3
bounds = np.linspace(f0, f1, nchunks + 1).astype(int)
jobs = [(i, int(bounds[i]), int(bounds[i + 1]), size, crf, preset)
for i in range(nchunks) if bounds[i + 1] > bounds[i]]
print(f" {total} frames · {size[0]}x{size[1]} · {len(jobs)} chunks · {workers} workers")
done = 0
t0 = time.time()
with mp.Pool(workers, initializer=_init) as pool:
for idx, cnt, dt in pool.imap_unordered(_work, jobs):
done += cnt
el = time.time() - t0
rate = done / max(el, 1e-6)
eta = (total - done) / max(rate, 1e-6)
print(f" chunk {idx:3d} {done:6d}/{total} {rate:5.1f} fps eta {eta:5.0f}s",
flush=True)
lst = CHUNKS / "list.txt"
lst.write_text("".join(f"file '{p.name}'\n" for p in sorted(CHUNKS.glob("part*.mp4"))))
silent = OUT / "picture.mp4"
subprocess.run(["ffmpeg", "-hide_banner", "-loglevel", "error", "-y",
"-f", "concat", "-safe", "0", "-i", str(lst),
"-c", "copy", str(silent)], check=True)
print(f" picture: {silent} ({silent.stat().st_size/1e6:.0f} MB, {time.time()-t0:.0f}s)")
return silent
def mux(picture: Path, audio: Path, out: Path) -> Path:
subprocess.run(
["ffmpeg", "-hide_banner", "-loglevel", "error", "-y",
"-i", str(picture), "-i", str(audio),
"-c:v", "copy", "-c:a", "aac", "-b:a", "256k", "-shortest",
"-movflags", "+faststart", str(out)], check=True)
return out
def still(frame_index: int, path: Path, size=(W, H)) -> Path:
from PIL import Image
tl = build_timeline()
Image.fromarray(render_frame(tl, frame_index, size)).save(path)
return path
PY
cat > src/catfilm/scenes/placeholder.py <<'PY'
"""Fallback scene, so the pipeline runs before every act is written."""
from __future__ import annotations
from ..render.canvas import Frame, draw_text
from ..config import INK_DIM
def render(ctx, size):
fr = Frame(*size)
fr.vector(lambda c: draw_text(
c, f"{ctx.span.act.name} · {ctx.tl:5.1f}s", size[0] / 2, size[1] / 2,
size=34, color=INK_DIM, align="center", alpha=0.5))
return fr.finish(grain=0.006, seed=ctx.frame)
PY
cat > src/catfilm/cli.py <<'PY'
from __future__ import annotations
import argparse
import sys
from pathlib import Path
from .config import GALLERY, H, OUT, W
def main(argv=None) -> int:
ap = argparse.ArgumentParser("catfilm", description="Functor — a short film about category theory")
sub = ap.add_subparsers(dest="cmd", required=True)
sub.add_parser("plan", help="print the timeline")
a = sub.add_parser("audio", help="synthesise narration + score")
a.add_argument("--force", action="store_true")
r = sub.add_parser("render", help="render the picture")
r.add_argument("--scene", help="render only this act")
r.add_argument("--scale", type=float, default=1.0)
r.add_argument("--crf", type=int, default=16)
r.add_argument("--preset", default="medium")
r.add_argument("--workers", type=int, default=None)
s = sub.add_parser("still", help="render one frame")
s.add_argument("at", help="seconds, mm:ss, or beat key")
s.add_argument("-o", "--out", default=None)
s.add_argument("--scale", type=float, default=1.0)
c = sub.add_parser("contact", help="contact sheet of one act")
c.add_argument("scene")
c.add_argument("-n", type=int, default=12)
b = sub.add_parser("build", help="audio + picture + mux")
b.add_argument("--scale", type=float, default=1.0)
b.add_argument("--crf", type=int, default=16)
b.add_argument("--preset", default="medium")
b.add_argument("--workers", type=int, default=None)
g = sub.add_parser("gallery", help="render the generative-art stills")
g.add_argument("--size", type=int, default=2400)
ns = ap.parse_args(argv)
size = (int(W * getattr(ns, "scale", 1.0)) // 2 * 2,
int(H * getattr(ns, "scale", 1.0)) // 2 * 2)
if ns.cmd == "plan":
from .timeline import build
print(build().summary()); return 0
if ns.cmd == "audio":
from .audio.narration import synthesize
from .audio.score import build_soundtrack
print("narration…"); synthesize(force=ns.force)
print("score…"); print(" ", build_soundtrack()); return 0
if ns.cmd == "render":
from .build import render_film
from .timeline import build
rng = None
if ns.scene:
tl = build()
from .config import FPS
match = [a for a in tl.acts if a.act.scene == ns.scene or a.act.name == ns.scene]
if not match:
print("no such act; try: " + ", ".join(a.act.scene for a in tl.acts)); return 2
rng = (int(match[0].start * FPS), int(match[-1].end * FPS))
render_film(size=size, crf=ns.crf, preset=ns.preset,
workers=ns.workers, frame_range=rng); return 0
if ns.cmd == "still":
from .build import still
from .timeline import build
from .config import FPS
tl = build()
at = ns.at
if ":" in at:
m, s_ = at.split(":"); t = int(m) * 60 + float(s_)
elif at in tl.slots:
sl = tl.slots[at]; t = sl.start + min(1.2, sl.dur * 0.5)
else:
t = float(at)
out = Path(ns.out) if ns.out else GALLERY / f"still_{at.replace(':','m')}.png"
print(still(int(t * FPS), out, size)); return 0
if ns.cmd == "contact":
from .contact import contact_sheet
print(contact_sheet(ns.scene, ns.n)); return 0
if ns.cmd == "build":
from .audio.narration import synthesize
from .audio.score import build_soundtrack
from .build import mux, render_film
print("narration…"); synthesize()
print("score…"); track = build_soundtrack()
print("picture…"); pic = render_film(size=size, crf=ns.crf, preset=ns.preset,
workers=ns.workers)
out = mux(pic, track, OUT / "functor.mp4")
print(f"\n ✦ {out} ({out.stat().st_size/1e6:.0f} MB)"); return 0
if ns.cmd == "gallery":
from .gallery import render_gallery
render_gallery(ns.size); return 0
return 1
if __name__ == "__main__":
sys.exit(main())
PY
cat > src/catfilm/contact.py <<'PY'
"""Contact sheets: a grid of stills from one act, for fast iteration."""
from __future__ import annotations
import numpy as np
from PIL import Image
from .build import render_frame
from .config import FPS, GALLERY
from .timeline import build
def contact_sheet(scene: str, n: int = 12, cols: int = 4, w: int = 640) -> str:
tl = build()
acts = [a for a in tl.acts if a.act.scene == scene or a.act.name == scene]
if not acts:
raise SystemExit("acts: " + ", ".join(a.act.scene for a in tl.acts))
t0, t1 = acts[0].start, acts[-1].end
size = (w, int(w * 9 / 16) // 2 * 2)
ts = np.linspace(t0 + 0.35, t1 - 0.35, n)
tiles = [render_frame(tl, int(t * FPS), size) for t in ts]
rows = []
for i in range(0, len(tiles), cols):
row = tiles[i:i + cols]
while len(row) < cols:
row.append(np.zeros_like(tiles[0]))
rows.append(np.concatenate(row, axis=1))
out = GALLERY / f"sheet_{scene}.png"
Image.fromarray(np.concatenate(rows, axis=0)).save(out)
return str(out)
PY
touch src/catfilm/audio/score.py src/catfilm/gallery.py
uv run catfilm plan >/dev/null && uv run catfilm still 0:05 --scale 0.5 && echo PIPELINE-OK
03:52:08Pipeline works end-to-end. Let me benchmark the expensive path before writing scenes:
03:52:11
Bash — Benchmark the glow render path at full resolution
uv run python - <<'PY'
import time, numpy as np
from catfilm.ifs import SYSTEMS, chaos_game
from catfilm.render.glow import accumulate, tone_map, bloom, fit_scale
s = SYSTEMS["spiral"]; size=(1920,1080)
for n,ss in [(600_000,2),(1_200_000,2),(2_400_000,2),(1_200_000,1)]:
t=time.time(); xy,rgb = chaos_game(s,n); t1=time.time()
c,sc = fit_scale(xy,size)
cnt,col = accumulate(xy,rgb,size,c,sc,ss); t2=time.time()
img = tone_map(cnt,col,ss); t3=time.time()
img = bloom(img,0.5); t4=time.time()
print(f"n={n//1000}k ss={ss}: chaos {t1-t:.2f} acc {t2-t1:.2f} tone {t3-t2:.2f} bloom {t4-t3:.2f} TOTAL {t4-t:.2f}")
PY
03:52:23Bloom dominates. Let me make it a proper mip pyramid:
03:52:34
Bash — Rewrite bloom as a pyramid and benchmark
python3 - <<'PY'
p='src/catfilm/render/glow.py'
s=open(p).read()
old_start = s.index("def blur(img")
old_end = s.index("def render_points(")
new = '''def blur(img: np.ndarray, sigma: float) -> np.ndarray:
from scipy.ndimage import convolve1d
k = _gauss1d(sigma)
out = convolve1d(img, k, axis=0, mode="constant")
return convolve1d(out, k, axis=1, mode="constant")
def _down2(a: np.ndarray) -> np.ndarray:
h, w = a.shape[:2]
a = a[: h // 2 * 2, : w // 2 * 2]
return a.reshape(h // 2, 2, w // 2, 2, -1).mean(axis=(1, 3))
def _up2(a: np.ndarray, shape) -> np.ndarray:
b = np.repeat(np.repeat(a, 2, axis=0), 2, axis=1)
return b[: shape[0], : shape[1]]
def bloom(img: np.ndarray, strength: float = 0.55, levels: int = 4,
sigma: float = 2.2) -> np.ndarray:
"""Multi-scale halo built on an image pyramid.
Each level blurs a half-size copy, so a very wide glow costs almost nothing.
This is what makes the light feel physical rather than drawn.
"""
if strength <= 0:
return img
shapes = [img.shape[:2]]
cur = img
acc = np.zeros_like(img)
wsum = 0.0
pyr = []
for i in range(levels):
cur = _down2(cur)
shapes.append(cur.shape[:2])
pyr.append(blur(cur, sigma))
for i, lvl in enumerate(pyr):
up = lvl
for j in range(i, -1, -1):
up = _up2(up, shapes[j])
w = 1.0 / (1.0 + i * 0.55)
acc += up * w
wsum += w
return np.clip(img + acc / wsum * strength, 0.0, 1.0)
'''
s = s[:old_start] + new + s[old_end:]
s = s.replace("bloom_strength: float = 0.5,\n saturation: float = 1.18,", "bloom_strength: float = 0.5,\n saturation: float = 1.18,\n bloom_levels: int = 4,")
s = s.replace("return bloom(img, bloom_strength)", "return bloom(img, bloom_strength, bloom_levels)")
open(p,'w').write(s)
print("ok")
PY
uv run python - <<'PY'
import time, numpy as np
from catfilm.ifs import SYSTEMS, chaos_game
from catfilm.render.glow import render_points, fit_scale
from PIL import Image
from catfilm.config import GALLERY, BG
s=SYSTEMS["spiral"]; size=(1920,1080)
xy,rgb=chaos_game(s,1_400_000)
c,sc=fit_scale(xy,size)
for _ in range(2):
t=time.time(); img=render_points(xy,rgb,size,c,sc,exposure=1.4,bloom_strength=0.6); print(f"{time.time()-t:.3f}s")
bg=np.array(BG,np.float32)/255
Image.fromarray((np.clip(bg+img,0,1)*255).astype(np.uint8)).save(GALLERY/"bloom.png")
PY
03:52:48
Bash — Fix pyramid padding and benchmark bloom
python3 - <<'PY'
p='src/catfilm/render/glow.py'
s=open(p).read()
s=s.replace('''def _up2(a: np.ndarray, shape) -> np.ndarray:
b = np.repeat(np.repeat(a, 2, axis=0), 2, axis=1)
return b[: shape[0], : shape[1]]''',
'''def _up2(a: np.ndarray, shape) -> np.ndarray:
b = np.repeat(np.repeat(a, 2, axis=0), 2, axis=1)
dh, dw = shape[0] - b.shape[0], shape[1] - b.shape[1]
if dh > 0 or dw > 0: # odd sizes lose a row/column on the way down
b = np.pad(b, ((0, max(dh, 0)), (0, max(dw, 0)), (0, 0)), mode="edge")
return b[: shape[0], : shape[1]]''')
open(p,'w').write(s); print("ok")
PY
uv run python - <<'PY'
import time, numpy as np
from catfilm.ifs import SYSTEMS, chaos_game
from catfilm.render.glow import render_points, fit_scale
from PIL import Image
from catfilm.config import GALLERY, BG
size=(1920,1080)
outs=[]
for k in ["sierpinski","spiral","crown"]:
xy,rgb=chaos_game(SYSTEMS[k],1_600_000)
c,sc=fit_scale(xy,size)
t=time.time(); img=render_points(xy,rgb,size,c,sc,exposure=1.5,bloom_strength=0.62); print(k,f"{time.time()-t:.3f}s")
outs.append(img)
bg=np.array(BG,np.float32)/255
sheet=np.concatenate([np.clip(bg+o,0,1)[::2,::2] for o in outs],axis=1)
Image.fromarray((sheet*255).astype(np.uint8)).save(GALLERY/"bloom.png")
PY
03:52:55
Read ← ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code/out/gallery/bloom.png
03:52:55 · 🖼 image returned to Claude — [Image: original 2880x540, displayed at 2000x375. Multiply coordinates by 1.44 to map to original image.]
03:53:02Colors are too bleached. Tuning the tone curve:
03:53:10
Bash — Tune saturation and exposure, render comparison
python3 - <<'PY'
p='src/catfilm/render/glow.py'
s=open(p).read()
s=s.replace(''' # hottest cores bleach toward white, the way real light does
core = np.clip((lum - 0.72) / 0.28, 0.0, 1.0)[..., None] ** 2
mean = mean + (1.0 - mean) * core * 0.85''',
''' # only the very hottest cores bleach toward white, the way real light does
core = np.clip((lum - 0.86) / 0.14, 0.0, 1.0)[..., None] ** 2
mean = mean + (1.0 - mean) * core * 0.55''')
s=s.replace('saturation: float = 1.18,\n knee','saturation: float = 1.45,\n knee')
s=s.replace('bloom_strength: float = 0.5,\n saturation: float = 1.18,','bloom_strength: float = 0.5,\n saturation: float = 1.45,')
open(p,'w').write(s)
p2='src/catfilm/ifs.py'
s=open(p2).read().replace("memory: float = 0.42,","memory: float = 0.30,")
open(p2,'w').write(s); print("ok")
PY
uv run python - <<'PY'
import numpy as np
from PIL import Image
from catfilm.ifs import SYSTEMS, chaos_game
from catfilm.render.glow import render_points, fit_scale
from catfilm.config import GALLERY, BG
size=(960,540); bg=np.array(BG,np.float32)/255
rows=[]
for sat,expo in [(1.45,1.5),(1.75,2.4)]:
tiles=[]
for k in ["sierpinski","spiral","crown","frond"]:
xy,rgb=chaos_game(SYSTEMS[k],1_400_000)
c,sc=fit_scale(xy,size,0.82)
img=render_points(xy,rgb,size,c,sc,exposure=expo,bloom_strength=0.62,saturation=sat)
tiles.append(np.clip(bg+img,0,1))
rows.append(np.concatenate(tiles,axis=1))
Image.fromarray((np.concatenate(rows,axis=0)*255).astype(np.uint8)).save(GALLERY/"tune.png")
print("ok")
PY
03:53:16
Read ← ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code/out/gallery/tune.png
03:53:17 · 🖼 image returned to Claude — [Image: original 3840x1080, displayed at 2000x563. Multiply coordinates by 1.92 to map to original image.]
03:53:44
Bash — Retune crown and check framing for all systems
python3 - <<'PY'
p='src/catfilm/ifs.py'
s=open(p).read()
s=s.replace(''' _mk(0.46, 0.46, 0.00, 0.00, -0.34, -0.26),
_mk(0.46, 0.46, 0.00, 0.00, 0.34, -0.26),
_mk(0.66, 0.66, 0.00, -0.36, 0.00, 0.22),
),
weights=(0.30, 0.30, 0.40),''',''' _mk(0.47, 0.47, 0.00, 0.00, -0.33, -0.24),
_mk(0.47, 0.47, 0.00, 0.00, 0.33, -0.24),
_mk(0.58, 0.58, 0.00, -0.30, 0.00, 0.24),
),
weights=(0.32, 0.32, 0.36),''')
open(p,'w').write(s)
p='src/catfilm/render/glow.py'
s=open(p).read().replace('saturation: float = 1.45,','saturation: float = 1.70,').replace('exposure: float = 1.0,\n bloom_strength','exposure: float = 2.0,\n bloom_strength')
open(p,'w').write(s); print("ok")
PY
uv run python - <<'PY'
import numpy as np
from catfilm.ifs import SYSTEMS, chaos_game
from catfilm.render.glow import fit_scale
size=(1920,1080)
for k,s in SYSTEMS.items():
xy,_=chaos_game(s,800_000)
lo,hi=xy.min(0),xy.max(0); q0,q1=np.quantile(xy,0.0008,axis=0),np.quantile(xy,0.9992,axis=0)
c,sc=fit_scale(xy,size,0.84)
# where do the true extremes land in pixels?
px=(lo-c)*sc+np.array(size)/2*np.array([1,-1]);
ex=((np.abs(lo-c)).max()*sc, (np.abs(hi-c)).max()*sc)
print(f"{k:11s} half-extent px {max(ex):6.0f} (frame half = {size[1]/2:.0f} v, {size[0]/2:.0f} h) {'OVER' if max(ex)>size[1]/2*1.02 else 'ok'}")
PY
03:53:57Now let me build the shared scene machinery with resolution-independent drawing:
03:54:36
Bash — Write shared scene machinery
python3 - <<'PY'
p='src/catfilm/render/canvas.py'
s=open(p).read()
s=s.replace('''class Frame:
def __init__(self, w: int = W, h: int = H, bg=BG):
self.w, self.h = w, h
self.buf = np.tile(
(np.array(bg, dtype=np.float32) / 255.0)[None, None, :], (h, w, 1)
)''','''class Frame:
"""A frame buffer.
Scenes always draw in a virtual 1920x1080 space; the frame scales that to
whatever the actual output resolution is, so previews and finals are the
same picture at different sizes.
"""
def __init__(self, w: int = W, h: int = H, bg=BG):
self.w, self.h = w, h
self.k = w / W # design-space -> device scale
self.buf = np.tile(
(np.array(bg, dtype=np.float32) / 255.0)[None, None, :], (h, w, 1)
)''')
s=s.replace(''' surf = skia.Surface(self.w, self.h)
with surf as c:
c.clear(skia.Color4f(0, 0, 0, 0))
draw(c)''',''' surf = skia.Surface(self.w, self.h)
with surf as c:
c.clear(skia.Color4f(0, 0, 0, 0))
if self.k != 1.0:
c.scale(self.k, self.k)
draw(c)''')
open(p,'w').write(s); print("ok")
PY
cat > src/catfilm/scenes/_common.py <<'PY'
"""Shared furniture for the scenes: caches, backgrounds, captions, the sigil."""
from __future__ import annotations
import math
from functools import lru_cache
import numpy as np
import skia
from ..config import (A_AMBER, A_BLUE, A_MINT, A_ROSE, A_VIOLET, BG, GENERATORS,
H, INK, INK_DIM, RULE, W)
from ..ifs import LETTERS, SYSTEMS, System, chaos_game
from ..render.canvas import (Frame, clamp01, draw_paragraph, draw_text, ease,
ease_out, measure, mix, paint, rgba, smooth,
smoother)
from ..render.diagram import arrow, node, polyline, self_loop
from ..render.glow import fit_scale, render_points
CX, CY = W / 2, H / 2
# ---------------------------------------------------------------------------
# Attractor cache — one chaos game per (system, seed, points) per process
# ---------------------------------------------------------------------------
@lru_cache(maxsize=24)
def points(key: str, n: int = 1_600_000, seed: int = 7):
return chaos_game(SYSTEMS[key], n, seed=seed)
@lru_cache(maxsize=16)
def frame_of(key: str, w: int, h: int, margin: float = 0.84, n: int = 1_600_000):
xy, _ = points(key, n)
return fit_scale(xy, (w, h), margin)
@lru_cache(maxsize=12)
def attractor_image(key: str, w: int, h: int, margin=0.84, n=1_600_000,
exposure=2.0, bloom=0.62, seed=7) -> np.ndarray:
"""A finished glow render of one system, cached — the expensive object."""
xy, rgb = points(key, n, seed)
c, s = fit_scale(xy, (w, h), margin)
return render_points(xy, rgb, (w, h), c, s, exposure=exposure,
bloom_strength=bloom)
def live_attractor(system: System, size, margin=0.84, n=700_000, exposure=2.0,
bloom=0.6, seed=7, center=None, scale=None) -> np.ndarray:
"""Render a system that is changing this frame (morphs, conjugations)."""
xy, rgb = chaos_game(system, n, seed=seed)
if center is None or scale is None:
c, s = fit_scale(xy, size, margin)
center = center if center is not None else c
scale = scale if scale is not None else s
return render_points(xy, rgb, size, center, scale, exposure=exposure,
bloom_strength=bloom)
# ---------------------------------------------------------------------------
# Background
# ---------------------------------------------------------------------------
@lru_cache(maxsize=4)
def _dust(w: int, h: int, n: int = 380, seed: int = 3):
rng = np.random.default_rng(seed)
return np.column_stack([
rng.uniform(0, W, n), rng.uniform(0, H, n),
rng.uniform(0.4, 1.7, n), rng.uniform(0, 1, n), rng.uniform(0.2, 1.0, n),
])
def dust(c, t: float, alpha: float = 1.0, drift: float = 5.0):
"""A slow field of motes. It keeps the black from reading as empty."""
if alpha <= 0:
return
for x, y, r, ph, br in _dust(W, H):
yy = (y + math.sin(t * 0.11 + ph * 6.283) * drift) % H
a = alpha * br * (0.10 + 0.09 * math.sin(t * 0.6 + ph * 6.283))
if a > 0.004:
c.drawCircle(x, yy, r, paint(INK, a))
def stage(ctx, size, bg=BG, dust_alpha: float = 1.0) -> Frame:
fr = Frame(*size, bg=bg)
if dust_alpha > 0:
fr.vector(lambda c: dust(c, ctx.t, dust_alpha * ctx.envelope), blend="add")
return fr
# ---------------------------------------------------------------------------
# Captions
# ---------------------------------------------------------------------------
def caption(c, text, y=H - 118, *, size=38, color=INK, alpha=1.0, reveal=1.0,
kind="serif", weight="regular", tracking=0.0, max_w=1360, glow=0.18):
draw_paragraph(c, text, CX, y, max_w, size=size, kind=kind, weight=weight,
color=color, alpha=alpha, align="center", leading=1.42,
tracking=tracking, reveal=reveal, rise=10, glow=glow)
def kicker(c, text, y=142, *, alpha=1.0, color=INK_DIM, size=23, reveal=1.0):
draw_text(c, text.upper(), CX, y, size=size, color=color, alpha=alpha,
align="center", tracking=0.30, reveal=reveal, kind="serif")
def hairline(c, y, x0=CX - 300, x1=CX + 300, alpha=0.5, color=RULE, t=1.0):
if alpha <= 0 or t <= 0:
return
m = (x0 + x1) / 2
half = (x1 - x0) / 2 * smoother(t)
c.drawLine(m - half, y, m + half, y, paint(color, alpha, width=1.2))
def formula(c, text, x, y, *, size=56, color=INK, alpha=1.0, reveal=1.0,
align="center", glow=0.30):
draw_text(c, text, x, y, size=size, kind="math", color=color, alpha=alpha,
align=align, reveal=reveal, glow=glow, rise=8)
# ---------------------------------------------------------------------------
# The sigil: one object, three arrows. The film's recurring mark.
# ---------------------------------------------------------------------------
def sigil(c, x, y, *, r=52.0, alpha=1.0, t=1.0, labels=True, node_r=11.0,
label_size=27, spin=0.0, width=2.2, colors=GENERATORS):
"""The free monoid on {a, b, c}, drawn as it will be drawn all film."""
if alpha <= 0:
return
for i, (col, lab) in enumerate(zip(colors, LETTERS)):
ang = -math.pi / 2 + i * 2 * math.pi / 3 + spin
tt = clamp01((t - i * 0.12) / 0.62)
self_loop(c, x, y, r=r, angle=ang, color=col, alpha=alpha, t=tt,
node_r=node_r, label=lab if labels else None,
label_size=label_size, width=width, head=r * 0.22,
glow=0.30)
node(c, x, y, r=node_r, color=INK, alpha=alpha, reveal=clamp01(t / 0.3))
# ---------------------------------------------------------------------------
# The three-letter legend used wherever colour means grammar
# ---------------------------------------------------------------------------
def letter_legend(c, x, y, *, alpha=1.0, reveal=1.0, gap=112, size=30, dot=7.5,
note=None):
for i, (col, lab) in enumerate(zip(GENERATORS, LETTERS)):
a = alpha * smooth((reveal - i * 0.16) / 0.5)
xx = x + (i - 1) * gap
c.drawCircle(xx - 22, y - size * 0.32, dot,
paint(col, a, blur=dot * 1.1))
c.drawCircle(xx - 22, y - size * 0.32, dot * 0.62, paint(col, a))
draw_text(c, lab, xx + 8, y, size=size, color=col, alpha=a, align="center")
if note:
draw_text(c, note, x, y + 44, size=23, color=INK_DIM,
alpha=alpha * smooth((reveal - 0.5) / 0.5), align="center",
tracking=0.06)
def matrix_block(c, m: np.ndarray, x, y, *, size=27, color=INK, alpha=1.0,
label=None, label_color=None, reveal=1.0, bracket=True):
"""A 2x3 affine matrix, set the way a book would set it."""
if alpha <= 0 or reveal <= 0:
return
rows = [f"{m[i,0]:+.2f} {m[i,1]:+.2f} {m[i,2]:+.2f}" for i in range(2)]
wmax = max(measure(r, "mono", size) for r in rows)
lh = size * 1.42
a = alpha * smooth(reveal)
if label:
draw_text(c, label, x - wmax / 2 - 34, y + lh * 0.30, size=size * 1.15,
color=label_color or color, alpha=a, align="right")
for i, r in enumerate(rows):
draw_text(c, r, x - wmax / 2, y + i * lh, size=size, kind="mono",
color=color, alpha=a)
if bracket:
bw, pad = 2.0, 12.0
top, bot = y - size * 0.95, y + lh + size * 0.30
for sx, xx in ((1, x - wmax / 2 - pad), (-1, x + wmax / 2 + pad)):
p = skia.Path()
p.moveTo(xx + sx * 9, top); p.lineTo(xx, top)
p.lineTo(xx, bot); p.lineTo(xx + sx * 9, bot)
c.drawPath(p, paint(color, a * 0.65, width=bw))
PY
uv run python -c "import catfilm.scenes._common as m; print('ok')"
03:54:54Now the scenes. Starting with the cold open, which sets the visual language:
03:55:21
Bash — Write opening and title scenes, render contact sheets
cat > src/catfilm/scenes/opening.py <<'PY'
"""Cold open: two dots, one arrow, and the only idea in the film."""
from __future__ import annotations
import math
from ._common import * # noqa: F403
from ..config import A_AMBER, A_BLUE, A_MINT, H, INK, INK_DIM, W
Y = CY - 40
# where the objects sit as the cast grows from one, to two, to three
P1 = [(CX, Y)]
P2 = [(CX - 300, Y), (CX + 300, Y)]
P3 = [(CX - 430, Y), (CX, Y), (CX + 430, Y)]
GHOSTS = ["a number", "a set", "a city", "a shape", "a program", "a person"]
def _lerp(a, b, t):
return (a[0] + (b[0] - a[0]) * t, a[1] + (b[1] - a[1]) * t)
def render(ctx, size):
fr = stage(ctx, size, dust_alpha=0.85)
# --- choreography -------------------------------------------------------
g2 = smoother(clamp01(ctx.since("o3") / 1.1)) # one dot -> two
g3 = smoother(clamp01(ctx.since("o5") / 1.1)) # two dots -> three
pa = _lerp(_lerp(P1[0], P2[0], g2), P3[0], g3)
pb = _lerp(P2[1], P3[1], g3)
pc = P3[2]
a_on = smooth(ctx.since("o1") / 1.3)
b_on = smooth(ctx.since("o3") / 1.1)
c_on = smooth(ctx.since("o5") / 1.0)
f_t = clamp01(ctx.since("o4") / 1.5)
g_t = clamp01((ctx.since("o5") - 1.0) / 1.5)
# the composite is drawn on the third clause of o7
s7 = ctx.slots["o7"]
comp_t = clamp01((ctx.t - (s7.start + s7.dur * 0.62)) / 1.6)
lab_t = clamp01(ctx.since("o8") / 1.4)
# highlight sweep during "from here to here… and from here to here"
hl_f = pulse(ctx.t, s7.start + 0.5, s7.start + 2.3, 0.4)
hl_g = pulse(ctx.t, s7.start + 2.5, s7.start + 4.3, 0.4)
def draw(c):
# objects
breathe = 1.0 + 0.045 * math.sin(ctx.t * 1.15)
node(c, *pa, r=13 * breathe, color=INK, reveal=a_on, halo=1.15)
node(c, *pb, r=13 * breathe, color=INK, reveal=b_on, halo=1.15)
node(c, *pc, r=13 * breathe, color=INK, reveal=c_on, halo=1.15)
# "it doesn't matter what it is" — the dot refuses every name offered
s2 = ctx.slots["o2"]
for i, word in enumerate(GHOSTS):
t0 = s2.start + 0.55 + i * 0.72
a = pulse(ctx.t, t0, t0 + 0.34, 0.30) * 0.85
if a > 0.01:
draw_text(c, word, pa[0], pa[1] - 78, size=34, color=INK_DIM,
alpha=a, align="center", tracking=0.04)
# arrows
arrow(c, pa, pb, color=A_BLUE, t=f_t, label="f", label_size=34,
label_off=-30, glow=0.30 + 0.55 * hl_f, width=2.4 + 1.5 * hl_f)
arrow(c, pb, pc, color=A_AMBER, t=g_t, label="g", label_size=34,
label_off=-30, glow=0.30 + 0.55 * hl_g, width=2.4 + 1.5 * hl_g)
# the composite: the arrow you did not have to draw
arrow(c, pa, pc, bend=0.155, color=A_MINT, t=comp_t, label_off=34,
label="g ∘ f" if lab_t > 0 else None, label_size=36,
label_reveal=lab_t, glow=0.34, width=2.6)
# vocabulary, arriving exactly when it is earned
kicker(c, "object", y=Y - 132, alpha=pulse(ctx.t, ctx.slots["o1"].start + 0.7,
ctx.slots["o2"].start - 0.2, 0.4) * 0.9)
kicker(c, "arrow", y=Y - 132, alpha=pulse(ctx.t, ctx.slots["o4"].start + 0.9,
ctx.slots["o5"].start - 0.3, 0.4) * 0.9)
kicker(c, "composition", y=Y + 250,
alpha=pulse(ctx.t, ctx.slots["o8"].start + 0.9,
ctx.slots["o8"].end - 0.2, 0.5) * 0.95, color=A_MINT)
# the law, whispered under the picture at the very end
a_law = smooth((ctx.since("o8") - 2.0) / 1.2) * ctx.fade_out(1.0)
formula(c, "g ∘ f", CX, Y + 190, size=0, alpha=0) # (spacing anchor)
if a_law > 0.01:
draw_text(c, "if f : A → B and g : B → C then g ∘ f : A → C",
CX, H - 148, size=30, kind="math", color=INK_DIM,
alpha=a_law * 0.9, align="center")
fr.vector(draw)
return fr.finish(grain=0.009, seed=ctx.frame)
PY
cat > src/catfilm/scenes/title.py <<'PY'
"""Title card."""
from __future__ import annotations
import math
import numpy as np
from ._common import * # noqa: F403
from ..config import A_MINT, H, INK, INK_DIM, W
def render(ctx, size):
fr = stage(ctx, size, dust_alpha=1.0)
# a ghost of what is coming, far under the type
a_bg = pulse(ctx.tl, 0.35, ctx.dur - 0.6, 0.9) * 0.20
if a_bg > 0.01:
img = attractor_image("sierpinski", size[0], size[1], margin=0.62)
fr.add(img, a_bg)
t = ctx.tl
def draw(c):
rv = clamp01((t - 0.30) / 1.5)
fade = ctx.fade_out(0.9)
draw_text(c, "FUNCTOR", CX, CY + 6, size=136, color=INK,
alpha=fade, align="center", tracking=0.30, reveal=rv,
rise=16, glow=0.22)
hairline(c, CY + 62, CX - 210, CX + 210, alpha=0.75 * fade,
t=clamp01((t - 1.3) / 0.9))
draw_text(c, "a short film about category theory", CX, CY + 124,
size=32, color=INK_DIM, alpha=fade, align="center",
tracking=0.18, reveal=clamp01((t - 1.6) / 1.1))
fr.vector(draw)
return fr.finish(grain=0.010, seed=ctx.frame)
PY
uv run catfilm contact opening -n 12 && uv run catfilm contact title -n 4
03:55:29
Bash — Fix imports and render contact sheets
python3 - <<'PY'
p='src/catfilm/scenes/_common.py'
s=open(p).read()
s=s.replace("""from ..render.canvas import (Frame, clamp01, draw_paragraph, draw_text, ease,
ease_out, measure, mix, paint, rgba, smooth,
smoother)""",
"""from ..render.canvas import (Frame, clamp01, draw_paragraph, draw_text, ease,
ease_in, ease_out, measure, mix, overshoot, paint,
pulse, rgba, seg, smooth, smoother, wrap)""")
s=s.replace("""from ..render.diagram import arrow, node, polyline, self_loop""",
"""from ..render.diagram import (arrow, arrowhead, commuting_mark, node, polyline,
self_loop, square)""")
open(p,'w').write(s); print("ok")
PY
uv run catfilm contact opening -n 12 && uv run catfilm contact title -n 4
03:55:35
Read ← ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code/out/gallery/sheet_opening.png
03:55:35 · 🖼 image returned to Claude — [Image: original 2560x1080, displayed at 2000x844. Multiply coordinates by 1.28 to map to original image.]
03:55:46Let me judge at full resolution rather than in thumbnails:
03:55:46
Bash — Render full-resolution stills
uv run catfilm still 0:36 -o out/gallery/s_open.png && uv run catfilm still 0:43 -o out/gallery/s_title.png && echo done
03:56:00
Read ← ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code/out/gallery/s_open.png
03:56:36Full-res looks right. Small spacing tweaks, then the next four scenes:
03:57:16
Bash — Write the category-definition scene
python3 - <<'PY'
p='src/catfilm/scenes/opening.py'
s=open(p).read()
s=s.replace("Y = CY - 40","Y = CY - 8")
s=s.replace('draw_text(c, "if f : A → B and g : B → C then g ∘ f : A → C",\n CX, H - 148,','draw_text(c, "if f : A → B and g : B → C then g ∘ f : A → C",\n CX, H - 170,')
s=s.replace("bend=0.155","bend=0.185").replace("width=2.6)","width=2.9)")
s=s.replace("width=2.4 + 1.5 * hl_f","width=2.8 + 1.6 * hl_f").replace("width=2.4 + 1.5 * hl_g","width=2.8 + 1.6 * hl_g")
open(p,'w').write(s)
# add a small-graph helper to _common
p='src/catfilm/scenes/_common.py'
s=open(p).read()
s += '''
# ---------------------------------------------------------------------------
# A miniature category, for the "everything is a category" grid
# ---------------------------------------------------------------------------
def mini_graph(c, nodes, edges, *, alpha=1.0, t=1.0, color=INK, arrow_color=None,
node_r=7.0, label_size=22, width=1.9, head=10.0, label_kind="serif",
edge_labels=True, obj_labels=True):
"""Draw a tiny labelled digraph.
``nodes``: {name: (x, y)} in design space. ``edges``: list of
(src, dst, label, bend).
"""
ac = arrow_color or color
for i, (s_, d_, lab, bend) in enumerate(edges):
tt = clamp01((t - 0.28 - i * 0.07) / 0.55)
arrow(c, nodes[s_], nodes[d_], bend=bend, color=ac, alpha=alpha, t=tt,
width=width, head=head, gap=(node_r + 5, node_r + 9),
label=lab if (edge_labels and lab) else None, label_size=label_size,
label_off=-19 if bend >= 0 else 19, glow=0.28,
label_kind=label_kind)
for i, (name, (x, y)) in enumerate(nodes.items()):
node(c, x, y, r=node_r, color=color, alpha=alpha,
reveal=clamp01((t - i * 0.05) / 0.36), halo=0.9,
label=name if obj_labels else None, label_size=label_size,
label_dy=-node_r - 15)
def card(c, cx, cy, w, h, *, alpha=1.0, t=1.0, title=None, subtitle=None,
color=RULE, title_color=INK_DIM, title_size=22):
"""The thin frame each example category sits inside."""
if alpha <= 0 or t <= 0:
return
k = smoother(t)
hw, hh = w / 2 * k, h / 2
r = skia.RRect.MakeRectXY(
skia.Rect.MakeLTRB(cx - hw, cy - hh, cx + hw, cy + hh), 6, 6)
c.drawRRect(r, paint(color, alpha * 0.62, width=1.2))
if title and k > 0.55:
a = alpha * smooth((t - 0.45) / 0.5)
draw_text(c, title.upper(), cx, cy - hh + 34, size=title_size,
color=title_color, alpha=a, align="center", tracking=0.22)
if subtitle and k > 0.7:
draw_text(c, subtitle, cx, cy + hh - 22, size=title_size - 1,
color=title_color, alpha=alpha * smooth((t - 0.6) / 0.4) * 0.8,
align="center", tracking=0.04)
'''
open(p,'w').write(s); print("ok")
PY
echo "--- category scene ---"
cat > src/catfilm/scenes/category.py <<'PY'
"""The definition: objects, arrows, composition — and the two laws."""
from __future__ import annotations
import math
from ._common import * # noqa: F403
from ..config import A_AMBER, A_BLUE, A_MINT, A_ROSE, A_VIOLET, H, INK, INK_DIM, W
Y = CY - 46
XS = (CX - 555, CX - 185, CX + 185, CX + 555)
NAMES = ("A", "B", "C", "D")
COLS = (A_BLUE, A_AMBER, A_VIOLET)
ELAB = ("f", "g", "h")
def render(ctx, size):
fr = stage(ctx, size, dust_alpha=0.7)
d_on = smooth((ctx.since("c4") - 0.6) / 0.9) # the fourth object
ids = clamp01((ctx.since("c3") - 1.4) / 1.6) # identity loops
dissolve = smoother(clamp01((ctx.since("c5") - 1.8) / 2.6)) # labels leave
# the three ingredients light up as they are named
s2 = ctx.slots["c2"]
ing = [pulse(ctx.t, s2.start + o, s2.start + o + 2.4, 0.5)
for o in (0.20, 1.75, 3.30)]
dots_t = clamp01((ctx.since("c2") - 0.2) / 0.9)
arrs_t = clamp01((ctx.since("c2") - 1.7) / 1.2)
comp_t = clamp01((ctx.since("c2") - 3.2) / 1.3)
# associativity: two bracketings, then the verdict
s4 = ctx.slots["c4"]
br1 = pulse(ctx.t, s4.start + 2.3, s4.start + 5.0, 0.55)
br2 = pulse(ctx.t, s4.start + 4.4, s4.start + 7.2, 0.55)
verdict = smooth((ctx.t - (s4.start + 6.6)) / 1.1) * (1 - dissolve * 0.85)
def pos(i):
return (XS[i], Y)
def draw(c):
lab_a = 1.0 - dissolve
# --- the ingredient tally, top of frame ----------------------------
for i, (n, word) in enumerate(zip("①②③", ("objects", "arrows", "composition"))):
xx = CX + (i - 1) * 300
a = (0.30 + 0.70 * ing[i]) * clamp01(ctx.since("c1") / 0.8) * (1 - dissolve)
col = mix(INK_DIM, (A_BLUE, A_AMBER, A_MINT)[i], ing[i])
draw_text(c, n, xx - 96, 152, size=30, color=col, alpha=a, align="center")
draw_text(c, word.upper(), xx + 14, 152, size=24, color=col, alpha=a,
align="center", tracking=0.20)
# --- the chain ------------------------------------------------------
for i in range(3):
tt = arrs_t if i < 2 else clamp01((ctx.since("c4") - 1.1) / 1.0)
if i == 2 and d_on <= 0.01:
continue
w = 2.7 + 1.6 * (br1 if i < 2 else 0) + 1.6 * (br2 if i > 0 else 0)
arrow(c, pos(i), pos(i + 1), color=COLS[i], alpha=1.0, t=tt,
label=ELAB[i] if lab_a > 0.02 else None, label_size=36,
label_off=-32, width=w, glow=0.30,
label_reveal=tt * lab_a)
# composition of the first two, shown as the arrow you get free
arrow(c, pos(0), pos(2), bend=0.20, color=A_MINT, t=comp_t,
label="g ∘ f" if lab_a > 0.02 else None, label_size=34,
label_off=32, width=2.7, glow=0.30, label_reveal=comp_t * lab_a)
# --- objects --------------------------------------------------------
for i in range(4):
if i == 3 and d_on <= 0.01:
continue
rv = dots_t if i < 3 else d_on
node(c, *pos(i), r=14, color=INK, reveal=rv, halo=1.1,
label=NAMES[i] if lab_a > 0.02 else None, label_size=38,
label_dy=-38, label_color=mix(INK, INK_DIM, dissolve))
# --- law one: every object can do nothing --------------------------
if ids > 0.01:
for i in range(4):
if i == 3 and d_on <= 0.01:
continue
tt = clamp01((ids - i * 0.10) / 0.6)
self_loop(c, *pos(i), r=44, angle=math.pi / 2, spread=0.60,
color=INK_DIM, alpha=0.85 * (1 - dissolve * 0.6), t=tt,
node_r=15, head=11,
label="id" if lab_a > 0.02 else None, label_size=25,
label_off=1.85, glow=0.22)
# --- law two: bracketing does not matter ---------------------------
for k, (act, lo, hi, col) in enumerate((
(br1, 0, 2, A_ROSE), (br2, 1, 3, A_ROSE))):
if act <= 0.01:
continue
bend = -0.30 if k == 0 else 0.30
arrow(c, pos(lo), pos(hi), bend=bend, color=col, alpha=act * 0.95,
t=1.0, width=2.4, glow=0.35, head=13, gap=(20, 22))
if br1 > 0.01 or br2 > 0.01:
txt = "( h ∘ g ) ∘ f" if br1 > br2 else "h ∘ ( g ∘ f )"
draw_text(c, txt, CX, Y - 210, size=44, kind="math", color=A_ROSE,
alpha=max(br1, br2), align="center")
if verdict > 0.01:
draw_text(c, "( h ∘ g ) ∘ f = h ∘ ( g ∘ f )", CX, Y + 250,
size=46, kind="math", color=A_MINT, alpha=verdict,
align="center", reveal=verdict, glow=0.25)
# --- the closing thought -------------------------------------------
a7 = smooth((ctx.since("c6") - 0.4) / 1.4) * ctx.fade_out(1.0)
if a7 > 0.01:
caption(c, "the shape of relationships — with the things themselves "
"left out", y=H - 132, size=37, color=INK, alpha=a7,
reveal=clamp01((ctx.since("c7") - 0.3) / 2.2))
fr.vector(draw)
return fr.finish(grain=0.009, seed=ctx.frame)
PY
uv run catfilm contact category -n 12
03:57:21
Read ← ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code/out/gallery/sheet_category.png
03:57:22 · 🖼 image returned to Claude — [Image: original 2560x1080, displayed at 2000x844. Multiply coordinates by 1.28 to map to original image.]
03:57:38
Bash — Render full-res stills of category scene
uv run catfilm still 1:22 -o out/gallery/s_cat1.png && uv run catfilm still 1:29 -o out/gallery/s_cat2.png && echo ok
03:57:45
Read ← ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code/out/gallery/s_cat1.png
03:58:02The identity loops are cramped. Let me fix the self-loop geometry properly:
03:58:07
Bash — Test self-loop geometry variants
uv run python - <<'PY'
from PIL import Image
import numpy as np, math
from catfilm.render.canvas import Frame, draw_text
from catfilm.render.diagram import self_loop, node
from catfilm.config import *
fr = Frame(1600, 420)
def d(c):
cfgs = [(30,44,0.60),(24,50,0.80),(26,46,0.95),(20,54,0.72),(28,58,0.85)]
for i,(nr,r,sp) in enumerate(cfgs):
x = 180+i*300
self_loop(c, x, 240, r=r, angle=math.pi/2, spread=sp, color=INK_DIM, node_r=nr, head=12, label="id", label_size=26, label_off=1.85)
node(c, x, 240, r=14, color=INK)
draw_text(c, f"nr={nr} r={r} sp={sp}", x, 130, size=20, color=INK_DIM, align="center")
fr.vector(d)
Image.fromarray(fr.finish(grain=0.004, vignette=0.1)).save(GALLERY/"loops.png")
print("ok")
PY
03:58:13
Read ← ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code/out/gallery/loops.png
03:58:36The loops are splaying flat. Let me rebuild them from actual circle geometry:
03:58:51
Bash — Rebuild self-loop from circle-circle intersection
python3 - <<'PY'
p='src/catfilm/render/diagram.py'
s=open(p).read()
a=s.index("def self_loop(")
b=s.index("# ---------------------------------------------------------------------------\n# Composite figures")
new = '''def self_loop(c, x, y, *, r=64.0, angle=-math.pi / 2, spread=0.62, color=INK,
alpha=1.0, width=2.4, t=1.0, node_r=13.0, head=14.0, label=None,
label_size=30, label_off=1.28, glow=0.35, roundness=0.46):
"""An arrow from an object to itself — the only kind a monoid has.
Built as a genuine circular arc: a loop circle of radius ``rho`` sitting at
distance ``d`` from the object, drawn between the two points where the two
circles cross. ``spread`` widens the mouth by pushing the loop closer in.
"""
if alpha <= 0 or t <= 0:
return
rho = r * roundness
d = r - rho
nr = max(node_r, 1.0)
# keep the two circles genuinely intersecting whatever the caller asks for
nr = min(max(nr, abs(d - rho) + 1.0), d + rho - 1.0)
nr *= 0.72 + 0.55 * spread
a_ = (d * d + nr * nr - rho * rho) / (2 * d)
h = math.sqrt(max(nr * nr - a_ * a_, 1e-6))
ux, uy = math.cos(angle), math.sin(angle)
nx, ny = -uy, ux
p0 = (x + ux * a_ + nx * h, y + uy * a_ + ny * h)
p1 = (x + ux * a_ - nx * h, y + uy * a_ - ny * h)
cx, cy = x + ux * d, y + uy * d
th0 = math.degrees(math.atan2(p0[1] - cy, p0[0] - cx))
th1 = math.degrees(math.atan2(p1[1] - cy, p1[0] - cx))
sweep = (th1 - th0) % 360.0 # the long way round, outside the object
rect = skia.Rect.MakeLTRB(cx - rho, cy - rho, cx + rho, cy + rho)
path = skia.Path()
path.addArc(rect, th0, sweep)
seg, pos, tan = _trim(path, 0.0, clamp01(t / 0.85))
if glow > 0:
c.drawPath(seg, paint(color, alpha * glow, width=width * 3.4, blur=width * 2.6))
c.drawPath(seg, paint(color, alpha, width=width))
arrowhead(c, pos, tan, head * smooth((t - 0.7) / 0.3), color, alpha)
if label:
lx = x + (d + rho) * label_off * math.cos(angle)
ly = y + (d + rho) * label_off * math.sin(angle)
draw_text(c, label, lx, ly + label_size * 0.36, size=label_size, color=color,
alpha=alpha, align="center", reveal=clamp01((t - 0.5) / 0.4))
'''
s = s[:a] + new + s[b:]
open(p,'w').write(s); print("ok")
PY
uv run python - <<'PY'
from PIL import Image
import math
from catfilm.render.canvas import Frame, draw_text
from catfilm.render.diagram import self_loop, node
from catfilm.config import *
fr = Frame(1600, 460)
def d(c):
cfgs=[(60,0.5,0.46),(60,0.9,0.46),(70,0.7,0.55),(56,1.2,0.40),(64,0.7,0.34)]
for i,(r,sp,ro) in enumerate(cfgs):
x=180+i*300
self_loop(c,x,250,r=r,angle=math.pi/2,spread=sp,roundness=ro,color=INK_DIM,node_r=15,head=13,label="id",label_size=27,label_off=1.30)
node(c,x,250,r=14,color=INK)
draw_text(c,f"r={r} sp={sp} ro={ro}",x,120,size=19,color=INK_DIM,align="center")
# a three-loop monoid at 3 sizes
fr.vector(d)
Image.fromarray(fr.finish(grain=0.004,vignette=0.1)).save(GALLERY/"loops.png"); print("ok")
PY
03:58:57
Read ← ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code/out/gallery/loops.png
03:59:21
Bash — Fix arc direction and test sigil
python3 - <<'PY'
p='src/catfilm/render/diagram.py'
s=open(p).read()
s=s.replace(''' sweep = (th1 - th0) % 360.0 # the long way round, outside the object
rect = skia.Rect.MakeLTRB(cx - rho, cy - rho, cx + rho, cy + rho)''',
''' sweep = (th1 - th0) % 360.0
# two arcs join the same pair of points; take the one that leaves the object
def _mid_dist(sw):
m = math.radians(th0 + sw / 2)
return math.hypot(cx + rho * math.cos(m) - x, cy + rho * math.sin(m) - y)
if _mid_dist(sweep) < _mid_dist(sweep - 360.0):
sweep -= 360.0
rect = skia.Rect.MakeLTRB(cx - rho, cy - rho, cx + rho, cy + rho)''')
open(p,'w').write(s); print("ok")
PY
uv run python - <<'PY'
from PIL import Image
import math
from catfilm.render.canvas import Frame, draw_text
from catfilm.render.diagram import self_loop, node
from catfilm.config import *
fr = Frame(1700, 700)
def d(c):
cfgs=[(60,0.5,0.46),(60,0.9,0.46),(70,0.7,0.55),(56,1.2,0.40),(64,0.7,0.34)]
for i,(r,sp,ro) in enumerate(cfgs):
x=190+i*320
self_loop(c,x,230,r=r,angle=math.pi/2,spread=sp,roundness=ro,color=INK_DIM,node_r=15,head=13,label="id",label_size=27,label_off=1.34)
node(c,x,230,r=14,color=INK)
draw_text(c,f"r={r} sp={sp} ro={ro}",x,120,size=19,color=INK_DIM,align="center")
# the sigil at 3 sizes
for j,(R,NR,LS) in enumerate([(58,11,26),(86,15,34),(120,20,44)]):
X=350+j*450
for i,(col,lab) in enumerate(zip(GENERATORS,"abc")):
ang=-math.pi/2+i*2*math.pi/3
self_loop(c,X,520,r=R,angle=ang,color=col,node_r=NR,head=R*0.20,label=lab,label_size=LS,label_off=1.30,width=2.4)
node(c,X,520,r=NR*0.75,color=INK)
fr.vector(d)
Image.fromarray(fr.finish(grain=0.004,vignette=0.1)).save(GALLERY/"loops.png"); print("ok")
PY
03:59:27
Read ← ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code/out/gallery/loops.png
03:59:36The sigil is exactly right. Let me lock in those parameters and write the next batch of scenes:
03:59:51
Bash — Apply sigil params and recompose category scene
python3 - <<'PY'
p='src/catfilm/scenes/_common.py'
s=open(p).read()
s=s.replace('''def sigil(c, x, y, *, r=52.0, alpha=1.0, t=1.0, labels=True, node_r=11.0,
label_size=27, spin=0.0, width=2.2, colors=GENERATORS):
"""The free monoid on {a, b, c}, drawn as it will be drawn all film."""
if alpha <= 0:
return
for i, (col, lab) in enumerate(zip(colors, LETTERS)):
ang = -math.pi / 2 + i * 2 * math.pi / 3 + spin
tt = clamp01((t - i * 0.12) / 0.62)
self_loop(c, x, y, r=r, angle=ang, color=col, alpha=alpha, t=tt,
node_r=node_r, label=lab if labels else None,
label_size=label_size, width=width, head=r * 0.22,
glow=0.30)
node(c, x, y, r=node_r, color=INK, alpha=alpha, reveal=clamp01(t / 0.3))''',
'''def sigil(c, x, y, *, r=86.0, alpha=1.0, t=1.0, labels=True, node_r=15.0,
label_size=34, spin=0.0, width=2.4, colors=GENERATORS, stagger=0.12,
label_off=1.30, dot_r=None):
"""The free monoid on {a, b, c}: one object, three arrows, nothing else.
The film's recurring mark. Everything that blooms later is this, translated.
"""
if alpha <= 0:
return
for i, (col, lab) in enumerate(zip(colors, LETTERS)):
ang = -math.pi / 2 + i * 2 * math.pi / 3 + spin
tt = clamp01((t - i * stagger) / 0.62)
self_loop(c, x, y, r=r, angle=ang, color=col, alpha=alpha, t=tt,
node_r=node_r, label=lab if labels else None,
label_size=label_size, width=width, head=r * 0.20,
glow=0.30, roundness=0.50, label_off=label_off)
node(c, x, y, r=dot_r or node_r * 0.78, color=INK, alpha=alpha,
reveal=clamp01(t / 0.3))''')
open(p,'w').write(s)
p='src/catfilm/scenes/category.py'
s=open(p).read()
s=s.replace(""" self_loop(c, *pos(i), r=44, angle=math.pi / 2, spread=0.60,
color=INK_DIM, alpha=0.85 * (1 - dissolve * 0.6), t=tt,
node_r=15, head=11,
label="id" if lab_a > 0.02 else None, label_size=25,
label_off=1.85, glow=0.22)""",
""" self_loop(c, *pos(i), r=72, angle=math.pi / 2, spread=0.70,
roundness=0.55, color=INK_DIM,
alpha=0.9 * (1 - dissolve * 0.55), t=tt,
node_r=16, head=12,
label="id" if lab_a > 0.02 else None, label_size=26,
label_off=1.30, glow=0.22)""")
s=s.replace("Y = CY - 46","Y = CY - 96")
s=s.replace('draw_text(c, txt, CX, Y - 210,','draw_text(c, txt, CX, Y - 200,')
s=s.replace('draw_text(c, "( h ∘ g ) ∘ f = h ∘ ( g ∘ f )", CX, Y + 250,','draw_text(c, "( h ∘ g ) ∘ f = h ∘ ( g ∘ f )", CX, Y + 320,')
s=s.replace(''' draw_text(c, n, xx - 96, 152, size=30, color=col, alpha=a, align="center")
draw_text(c, word.upper(), xx + 14, 152, size=24, color=col, alpha=a,
align="center", tracking=0.20)''',
''' draw_text(c, f"{n} {word.upper()}", xx, 148, size=25, color=col,
alpha=a, align="center", tracking=0.18)''')
open(p,'w').write(s); print("ok")
PY
uv run catfilm still 1:22 -o out/gallery/s_cat1.png && uv run catfilm still 1:31 -o out/gallery/s_cat2.png && uv run python -c "
from PIL import Image; import numpy as np
a=[np.array(Image.open(f'out/gallery/s_cat{i}.png'))[::2,::2] for i in (1,2)]
Image.fromarray(np.concatenate(a,0)).save('out/gallery/cmp.png')"
03:59:57
Read ← ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code/out/gallery/cmp.png
04:00:16Identity loops fixed. Now three more scenes in one pass:
04:01:05
Bash — Write examples and monoid scenes
cat > src/catfilm/scenes/examples.py <<'PY'
"""Five categories that were already there before anyone named them."""
from __future__ import annotations
import math
import numpy as np
import skia
from ._common import * # noqa: F403
from ..config import (A_AMBER, A_BLUE, A_MINT, A_ROSE, A_VIOLET, H, INK,
INK_DIM, RULE, W)
CW, CH = 520, 292
ROW1, ROW2 = CY - 168, CY + 190
SLOTS = [(CX - 580, ROW1), (CX, ROW1), (CX + 580, ROW1),
(CX - 300, ROW2), (CX + 300, ROW2)]
TITLES = [("sets", "and functions"), ("numbers", "and “at most”"),
("places", "and journeys"), ("types", "and programs"),
("ingredients", "and steps")]
HUES = [A_BLUE, A_AMBER, A_VIOLET, A_MINT, A_ROSE]
# --- the drawing inside each card ------------------------------------------
def _sets(c, x, y, col, a, t):
rng = np.random.default_rng(4)
lx, rx = x - 116, x + 116
pts_l = [(lx + rng.uniform(-46, 46), y + rng.uniform(-44, 44)) for _ in range(5)]
pts_r = [(rx + rng.uniform(-40, 40), y + rng.uniform(-38, 38)) for _ in range(3)]
for cx_, w_ in ((lx, 62), (rx, 56)):
c.drawOval(skia.Rect.MakeLTRB(cx_ - w_, y - 58, cx_ + w_, y + 58),
paint(RULE, a * 0.85 * smooth(t), width=1.3))
hit = [0, 1, 1, 2, 2]
for i, p in enumerate(pts_l):
tt = clamp01((t - 0.30 - i * 0.05) / 0.4)
if tt > 0:
q = pts_r[hit[i]]
c.drawLine(p[0], p[1], p[0] + (q[0] - p[0]) * tt,
p[1] + (q[1] - p[1]) * tt, paint(col, a * 0.75, width=1.5))
for p in pts_l + pts_r:
c.drawCircle(p[0], p[1], 4.2, paint(INK, a * smooth(t)))
def _numbers(c, x, y, col, a, t):
vals = ["1", "2", "5", "9"]
for i, v in enumerate(vals):
xx = x + (i - 1.5) * 96
node(c, xx, y + 8, r=7, color=INK, alpha=a, reveal=clamp01((t - i * .06) / .35),
label=v, label_size=27, label_dy=-26)
if i:
arrow(c, (x + (i - 2.5) * 96, y + 8), (xx, y + 8), color=col, alpha=a,
t=clamp01((t - .25 - i * .08) / .45), width=1.8, head=9,
gap=(12, 15), glow=0.25)
draw_text(c, "x ≤ y", x, y + 62, size=25, kind="math", color=col,
alpha=a * smooth((t - .6) / .4), align="center")
def _places(c, x, y, col, a, t):
P = {"": (x - 118, y - 30), " ": (x + 10, y - 56), " ": (x + 112, y + 18),
" ": (x - 44, y + 52)}
ks = list(P)
E = [(0, 1, .16), (1, 2, .16), (0, 3, -.18), (3, 2, .16), (0, 2, .34)]
for i, (s_, d_, b) in enumerate(E):
arrow(c, P[ks[s_]], P[ks[d_]], bend=b, color=col, alpha=a * .95,
t=clamp01((t - .22 - i * .07) / .5), width=1.7, head=9,
gap=(11, 14), glow=0.25)
for i, k in enumerate(ks):
node(c, *P[k], r=6.5, color=INK, alpha=a, reveal=clamp01((t - i * .05) / .35))
def _types(c, x, y, col, a, t):
words = ["String", "Int", "Bool"]
xs = [x - 148, x + 4, x + 140]
for i, (w, xx) in enumerate(zip(words, xs)):
draw_text(c, w, xx, y + 8, size=27, kind="mono", color=INK, alpha=a,
align="center", reveal=clamp01((t - i * .08) / .4))
for i in range(2):
a0 = xs[i] + measure(words[i], "mono", 27) / 2 + 14
a1 = xs[i + 1] - measure(words[i + 1], "mono", 27) / 2 - 14
arrow(c, (a0, y), (a1, y), color=col, alpha=a,
t=clamp01((t - .35 - i * .12) / .45), width=1.8, head=9,
gap=(0, 3), glow=0.25)
draw_text(c, "length", (xs[0] + xs[1]) / 2, y - 26, size=20, kind="mono",
color=col, alpha=a * smooth((t - .65) / .35), align="center")
draw_text(c, "isEven", (xs[1] + xs[2]) / 2, y - 26, size=20, kind="mono",
color=col, alpha=a * smooth((t - .75) / .35), align="center")
def _recipe(c, x, y, col, a, t):
words = ["flour", "dough", "loaf"]
labs = ["knead", "bake"]
xs = [x - 150, x, x + 150]
for i, (w, xx) in enumerate(zip(words, xs)):
node(c, xx, y + 10, r=6.5, color=INK, alpha=a,
reveal=clamp01((t - i * .06) / .35), label=w, label_size=24,
label_dy=-24)
for i in range(2):
arrow(c, (xs[i], y + 10), (xs[i + 1], y + 10), color=col, alpha=a,
t=clamp01((t - .3 - i * .12) / .45), width=1.8, head=9,
gap=(12, 15), label=labs[i], label_size=21, label_off=24, glow=0.25)
DRAW = [_sets, _numbers, _places, _types, _recipe]
def render(ctx, size):
fr = stage(ctx, size, dust_alpha=0.7)
# each card arrives on the sentence that describes it
starts = [ctx.slots["e2"].start + 0.9, ctx.slots["e3"].start + 1.0,
ctx.slots["e4"].start + 0.5, ctx.slots["e4"].start + 3.2,
ctx.slots["e4"].start + 6.0]
ts = [clamp01((ctx.t - s) / 1.9) for s in starts]
chorus = smooth((ctx.since("e5") - 0.8) / 1.6)
def draw(c):
for i, ((x, y), (ta, tb), col, dr, tt) in enumerate(
zip(SLOTS, TITLES, HUES, DRAW, ts)):
if tt <= 0.005:
continue
a = 0.55 + 0.45 * chorus
card(c, x, y, CW, CH, alpha=a, t=tt, title=f"{ta} {tb}",
title_color=mix(INK_DIM, col, 0.35 + 0.5 * chorus))
glow_a = a * (0.85 + 0.15 * chorus)
dr(c, x, y + 18, mix(col, INK, 0.10), glow_a, clamp01((tt - .18) / .82))
a5 = smooth((ctx.since("e5") - 1.4) / 1.8) * ctx.fade_out(0.9)
if a5 > 0.01:
caption(c, "every theorem about categories is a theorem "
"about all of them at once", y=H - 92, size=36, color=INK,
alpha=a5, reveal=clamp01((ctx.since("e5") - 1.6) / 2.2))
fr.vector(draw)
return fr.finish(grain=0.009, seed=ctx.frame)
PY
cat > src/catfilm/scenes/monoid.py <<'PY'
"""One object, three arrows: a category made entirely of words."""
from __future__ import annotations
import math
import numpy as np
from ._common import * # noqa: F403
from ..config import GENERATORS, H, INK, INK_DIM, W
from ..ifs import LETTERS
SX, SY = CX, CY - 30
@lru_cache(maxsize=1)
def _cloud(n=64, seed=11):
"""Words scattered in a ring — the arrows of this category, all of them."""
rng = np.random.default_rng(seed)
out = []
for i in range(n):
L = int(rng.integers(2, 7))
w = "".join(rng.choice(list(LETTERS), L))
ang = rng.uniform(0, 2 * math.pi)
rad = 250 + 340 * math.sqrt(rng.uniform(0.05, 1.0))
x = SX + math.cos(ang) * rad * 1.42
y = SY + math.sin(ang) * rad * 0.86
out.append((w, x, y, rng.uniform(0, 1), 22 + 16 * rng.uniform(0, 1) ** 2))
return tuple(out)
def _word(c, w, x, y, size, alpha, drift=0.0):
"""A word, each letter in the colour of the arrow it names."""
tot = sum(measure(ch, "serif", size) for ch in w) + 0.03 * size * (len(w) - 1)
xx = x - tot / 2
for ch in w:
col = GENERATORS[LETTERS.index(ch)]
draw_text(c, ch, xx, y + drift, size=size, color=col, alpha=alpha)
xx += measure(ch, "serif", size) + 0.03 * size
def render(ctx, size):
fr = stage(ctx, size, dust_alpha=0.6)
build = clamp01((ctx.since("m2") - 0.9) / 2.6) # the three loops arrive
escape = pulse(ctx.t, ctx.slots["m3"].start + 0.6,
ctx.slots["m3"].start + 2.6, 0.5) # the failed way out
cloud_t = clamp01((ctx.since("m4") - 0.6) / 7.0)
thicken = smooth((ctx.since("m5") - 0.4) / 2.4)
def draw(c):
# the mark itself
node_only = clamp01(ctx.since("m1") / 1.2)
sigil(c, SX, SY, r=112, node_r=19, label_size=44, alpha=1.0,
t=build if build > 0 else 0.0, label_off=1.26, width=2.8)
if build <= 0.02:
node(c, SX, SY, r=15, color=INK, reveal=node_only)
# "there is nowhere to go" — an arrow leaves and is turned back
if escape > 0.01:
ang = -0.30
p0 = (SX + 150 * math.cos(ang), SY + 150 * math.sin(ang))
p1 = (SX + 470 * math.cos(ang), SY + 470 * math.sin(ang))
arrow(c, p0, p1, color=INK_DIM, alpha=escape * 0.55, t=1.0,
width=2.0, dash=(9.0, 11.0), head=12, glow=0.0)
draw_text(c, "?", p1[0] + 42, p1[1] + 12, size=40, color=INK_DIM,
alpha=escape * 0.6, align="center")
# every arrow this category has
for i, (w, x, y, ph, sz) in enumerate(_cloud()):
tt = clamp01((cloud_t - (i / len(_cloud())) * 0.85) / 0.15)
a = tt * (0.30 + 0.55 * thicken) * (0.55 + 0.45 * ph)
if a > 0.008:
_word(c, w, x, y, sz, a, drift=math.sin(ctx.t * 0.35 + ph * 6.3) * 5)
# the named examples, close in and legible
for i, (w, dx, dy) in enumerate((("ab", -330, -195), ("cca", 330, -185),
("bbbb", -300, 230), ("acab", 320, 235))):
t0 = ctx.slots["m4"].start + 1.6 + i * 1.35
a = pulse(ctx.t, t0, t0 + 3.4, 0.6) * 0.95
if a > 0.01:
_word(c, w, SX + dx, SY + dy, 52, a)
a5 = smooth((ctx.since("m5") - 1.2) / 1.6) * ctx.fade_out(0.9)
if a5 > 0.01:
caption(c, "no shape · no picture · a bag of words", y=H - 96,
size=34, color=INK_DIM, alpha=a5, tracking=0.10,
reveal=clamp01((ctx.since("m5") - 1.4) / 1.6))
fr.vector(draw)
return fr.finish(grain=0.009, seed=ctx.frame)
PY
uv run catfilm contact examples -n 8 && uv run catfilm contact monoid -n 8
04:01:12
Read ← ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code/out/gallery/sheet_examples.png
04:01:12 · 🖼 image returned to Claude — [Image: original 2560x720, displayed at 2000x563. Multiply coordinates by 1.28 to map to original image.]
04:01:21
Read ← ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code/out/gallery/sheet_monoid.png
04:01:21 · 🖼 image returned to Claude — [Image: original 2560x720, displayed at 2000x563. Multiply coordinates by 1.28 to map to original image.]
04:01:48
Bash — Scale up examples cards and monoid sigil
python3 - <<'PY'
p='src/catfilm/scenes/examples.py'
s=open(p).read()
s=s.replace("CW, CH = 520, 292","CW, CH = 600, 348")
s=s.replace("ROW1, ROW2 = CY - 168, CY + 190","ROW1, ROW2 = CY - 196, CY + 200")
s=s.replace("SLOTS = [(CX - 580, ROW1), (CX, ROW1), (CX + 580, ROW1),\n (CX - 300, ROW2), (CX + 300, ROW2)]",
"SLOTS = [(CX - 640, ROW1), (CX, ROW1), (CX + 640, ROW1),\n (CX - 330, ROW2), (CX + 330, ROW2)]")
s=s.replace("a = 0.55 + 0.45 * chorus","a = 0.78 + 0.22 * chorus")
s=s.replace("title_color=mix(INK_DIM, col, 0.35 + 0.5 * chorus))","title_color=mix(INK_DIM, col, 0.40 + 0.5 * chorus),\n title_size=25)")
# scale up the card interiors
for old,new in [("rng.uniform(-46, 46)","rng.uniform(-54, 54)"),("rng.uniform(-44, 44)","rng.uniform(-52, 52)"),
("rng.uniform(-40, 40)","rng.uniform(-48, 48)"),("rng.uniform(-38, 38)","rng.uniform(-46, 46)"),
("lx, rx = x - 116, x + 116","lx, rx = x - 132, x + 132"),
("((lx, 62), (rx, 56))","((lx, 72), (rx, 66))"),("y - 58, cx_ + w_, y + 58","y - 68, cx_ + w_, y + 68"),
("c.drawCircle(p[0], p[1], 4.2","c.drawCircle(p[0], p[1], 5.0"),
("(i - 1.5) * 96","(i - 1.5) * 110"),("(i - 2.5) * 96","(i - 2.5) * 110"),
('r=7, color=INK','r=8, color=INK'),('label_size=27, label_dy=-26','label_size=30, label_dy=-30'),
('draw_text(c, "x ≤ y", x, y + 62, size=25','draw_text(c, "x ≤ y", x, y + 74, size=28'),
("(x - 118, y - 30)","(x - 136, y - 36)"),("(x + 10, y - 56)","(x + 12, y - 64)"),
("(x + 112, y + 18)","(x + 130, y + 22)"),("(x - 44, y + 52)","(x - 50, y + 60)"),
("r=6.5, color=INK, alpha=a, reveal=clamp01((t - i * .05) / .35))","r=7.5, color=INK, alpha=a, reveal=clamp01((t - i * .05) / .35))"),
("xs = [x - 148, x + 4, x + 140]","xs = [x - 168, x + 6, x + 160]"),
('size=27, kind="mono", color=INK','size=30, kind="mono", color=INK'),
('measure(words[i], "mono", 27)','measure(words[i], "mono", 30)'),
('measure(words[i + 1], "mono", 27)','measure(words[i + 1], "mono", 30)'),
('size=20, kind="mono",\n color=col','size=22, kind="mono",\n color=col'),
("xs = [x - 150, x, x + 150]","xs = [x - 172, x, x + 172]"),
("r=6.5, color=INK, alpha=a,\n reveal","r=7.5, color=INK, alpha=a,\n reveal"),
("label_size=24,\n label_dy=-24","label_size=27,\n label_dy=-27"),
("label_size=21, label_off=24","label_size=23, label_off=26"),
("width=1.8, head=9","width=2.0, head=10"),("width=1.7, head=9","width=1.9, head=10")]:
s=s.replace(old,new)
open(p,'w').write(s)
p='src/catfilm/scenes/monoid.py'
s=open(p).read()
s=s.replace("SX, SY = CX, CY - 30","SX, SY = CX, CY - 6")
s=s.replace("rad = 250 + 340 * math.sqrt(rng.uniform(0.05, 1.0))","rad = 265 + 330 * math.sqrt(rng.uniform(0.05, 1.0))")
s=s.replace("y = SY + math.sin(ang) * rad * 0.86","y = SY + math.sin(ang) * rad * 0.80")
s=s.replace("a = tt * (0.30 + 0.55 * thicken) * (0.55 + 0.45 * ph)","a = tt * (0.34 + 0.60 * thicken) * (0.55 + 0.45 * ph)")
s=s.replace("sigil(c, SX, SY, r=112, node_r=19, label_size=44","sigil(c, SX, SY, r=132, node_r=22, label_size=50")
open(p,'w').write(s); print("ok")
PY
uv run catfilm still 2:07 -o out/gallery/s_ex.png && uv run catfilm still 2:53 -o out/gallery/s_mon.png && echo ok
04:01:56
Read ← ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code/out/gallery/s_ex.png
04:02:12
Read ← ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code/out/gallery/s_mon.png
04:02:39Fixing the sets card, then writing the functor and the centerpiece bloom scene:
04:03:11
Bash — Write functor scene
python3 - <<'PY'
p='src/catfilm/scenes/examples.py'
s=open(p).read()
s=s.replace('''def _sets(c, x, y, col, a, t):
rng = np.random.default_rng(4)
lx, rx = x - 132, x + 132
pts_l = [(lx + rng.uniform(-54, 54), y + rng.uniform(-52, 52)) for _ in range(5)]
pts_r = [(rx + rng.uniform(-48, 48), y + rng.uniform(-46, 46)) for _ in range(3)]
for cx_, w_ in ((lx, 72), (rx, 66)):
c.drawOval(skia.Rect.MakeLTRB(cx_ - w_, y - 68, cx_ + w_, y + 68),
paint(RULE, a * 0.85 * smooth(t), width=1.3))''',
'''def _blob_pts(cx, cy, rx, ry, n, rng):
"""Points that actually sit inside the blob that contains them."""
out = []
for _ in range(n):
while True:
u, v = rng.uniform(-1, 1), rng.uniform(-1, 1)
if u * u + v * v <= 0.62:
out.append((cx + u * rx, cy + v * ry))
break
return out
def _sets(c, x, y, col, a, t):
rng = np.random.default_rng(4)
lx, rx = x - 126, x + 126
pts_l = _blob_pts(lx, y, 66, 62, 5, rng)
pts_r = _blob_pts(rx, y, 60, 58, 3, rng)
for cx_, w_, h_ in ((lx, 76, 72), (rx, 70, 68)):
c.drawOval(skia.Rect.MakeLTRB(cx_ - w_, y - h_, cx_ + w_, y + h_),
paint(RULE, a * 0.85 * smooth(t), width=1.3))''')
s=s.replace("CW, CH = 600, 348","CW, CH = 600, 348\nCH2 = 268")
s=s.replace("card(c, x, y, CW, CH,","card(c, x, y, CW, CH if i < 3 else CH2,")
s=s.replace("dr(c, x, y + 18,","dr(c, x, y + (18 if i < 3 else 6),")
open(p,'w').write(s); print("ok")
PY
cat > src/catfilm/scenes/functor.py <<'PY'
"""A functor: a translation between worlds that keeps the shape."""
from __future__ import annotations
import math
import skia
from ._common import * # noqa: F403
from ..config import (A_AMBER, A_BLUE, A_MINT, A_ROSE, A_VIOLET, H, INK,
INK_DIM, RULE, W)
LX, RX, PY_ = CX - 470, CX + 470, CY - 96
# the same abstract triangle, sitting differently in each world
C_POS = {"A": (LX - 175, PY_ - 92), "B": (LX + 175, PY_ - 92), "C": (LX, PY_ + 146)}
D_POS = {"A": (RX - 205, PY_ + 62), "B": (RX + 40, PY_ - 128), "C": (RX + 200, PY_ + 118)}
def render(ctx, size):
fr = stage(ctx, size, dust_alpha=0.65)
worlds = clamp01(ctx.since("f1") / 1.4)
d_on = clamp01((ctx.since("f1") - 2.2) / 1.4)
trans = clamp01((ctx.since("f2") - 0.4) / 2.4) # object correspondences
law = clamp01((ctx.since("f3") - 0.1) / 1.6)
# f4: "translate then combine — or combine then translate"
s4 = ctx.slots["f4"]
route_a = pulse(ctx.t, s4.start + 0.1, s4.start + 2.6, 0.55)
route_b = pulse(ctx.t, s4.start + 2.5, s4.start + 5.2, 0.55)
agree = smooth((ctx.t - (s4.start + 4.8)) / 1.2)
leave = smoother(clamp01((ctx.since("f6") - 0.9) / 1.8)) # hand off to the bloom
def draw(c):
gone = 1 - leave
# --- the two worlds -------------------------------------------------
for (pos, on, name, hue) in ((C_POS, worlds, "C", INK),
(D_POS, d_on, "D", INK)):
a = on * gone
if a <= 0.01:
continue
cx_ = LX if name == "C" else RX
draw_text(c, name, cx_, PY_ - 268, size=52, color=INK_DIM, alpha=a * 0.9,
align="center", reveal=on)
# arrows inside C
for (s_, d_, lab, col, bend) in (("A", "B", "f", A_BLUE, 0.0),
("B", "C", "g", A_AMBER, 0.0),
("A", "C", "g ∘ f", A_MINT, 0.22)):
hl = route_b if lab == "g ∘ f" else 0.0
arrow(c, C_POS[s_], C_POS[d_], bend=bend, color=col,
alpha=worlds * gone, t=clamp01((worlds - 0.25) / 0.6),
label=lab, label_size=32, label_off=-30 if bend == 0 else 34,
width=2.6 + 1.8 * hl, glow=0.30 + 0.5 * hl)
for i, (k, p) in enumerate(C_POS.items()):
node(c, *p, r=13, color=INK, alpha=gone,
reveal=clamp01((worlds - i * 0.06) / 0.5), label=k,
label_size=34, label_dy=-34)
# arrows inside D — the images
for (s_, d_, lab, col, bend) in (("A", "B", "F(f)", A_BLUE, -0.10),
("B", "C", "F(g)", A_AMBER, 0.14),
("A", "C", "F(g) ∘ F(f)", A_MINT, 0.30)):
hl = route_a if lab.startswith("F(g) ∘") else (
route_b if lab in ("F(f)", "F(g)") else 0.0)
arrow(c, D_POS[s_], D_POS[d_], bend=bend, color=col,
alpha=d_on * gone, t=clamp01((d_on - 0.25) / 0.6),
label=lab, label_size=28,
label_off=-30 if lab != "F(g) ∘ F(f)" else 40,
width=2.6 + 1.8 * hl, glow=0.30 + 0.5 * hl)
for i, (k, p) in enumerate(D_POS.items()):
node(c, *p, r=13, color=INK, alpha=gone,
reveal=clamp01((d_on - i * 0.06) / 0.5), label=f"F({k})",
label_size=30, label_dy=-34)
# --- the translation itself ----------------------------------------
if trans > 0.01:
for i, k in enumerate("ABC"):
tt = clamp01((trans - i * 0.13) / 0.5)
p, q = C_POS[k], D_POS[k]
c.drawLine(p[0], p[1], p[0] + (q[0] - p[0]) * tt,
p[1] + (q[1] - p[1]) * tt,
paint(INK_DIM, 0.24 * gone * trans, width=1.3))
draw_text(c, "F", CX, PY_ - 200, size=64, color=INK,
alpha=trans * gone * 0.95, align="center", glow=0.3)
arrow(c, (CX - 92, PY_ - 214), (CX + 92, PY_ - 214), color=INK_DIM,
alpha=trans * gone * 0.75, t=trans, width=2.0, head=12,
gap=(0, 0), glow=0.2)
# --- the one law ----------------------------------------------------
if law > 0.01:
col = mix(INK, A_MINT, agree * 0.75)
formula(c, "F ( g ∘ f ) = F ( g ) ∘ F ( f )", CX, H - 128,
size=62, color=col, alpha=law * gone, reveal=law, glow=0.28)
draw_text(c, "combine, then translate "
"translate, then combine",
CX, H - 74, size=23, color=INK_DIM,
alpha=law * gone * 0.75, align="center", tracking=0.06)
# --- hand off to the bag of words ----------------------------------
if leave > 0.01:
sigil(c, CX, CY - 40, r=118 * (0.6 + 0.4 * leave), node_r=20,
label_size=46, alpha=leave, t=leave)
fr.vector(draw)
return fr.finish(grain=0.009, seed=ctx.frame)
PY
uv run catfilm contact functor -n 8
04:03:18
Read ← ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code/out/gallery/sheet_functor.png
04:03:18 · 🖼 image returned to Claude — [Image: original 2560x720, displayed at 2000x563. Multiply coordinates by 1.28 to map to original image.]
04:03:57Small functor tweaks, then the centerpiece — where the words become a picture:
04:04:45
Bash — Write the bloom centerpiece scene
python3 - <<'PY'
p='src/catfilm/scenes/functor.py'
s=open(p).read()
s=s.replace("LX, RX, PY_ = CX - 470, CX + 470, CY - 96","LX, RX, PY_ = CX - 470, CX + 470, CY - 56")
s=s.replace('paint(INK_DIM, 0.24 * gone * trans, width=1.3))','paint(INK_DIM, 0.34 * gone * trans, width=1.4))')
s=s.replace('draw_text(c, "F", CX, PY_ - 200, size=64,','draw_text(c, "F", CX, PY_ - 218, size=78,')
s=s.replace('arrow(c, (CX - 92, PY_ - 214), (CX + 92, PY_ - 214), color=INK_DIM,\n alpha=trans * gone * 0.75, t=trans, width=2.0, head=12,\n gap=(0, 0), glow=0.2)',
'arrow(c, (CX - 118, PY_ - 236), (CX + 118, PY_ - 236), color=INK_DIM,\n alpha=trans * gone * 0.8, t=trans, width=2.2, head=14,\n gap=(0, 0), glow=0.2)')
s=s.replace('size=52, color=INK_DIM, alpha=a * 0.9,\n align="center", reveal=on)','size=50, color=INK_DIM, alpha=a * 0.85,\n align="center", reveal=on)')
s=s.replace('draw_text(c, name, cx_, PY_ - 268,','draw_text(c, name, cx_, PY_ - 300,')
open(p,'w').write(s)
# plane<->screen helper
p='src/catfilm/scenes/_common.py'
s=open(p).read()
s += '''
# ---------------------------------------------------------------------------
# The plane: one mapping shared by the diagrams and the glow, so the abstract
# triangles and the attractor they converge to are drawn in the same space.
# ---------------------------------------------------------------------------
def plane_center(xs: float, ys: float, S: float) -> tuple[float, float]:
"""Glow-renderer centre that puts plane-origin at screen point (xs, ys)."""
return ((W / 2 - xs) / S, (ys - H / 2) / S)
def to_screen(pts, xs: float, ys: float, S: float):
p = np.asarray(pts, dtype=np.float64)
return np.column_stack([xs + p[:, 0] * S, ys - p[:, 1] * S])
def word_color(word, memory: float = 0.30):
"""The colour the chaos game would give a point produced by this word."""
col = np.array([0.5, 0.5, 0.5], dtype=np.float64)
for ch in word: # applied left to right, last one outermost
col = col * memory + np.array(GENERATORS[LETTERS.index(ch)]) / 255.0 * (1 - memory)
return tuple(int(round(v * 255)) for v in np.clip(col, 0, 1))
def dot_grid(c, xs, ys, S, *, alpha=1.0, n=9, span=0.55, r=1.7, color=RULE):
"""A whisper of a coordinate plane."""
if alpha <= 0:
return
for i in range(n):
for j in range(n):
x = -span + 2 * span * i / (n - 1)
y = -span + 2 * span * j / (n - 1)
c.drawCircle(xs + x * S, ys - y * S, r, paint(color, alpha))
'''
open(p,'w').write(s); print("ok")
PY
cat > src/catfilm/scenes/bloom.py <<'PY'
"""The centrepiece: three matrices, and a picture nobody drew.
Everything on screen here is the image of the free monoid on {a, b, c} under
one functor into the affine maps of the plane. The triangles at each depth are
the images of *all words of that length*; the glowing limit is what the words
converge to.
"""
from __future__ import annotations
import math
import numpy as np
import skia
from ._common import * # noqa: F403
from ..config import (A_AMBER, A_BLUE, A_MINT, A_VIOLET, GENERATORS, H, INK,
INK_DIM, RULE, W)
from ..core import words
from ..ifs import LETTERS, SYSTEMS, UNIT_TRIANGLE, chaos_game
from ..render.glow import render_points
SYS = SYSTEMS["sierpinski"]
FUN = SYS.functor()
SMALL = (CX + 352, CY - 26, 380.0) # plane, while the maths is on the left
BIG = (CX, CY - 24, 880.0) # plane, once it takes the frame
SIGIL_X, SIGIL_Y = CX - 520, CY - 40
@lru_cache(maxsize=8)
def _tris(depth: int):
"""Every word of length ``depth``, as a triangle and the colour of its word."""
out = []
for w in words(LETTERS, depth):
arr = SYS.functor()(SYSTEMS["sierpinski"].functor().source.source_of(w, "•"))
out.append((arr.apply(UNIT_TRIANGLE), word_color(w)))
return tuple(out)
def _plane(ctx):
k = smoother(clamp01((ctx.since("b6") - 0.9) / 2.4))
return tuple(a + (b - a) * k for a, b in zip(SMALL, BIG)) + (k,)
def render(ctx, size):
fr = stage(ctx, size, dust_alpha=0.55)
xs, ys, S, opened = _plane(ctx)
t_ladder = ctx.t - (ctx.slots["b6"].speech_end + 0.25)
t_full = ctx.slots["b8"].start - 0.55 # the bloom is complete by here
bloom_t = clamp01((ctx.t - (t_full - 2.1)) / 2.1)
# --- the glowing limit --------------------------------------------------
if bloom_t > 0.005:
xy, rgb = points("sierpinski", 1_800_000)
img = render_points(xy, rgb, size,
plane_center(xs * fr.k, ys * fr.k, S * fr.k),
S * fr.k, exposure=1.1 + 2.2 * bloom_t,
bloom_strength=0.66, ss=2)
fr.add(img, ease_out(bloom_t, 2.0))
def draw(c):
left = 1.0 - opened # the workings fade as it opens
# --- the plane itself ----------------------------------------------
grid_a = 0.34 * clamp01(ctx.since("b1") / 1.6) * (1 - bloom_t * 0.85)
dot_grid(c, xs, ys, S, alpha=grid_a, n=9, span=0.62, r=1.8)
# --- the source: one object, three arrows --------------------------
if left > 0.01:
sigil(c, SIGIL_X, SIGIL_Y, r=96, node_r=17, label_size=38,
alpha=left, t=clamp01(ctx.since("b1") / 1.2), label_off=1.28)
a_f = clamp01((ctx.since("b1") - 1.8) / 1.2) * left
arrow(c, (SIGIL_X + 168, SIGIL_Y), (xs - S * 0.72, ys),
color=INK_DIM, alpha=a_f * 0.85, t=a_f, width=2.2, head=13,
gap=(0, 8), glow=0.18)
draw_text(c, "F", (SIGIL_X + 168 + xs - S * 0.72) / 2, ys - 26,
size=44, color=INK, alpha=a_f * 0.9, align="center")
draw_text(c, "the plane", xs, ys + S * 0.78, size=27, color=INK_DIM,
alpha=a_f * 0.8 * (1 - opened), align="center", tracking=0.14)
# --- the three choices ---------------------------------------------
a_m = clamp01((ctx.since("b3") - 0.2) / 2.2) * left
if a_m > 0.01:
for i, (col, lab) in enumerate(zip(GENERATORS, LETTERS)):
tt = clamp01((a_m - i * 0.18) / 0.5)
matrix_block(c, SYS.maps[i].mat[:2], SIGIL_X + 8, CY + 150 + i * 96,
size=25, color=col, alpha=a_m, label=f"{lab} ↦",
label_color=col, reveal=tt)
# --- the images of the unit triangle, one per letter ---------------
seed_t = clamp01((ctx.since("b3") - 0.4) / 1.2)
kids_t = clamp01((ctx.since("b3") - 1.6) / 2.4)
if seed_t > 0.01 and t_ladder < -0.2:
pts = to_screen(UNIT_TRIANGLE, xs, ys, S)
polyline(c, pts, color=INK, alpha=0.55 * (1 - kids_t * 0.5),
width=2.0, t=seed_t, close=True, glow=0.25)
if kids_t > 0.01 and t_ladder < -0.2:
for i, (tri, col) in enumerate(_tris(1)):
tt = clamp01((kids_t - i * 0.15) / 0.5)
polyline(c, to_screen(tri, xs, ys, S), color=col, alpha=0.95,
width=2.2, t=tt, close=True, glow=0.35)
# --- one word, walked: a then b ------------------------------------
s5 = ctx.slots["b5"]
w_t = clamp01((ctx.t - (s5.start + 1.2)) / 4.2)
if 0.005 < w_t < 0.999 and t_ladder < -0.2:
step = w_t * 2.0
k0 = clamp01(step)
k1 = clamp01(step - 1.0)
F = SYS.functor()
M = SYS.source_maps if False else SYS.maps
base = UNIT_TRIANGLE
cur = base * (1 - k0) + M[0].apply(base) * k0
cur = cur * (1 - k1) + M[1].apply(cur) * k1
col = mix(GENERATORS[0], GENERATORS[1], k1)
polyline(c, to_screen(cur, xs, ys, S), color=col, alpha=0.98,
width=2.6, close=True, glow=0.45)
_w = "ab"
draw_text(c, "a" if k1 < 0.02 else "ab", xs, ys - S * 0.72,
size=50, color=col, alpha=0.95, align="center")
# --- the ladder: every word of length 1, 2, 3, … -------------------
if -0.2 < t_ladder:
steps = [(0.00, 1), (0.52, 2), (0.98, 3), (1.38, 4), (1.74, 5), (2.06, 6)]
for t0, d in steps:
a = pulse(t_ladder, t0, t0 + 0.60, 0.26) * (1 - bloom_t)
if a <= 0.01:
continue
wdt = max(0.7, 2.4 - 0.28 * d)
for tri, col in _tris(d):
polyline(c, to_screen(tri, xs, ys, S), color=col,
alpha=a * 0.95, width=wdt, close=True,
glow=0.30 if d < 5 else 0.0)
draw_text(c, f"{3 ** d} words", CX, H - 96, size=30,
color=INK_DIM, alpha=a * 0.8, align="center",
tracking=0.12)
# --- the caption after the reveal ----------------------------------
a8 = smooth((ctx.since("b8") - 0.2) / 1.0)
if a8 > 0.01:
fade = min(1.0, ctx.fade_out(1.2))
draw_text(c, "nobody drew this", CX, 128, size=30, color=INK_DIM,
alpha=a8 * 0.85 * fade * (1 - clamp01(ctx.since("b10") / 2.0)),
align="center", tracking=0.24,
reveal=clamp01(ctx.since("b8") / 1.2))
a10 = smooth((ctx.since("b10") - 1.0) / 1.6) * fade
if a10 > 0.01:
letter_legend(c, CX, H - 92, alpha=a10, reveal=a10, gap=132,
size=34, dot=8.5,
note="colour is the last letter of the word")
fr.vector(draw)
return fr.finish(grain=0.010, seed=ctx.frame)
PY
uv run catfilm contact bloom -n 12 2>&1 | tail -3
04:04:52
Read ← ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code/out/gallery/sheet_bloom.png
04:04:52 · 🖼 image returned to Claude — [Image: original 2560x1080, displayed at 2000x844. Multiply coordinates by 1.28 to map to original image.]
04:05:23The plane→glow mapping breaks at non-native resolutions. Fixing:
04:05:32
Bash — Fix plane mapping for arbitrary resolutions
python3 - <<'PY'
p='src/catfilm/scenes/_common.py'
s=open(p).read()
s=s.replace('''def plane_center(xs: float, ys: float, S: float) -> tuple[float, float]:
"""Glow-renderer centre that puts plane-origin at screen point (xs, ys)."""
return ((W / 2 - xs) / S, (ys - H / 2) / S)''',
'''def plane_center(xs: float, ys: float, S: float, size) -> tuple[float, float]:
"""Glow-renderer centre that puts the plane origin at design point (xs, ys).
``size`` is the device resolution; the design space is always 1920x1080, so
a half-size preview and the final render frame the same picture.
"""
k = size[0] / W
return ((size[0] / 2 - xs * k) / (S * k), (ys * k - size[1] / 2) / (S * k))''')
open(p,'w').write(s)
p='src/catfilm/scenes/bloom.py'
s=open(p).read()
s=s.replace(''' img = render_points(xy, rgb, size,
plane_center(xs * fr.k, ys * fr.k, S * fr.k),
S * fr.k, exposure=1.1 + 2.2 * bloom_t,
bloom_strength=0.66, ss=2)''',
''' img = render_points(xy, rgb, size, plane_center(xs, ys, S, size),
S * fr.k, exposure=1.1 + 2.2 * bloom_t,
bloom_strength=0.66, ss=2)''')
# tidy the matrix column: give it room and stop it colliding with the caption
s=s.replace("matrix_block(c, SYS.maps[i].mat[:2], SIGIL_X + 8, CY + 150 + i * 96,\n size=25,","matrix_block(c, SYS.maps[i].mat[:2], SIGIL_X + 26, CY + 128 + i * 104,\n size=26,")
open(p,'w').write(s); print("ok")
PY
uv run catfilm still 5:20 -o out/gallery/s_bl1.png && uv run catfilm still 4:52 -o out/gallery/s_bl2.png && uv run catfilm still 4:20 -o out/gallery/s_bl3.png && echo ok
04:05:40
Read ← ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code/out/gallery/s_bl1.png
04:05:47
Read ← ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code/out/gallery/s_bl3.png
04:06:20The bloom reveal works. Now let me check whether continuous functor morphs stay contractive — that decides how the variants scene transitions:
04:06:26
Bash — Check contractivity along functor interpolation paths
uv run python - <<'PY'
import numpy as np, itertools
from catfilm.ifs import SYSTEMS, blend_systems
keys=list(SYSTEMS)
print("max singular value along linear interpolation paths (must stay < ~0.97):")
bad=[]
for a,b in itertools.permutations(keys,2):
m=0
for t in np.linspace(0,1,41):
s=blend_systems(SYSTEMS[a],SYSTEMS[b],float(t))
m=max(m,max(f.contraction for f in s.maps))
flag = "" if m<0.97 else " <-- DIVERGES"
if m>=0.97: bad.append((a,b,round(m,3)))
print(" bad pairs:", bad if bad else "none")
# a good tour order minimising visual jump
order=["sierpinski","lattice","pinwheel","crown","fold","spiral","frond"]
print("\ntour:", " -> ".join(order))
for a,b in zip(order,order[1:]+order[:1]):
m=max(max(f.contraction for f in blend_systems(SYSTEMS[a],SYSTEMS[b],float(t)).maps) for t in np.linspace(0,1,41))
print(f" {a:11s} -> {b:11s} max contraction {m:.3f}")
PY
04:07:02All morph paths stay contractive — I can use genuine continuous functor morphs. Adding the machinery:
04:07:16
Bash — Add morph and panel helpers, benchmark morph frames
python3 - <<'PY'
p='src/catfilm/render/canvas.py'
s=open(p).read()
s=s.replace(''' def over(self, rgb: np.ndarray, a: np.ndarray):''',
''' def add_at(self, img: np.ndarray, x: int, y: int, alpha: float = 1.0):
"""Additively composite a small image with its top-left at (x, y)."""
if alpha <= 0:
return
h, w = img.shape[:2]
x0, y0 = max(0, x), max(0, y)
x1, y1 = min(self.w, x + w), min(self.h, y + h)
if x1 <= x0 or y1 <= y0:
return
self.buf[y0:y1, x0:x1] += img[y0 - y:y1 - y, x0 - x:x1 - x] * float(alpha)
def over(self, rgb: np.ndarray, a: np.ndarray):''')
open(p,'w').write(s)
p='src/catfilm/scenes/_common.py'
s=open(p).read()
s += '''
# ---------------------------------------------------------------------------
# Morphing between functors.
#
# Every intermediate is a genuine functor — three matrices are three matrices —
# so the whole slide is a continuous path through the space of translations,
# and each frame really is a picture of the same free monoid.
# ---------------------------------------------------------------------------
from ..ifs import blend_systems # noqa: E402
@lru_cache(maxsize=32)
def _fit(key: str, w: int, h: int, margin: float):
xy, _ = points(key, 800_000)
return fit_scale(xy, (w, h), margin)
def morph_state(k0: str, k1: str, t: float, size, margin=0.80):
"""The blended system, plus a framing that eases between the two ends."""
t = clamp01(t)
sys_ = blend_systems(SYSTEMS[k0], SYSTEMS[k1], t, f"{k0}→{k1}")
(c0, s0), (c1, s1) = _fit(k0, *size, margin), _fit(k1, *size, margin)
e = smoother(t)
ctr = (c0[0] + (c1[0] - c0[0]) * e, c0[1] + (c1[1] - c0[1]) * e)
scl = s0 + (s1 - s0) * e
return sys_, ctr, scl
def morph_image(k0: str, k1: str, t: float, size, *, n=760_000, margin=0.80,
exposure=2.1, bloom=0.62, seed=7):
"""Render one frame of a morph. A fixed seed keeps the motes coherent."""
sys_, ctr, scl = morph_state(k0, k1, t, size, margin)
xy, rgb = chaos_game(sys_, n, seed=seed)
return render_points(xy, rgb, size, ctr, scl, exposure=exposure,
bloom_strength=bloom)
def panel(xy, rgb, size, *, transform=None, margin=0.78, exposure=2.0,
bloom=0.55, center=None, scale=None):
"""A small glowing render, for putting pictures at the corners of a square."""
p = transform.apply(xy) if transform is not None else xy
if center is None or scale is None:
center, scale = fit_scale(p, size, margin)
return render_points(p.astype(np.float32), rgb, size, center, scale,
exposure=exposure, bloom_strength=bloom, ss=2)
'''
open(p,'w').write(s)
p='src/catfilm/scenes/bloom.py'
s=open(p).read()
s=s.replace("BIG = (CX, CY - 24, 880.0)","BIG = (CX, CY + 18, 862.0)")
s=s.replace('draw_text(c, "nobody drew this", CX, 128,','draw_text(c, "nobody drew this", CX, 92,')
s=s.replace('letter_legend(c, CX, H - 92,','letter_legend(c, CX, H - 68,')
open(p,'w').write(s); print("ok")
PY
uv run python -c "
import numpy as np, time
from catfilm.scenes._common import morph_image
t=time.time(); img=morph_image('sierpinski','frond',0.5,(1920,1080)); print(f'morph frame {time.time()-t:.2f}s', img.shape)
t=time.time(); img=morph_image('sierpinski','frond',0.6,(1920,1080)); print(f'morph frame {time.time()-t:.2f}s')"
04:07:39Now the remaining scenes — variants, natural transformations, Yoneda, finale, credits:
04:08:38
Bash — Write variants and natural transformation scenes
cat > src/catfilm/scenes/variants.py <<'PY'
"""Keep every word; change only the translation.
The picture slides continuously from one functor to the next. Each frame in
between is itself a functor — three matrices are three matrices — so nothing
here is a dissolve between two images: it is one category, translated a little
differently every thirtieth of a second.
"""
from __future__ import annotations
import math
import numpy as np
from ._common import * # noqa: F403
from ..config import GENERATORS, H, INK, INK_DIM, W
from ..ifs import LETTERS, SYSTEMS
RAIL_X = 196
TOUR = ["sierpinski", "frond", "fold", "spiral"]
def _leg(ctx):
"""Which morph we are in, and how far through it."""
m = [(ctx.slots["v1"].start + 3.4, 2.9),
(ctx.slots["v3"].start - 0.7, 2.5),
(ctx.slots["v4"].start - 0.7, 2.5)]
for i, (t0, d) in enumerate(m):
if ctx.t < t0:
return i, 0.0
if ctx.t < t0 + d:
return i, smoother((ctx.t - t0) / d)
return len(m) - 1, 1.0
def render(ctx, size):
fr = stage(ctx, size, dust_alpha=0.5)
i, u = _leg(ctx)
k0, k1 = TOUR[i], TOUR[i + 1]
img = morph_image(k0, k1, u, size, n=820_000, margin=0.74,
exposure=2.2, bloom=0.62)
fr.add(img, ctx.envelope)
sys_, _, _ = morph_state(k0, k1, u, size, 0.74)
moving = 0.18 < u < 0.86
def draw(c):
a = ctx.envelope
pulse_sig = 1.0 + 0.6 * pulse(ctx.t, ctx.slots["v5"].start + 0.4,
ctx.slots["v5"].start + 4.0, 0.9)
# --- the rail: what is *not* changing ------------------------------
sigil(c, RAIL_X, 268, r=76, node_r=14, label_size=31, alpha=a * 0.95,
t=1.0, label_off=1.28, width=2.2 + 0.7 * (pulse_sig - 1))
draw_text(c, "unchanged", RAIL_X, 404, size=23, color=INK_DIM,
alpha=a * (0.55 + 0.45 * (pulse_sig - 1)), align="center",
tracking=0.22)
hairline(c, 442, RAIL_X - 96, RAIL_X + 96, alpha=a * 0.5)
# --- the rail: what *is* changing ----------------------------------
draw_text(c, "changed", RAIL_X, 512, size=23, color=INK_DIM,
alpha=a * (0.45 + 0.5 * (1 if moving else 0.25)),
align="center", tracking=0.22)
for j, col in enumerate(GENERATORS):
matrix_block(c, sys_.maps[j].mat[:2], RAIL_X + 18, 580 + j * 104,
size=25, color=col, alpha=a * (0.72 + 0.28 * moving),
label=f"{LETTERS[j]} ↦", label_color=col)
# --- what we are looking at ----------------------------------------
name = SYSTEMS[k1 if u > 0.5 else k0]
a_name = a * (1 - pulse(ctx.t, 0, 0, 0)) * (0.85 if not moving else 0.25)
draw_text(c, name.name, CX + 120, H - 108, size=34, color=INK,
alpha=a_name, align="center", tracking=0.10)
draw_text(c, name.subtitle, CX + 120, H - 70, size=24, color=INK_DIM,
alpha=a_name * 0.8, align="center", tracking=0.06)
# --- the point, said plainly ---------------------------------------
a6 = smooth((ctx.since("v6") - 0.6) / 1.4) * ctx.fade_out(1.0)
if a6 > 0.01:
caption(c, "prove it upstairs — where there are no pictures — "
"and it is true in every world downstairs at once",
y=H - 118, size=35, color=INK, alpha=a6, max_w=1180,
reveal=clamp01((ctx.since("v7") - 0.2) / 2.6))
fr.vector(draw)
return fr.finish(grain=0.010, seed=ctx.frame)
PY
cat > src/catfilm/scenes/natural.py <<'PY'
"""Natural transformations — and the square that category theory exists for."""
from __future__ import annotations
import math
import numpy as np
from ._common import * # noqa: F403
from ..config import (A_AMBER, A_BLUE, A_MINT, A_ROSE, A_VIOLET, H, INK,
INK_DIM, RULE, W)
from ..ifs import LETTERS, SYSTEMS, Aff, _mk, naturality
from ..render.glow import fit_scale
# α: one map of the plane — a turn and a lean. Nothing to do with fractals.
ALPHA = _mk(1.06, 0.86, 0.46, 0.34, 0.02, 0.0)
F_SYS = SYSTEMS["sierpinski"]
G_SYS = F_SYS.conjugate(ALPHA, "α · Sierpiński · α⁻¹")
WORD = "c" # the arrow we test the square on
FW = F_SYS.maps[LETTERS.index(WORD)]
GW = G_SYS.maps[LETTERS.index(WORD)]
PW, PH = 470, 330 # corner picture size
@lru_cache(maxsize=1)
def _cloud():
return points("sierpinski", 900_000)
@lru_cache(maxsize=8)
def _corner(kind: str, w: int, h: int):
"""The four pictures of the naturality square, in a shared frame."""
xy, rgb = _cloud()
T = {"tl": None, "tr": FW, "bl": ALPHA,
"br": ALPHA.then(Aff.identity()) if False else None}[kind]
if kind == "br":
pts = ALPHA.apply(FW.apply(xy)) # = G(w) applied to α — same thing
elif T is None:
pts = xy
else:
pts = T.apply(xy)
# every corner is framed by the union of the whole square, so the geometry
# is comparable rather than each panel being auto-zoomed
allp = np.concatenate([xy, ALPHA.apply(xy)])
ctr, scl = fit_scale(allp, (w, h), 0.80)
return render_points(pts.astype(np.float32), rgb, (w, h), ctr, scl,
exposure=2.0, bloom_strength=0.5, ss=2)
def render(ctx, size):
fr = stage(ctx, size, dust_alpha=0.6)
k = fr.k
# ---- act structure -----------------------------------------------------
hist = pulse(ctx.t, ctx.slots["n3"].start - 0.3,
ctx.slots["n5"].speech_end + 0.6, 0.9)
sq_sym = pulse(ctx.t, ctx.slots["n6"].start + 0.6,
ctx.slots["n8"].start - 0.2, 0.9)
show_alpha = pulse(ctx.t, ctx.slots["n9"].start + 0.4,
ctx.slots["n10"].speech_end + 0.5, 0.8)
pics = clamp01((ctx.t - (ctx.slots["n11"].start - 0.6)) / 2.4)
ends = ctx.fade_out(1.0)
# ---- the four pictures -------------------------------------------------
if pics > 0.01:
pw, ph = int(PW * k), int(PH * k)
cells = {"tl": (CX - 300, CY - 122), "tr": (CX + 300, CY - 122),
"bl": (CX - 300, CY + 190), "br": (CX + 300, CY + 190)}
order = ["tl", "tr", "bl", "br"]
for j, name in enumerate(order):
a = clamp01((pics - j * 0.13) / 0.45) * ends
if a <= 0.01:
continue
img = _corner(name, pw, ph)
cx_, cy_ = cells[name]
fr.add_at(img, int((cx_ - PW / 2) * k), int((cy_ - PH / 2) * k), a)
# ---- α, before it is applied to anything ------------------------------
if show_alpha > 0.01 and pics < 0.5:
xy, rgb = _cloud()
u = smoother(clamp01((ctx.since("n10") - 0.8) / 3.0))
M = Aff.of((1 - u) * np.eye(3) + u * ALPHA.mat)
pts = M.apply(xy)
ctr, scl = fit_scale(np.concatenate([xy, ALPHA.apply(xy)]), size, 0.62)
img = render_points(pts.astype(np.float32), rgb, size, ctr, scl,
exposure=2.1, bloom_strength=0.6)
fr.add(img, show_alpha * (1 - pics) * ends)
def draw(c):
# --- the two functors, and the question ----------------------------
a1 = pulse(ctx.t, ctx.tl and ctx.slots["n1"].start,
ctx.slots["n2"].speech_end + 0.4, 0.8)
if a1 > 0.01:
for sx, lab, col in ((CX - 330, "F", A_BLUE), (CX + 330, "G", A_AMBER)):
sigil(c, sx, CY - 40, r=92, node_r=16, label_size=34,
alpha=a1 * 0.9, t=1.0, label_off=1.28)
draw_text(c, lab, sx, CY + 190, size=48, color=col,
alpha=a1 * 0.95, align="center")
draw_text(c, "≟", CX, CY - 18, size=76, kind="math", color=INK_DIM,
alpha=a1 * 0.8, align="center")
draw_text(c, "when are two translations the same translation?",
CX, H - 150, size=35, color=INK, alpha=a1 * 0.95,
align="center", reveal=clamp01(ctx.since("n1") / 2.4))
# --- 1945 -----------------------------------------------------------
if hist > 0.01:
draw_text(c, "1945", CX, 300, size=104, color=INK, alpha=hist,
align="center", tracking=0.22,
reveal=clamp01((ctx.since("n3") - 0.2) / 1.4), glow=0.2)
hairline(c, 350, CX - 190, CX + 190, alpha=hist * 0.6,
t=clamp01((ctx.since("n3") - 1.0) / 1.0))
draw_text(c, "Samuel Eilenberg · Saunders Mac Lane", CX, 412,
size=36, color=INK_DIM, alpha=hist,
align="center", tracking=0.08,
reveal=clamp01((ctx.since("n3") - 1.4) / 1.8))
a4 = smooth((ctx.since("n4") - 0.2) / 1.2) * hist
caption(c, "“this construction works ", y=0, alpha=0) # spacing noop
draw_text(c, "“ … works naturally — without anyone having to choose ”",
CX, 560, size=40, color=INK, alpha=a4, align="center",
reveal=clamp01((ctx.since("n4") - 0.4) / 2.4))
a5 = smooth((ctx.since("n5") - 0.4) / 1.2) * hist
if a5 > 0.01:
for j, line in enumerate((
"to define natural, they had to invent the functor",
"to define the functor, they had to invent the category")):
draw_text(c, line, CX, 700 + j * 56, size=30, color=INK_DIM,
alpha=a5, align="center",
reveal=clamp01((ctx.since("n5") - 1.2 - j * 1.6) / 1.8))
# --- the square, in symbols ----------------------------------------
if sq_sym > 0.01:
hw, hh = 330, 150
corners = ((CX - hw, CY - hh), (CX + hw, CY - hh),
(CX - hw, CY + hh), (CX + hw, CY + hh))
t = clamp01((ctx.since("n6") - 1.0) / 2.6)
com = pulse(ctx.t, ctx.slots["n7"].start + 1.6,
ctx.slots["n7"].speech_end + 1.0, 0.8)
square(c, corners,
(["F(X)", "F(Y)", "G(X)", "G(Y)"], ["F(f)", "α", "α", "G(f)"]),
color=INK, arrow_color=A_BLUE, obj_color=INK,
alpha=sq_sym, t=t, commute=com, label_size=32, obj_size=38)
draw_text(c, "across then down = down then across", CX, H - 138,
size=33, color=mix(INK_DIM, A_MINT, com), alpha=sq_sym * 0.95,
align="center", reveal=clamp01((ctx.since("n7") - 0.4) / 2.0))
# --- α on its own ---------------------------------------------------
if show_alpha > 0.01 and pics < 0.5:
a = show_alpha * (1 - pics)
matrix_block(c, ALPHA.mat[:2], CX, 214, size=30, color=A_ROSE,
alpha=a, label="α ↦", label_color=A_ROSE)
draw_text(c, "one map of the plane — a turn and a lean", CX, H - 132,
size=32, color=INK_DIM, alpha=a * 0.9, align="center",
reveal=clamp01((ctx.since("n9") - 0.6) / 2.2))
# --- the square, in pictures ---------------------------------------
if pics > 0.01:
a = pics * ends
cells = {"tl": (CX - 300, CY - 122), "tr": (CX + 300, CY - 122),
"bl": (CX - 300, CY + 190), "br": (CX + 300, CY + 190)}
E = ((("tl", "tr"), f"F({WORD})", A_BLUE, 0.0, -26),
(("tl", "bl"), "α", A_ROSE, 0.0, -36),
(("tr", "br"), "α", A_ROSE, 0.0, 40),
(("bl", "br"), f"G({WORD})", A_AMBER, 0.0, 34))
for j, ((s_, d_), lab, col, bend, off) in enumerate(E):
p, q = cells[s_], cells[d_]
arrow(c, p, q, bend=bend, color=col, alpha=a * 0.95,
t=clamp01((pics - 0.35 - j * 0.09) / 0.4), width=2.6,
label=lab, label_size=30, label_off=off,
gap=(PW / 2 - 24, PW / 2 - 12) if j in (0, 3)
else (PH / 2 - 10, PH / 2 - 4), glow=0.32)
com = smooth((ctx.since("n12") - 0.8) / 1.2)
commuting_mark(c, CX, CY + 34, r=22, color=A_MINT, alpha=a, t=com)
a13 = smooth((ctx.since("n13") - 0.2) / 1.2) * a
if a13 > 0.01:
draw_text(c, "different in every number · identical in every "
"relationship", CX, H - 66, size=33, color=INK,
alpha=a13, align="center",
reveal=clamp01((ctx.since("n13") - 0.4) / 2.4))
fr.vector(draw)
return fr.finish(grain=0.010, seed=ctx.frame)
PY
uv run catfilm contact variants -n 8 2>&1 | tail -2 && uv run catfilm contact natural -n 12 2>&1 | tail -2
04:08:47
Read ← ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code/out/gallery/sheet_variants.png
04:08:47 · 🖼 image returned to Claude — [Image: original 2560x720, displayed at 2000x563. Multiply coordinates by 1.28 to map to original image.]
04:09:03
Read ← ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code/out/gallery/sheet_natural.png
04:09:03 · 🖼 image returned to Claude — [Image: original 2560x1080, displayed at 2000x844. Multiply coordinates by 1.28 to map to original image.]
04:09:25Good bones. Let me fix the timing of the fold system and enlarge the picture-square:
04:09:49
Bash — Fix variants timing and rework natural scene layout
python3 - <<'PY'
# --- script: give each functor in the tour real screen time -----------------
p='src/catfilm/script.py'
s=open(p).read()
s=s.replace('B("v3", "And again.", hold=2.4),','B("v3", "And again.", hold=5.2),')
s=s.replace('B("v4", "And again.", hold=2.6),','B("v4", "And again.", hold=5.4),')
open(p,'w').write(s)
# --- variants: stop the name colliding with the closing caption ------------
p='src/catfilm/scenes/variants.py'
s=open(p).read()
s=s.replace(''' name = SYSTEMS[k1 if u > 0.5 else k0]
a_name = a * (1 - pulse(ctx.t, 0, 0, 0)) * (0.85 if not moving else 0.25)''',
''' name = SYSTEMS[k1 if u > 0.5 else k0]
clear = 1 - smooth((ctx.since("v6") - 0.2) / 1.2) # make way for the line
a_name = a * clear * (0.9 if not moving else 0.25)''')
s=s.replace("m = [(ctx.slots[\"v1\"].start + 3.4, 2.9),\n (ctx.slots[\"v3\"].start - 0.7, 2.5),\n (ctx.slots[\"v4\"].start - 0.7, 2.5)]",
"m = [(ctx.slots[\"v1\"].start + 3.4, 2.9),\n (ctx.slots[\"v3\"].start - 0.6, 2.3),\n (ctx.slots[\"v4\"].start - 0.6, 2.3)]")
open(p,'w').write(s)
# --- natural: bigger picture square, better opening ------------------------
p='src/catfilm/scenes/natural.py'
s=open(p).read()
s=s.replace("PW, PH = 470, 330 # corner picture size",
"PW, PH = 528, 306 # corner picture size\nCELLS = {\"tl\": (CX - 402, CY - 168), \"tr\": (CX + 402, CY - 168),\n \"bl\": (CX - 402, CY + 202), \"br\": (CX + 402, CY + 202)}")
s=s.replace(''' cells = {"tl": (CX - 300, CY - 122), "tr": (CX + 300, CY - 122),
"bl": (CX - 300, CY + 190), "br": (CX + 300, CY + 190)}
order = ["tl", "tr", "bl", "br"]''',''' order = ["tl", "tr", "bl", "br"]
cells = CELLS''')
s=s.replace(''' cells = {"tl": (CX - 300, CY - 122), "tr": (CX + 300, CY - 122),
"bl": (CX - 300, CY + 190), "br": (CX + 300, CY + 190)}
E = ''',''' cells = CELLS
E = ''')
s=s.replace('commuting_mark(c, CX, CY + 34, r=22,','commuting_mark(c, CX, CY + 20, r=24,')
s=s.replace(''' gap=(PW / 2 - 24, PW / 2 - 12) if j in (0, 3)
else (PH / 2 - 10, PH / 2 - 4), glow=0.32)''',
''' gap=(PW / 2 - 18, PW / 2 - 6) if j in (0, 3)
else (PH / 2 - 6, PH / 2 - 2), glow=0.32)''')
# opening: one source, two translations
s=s.replace(''' if a1 > 0.01:
for sx, lab, col in ((CX - 330, "F", A_BLUE), (CX + 330, "G", A_AMBER)):
sigil(c, sx, CY - 40, r=92, node_r=16, label_size=34,
alpha=a1 * 0.9, t=1.0, label_off=1.28)
draw_text(c, lab, sx, CY + 190, size=48, color=col,
alpha=a1 * 0.95, align="center")
draw_text(c, "≟", CX, CY - 18, size=76, kind="math", color=INK_DIM,
alpha=a1 * 0.8, align="center")''',
''' if a1 > 0.01:
sigil(c, CX - 560, CY, r=96, node_r=17, label_size=36,
alpha=a1 * 0.95, t=1.0, label_off=1.28)
for dy, lab, col in ((-206, "F", A_BLUE), (206, "G", A_AMBER)):
arrow(c, (CX - 430, CY), (CX - 60, CY + dy), color=col,
alpha=a1 * 0.9, t=clamp01((a1 - 0.2) / 0.5), width=2.6,
label=lab, label_size=40, label_off=-30 if dy < 0 else 30,
glow=0.3)
draw_text(c, "≟", CX + 250, CY + 16, size=88, kind="math",
color=INK_DIM, alpha=a1 * 0.75, align="center")''')
s=s.replace(' caption(c, "“this construction works ", y=0, alpha=0) # spacing noop\n','')
s=s.replace("hw, hh = 330, 150","hw, hh = 382, 176")
open(p,'w').write(s); print("ok")
PY
python3 - <<'PY'
# opening thumbnails for n1/n2: the two translations, as pictures
p='src/catfilm/scenes/natural.py'
s=open(p).read()
s=s.replace(''' # ---- α, before it is applied to anything ------------------------------''',
''' # ---- the two translations, as pictures --------------------------------
a1 = pulse(ctx.t, ctx.slots["n1"].start, ctx.slots["n2"].speech_end + 0.4, 0.8)
if a1 > 0.01:
tw, th = int(340 * k), int(300 * k)
for dy, key in ((-206, "sierpinski"), (206, "spiral")):
img = attractor_image(key, tw, th, margin=0.80, n=700_000)
fr.add_at(img, int((CX + 40) * k), int((CY + dy - 150) * k),
a1 * clamp01((a1 - 0.25) / 0.5))
# ---- α, before it is applied to anything ------------------------------''')
s=s.replace(''' a1 = pulse(ctx.t, ctx.tl and ctx.slots["n1"].start,
ctx.slots["n2"].speech_end + 0.4, 0.8)
if a1 > 0.01:''',''' if a1 > 0.01:''')
s=s.replace('draw_text(c, "≟", CX + 250, CY + 16,','draw_text(c, "≟", CX + 620, CY + 16,')
s=s.replace('arrow(c, (CX - 430, CY), (CX - 60, CY + dy),','arrow(c, (CX - 430, CY), (CX - 20, CY + dy),')
open(p,'w').write(s); print("ok2")
PY
uv run catfilm contact natural -n 12 2>&1 | tail -1
04:09:58
Bash — Render key natural-scene stills
uv run catfilm still n11 -o out/gallery/s_nat_sq.png && uv run catfilm still n1 -o out/gallery/s_nat_open.png && uv run python -c "
from PIL import Image; import numpy as np
a=[np.array(Image.open(f'out/gallery/s_nat_{k}.png'))[::2,::2] for k in ('open','sq')]
Image.fromarray(np.concatenate(a,0)).save('out/gallery/cmp.png')"
04:10:06
Read ← ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code/out/gallery/cmp.png
04:11:22
Bash — Write the Yoneda scene
python3 - <<'PY'
p='src/catfilm/scenes/natural.py'
s=open(p).read()
s=s.replace('PW, PH = 528, 306 # corner picture size\nCELLS = {"tl": (CX - 402, CY - 168), "tr": (CX + 402, CY - 168),\n "bl": (CX - 402, CY + 202), "br": (CX + 402, CY + 202)}',
'PW, PH = 556, 322 # corner picture size\nCELLS = {"tl": (CX - 410, CY - 214), "tr": (CX + 410, CY - 214),\n "bl": (CX - 410, CY + 194), "br": (CX + 410, CY + 194)}')
s=s.replace('ctr, scl = fit_scale(allp, (w, h), 0.80)','ctr, scl = fit_scale(allp, (w, h), 0.94)')
s=s.replace(''' gap=(PW / 2 - 18, PW / 2 - 6) if j in (0, 3)
else (PH / 2 - 6, PH / 2 - 2), glow=0.32)''',
''' gap=(PW / 2 - 20, PW / 2 - 8) if j in (0, 3)
else (PH / 2 - 26, PH / 2 - 18), glow=0.32)''')
s=s.replace('commuting_mark(c, CX, CY + 20, r=24,','commuting_mark(c, CX, CY - 10, r=24,')
s=s.replace('draw_text(c, "different in every number · identical in every "\n "relationship", CX, H - 66,','draw_text(c, "different in every number · identical in every "\n "relationship", CX, H - 48,')
open(p,'w').write(s); print("ok")
PY
cat > src/catfilm/scenes/yoneda.py <<'PY'
"""The Yoneda lemma: a thing is what its relationships say it is."""
from __future__ import annotations
import math
import numpy as np
import skia
from ._common import * # noqa: F403
from ..config import (A_AMBER, A_BLUE, A_MINT, A_ROSE, A_VIOLET, GENERATORS, H,
INK, INK_DIM, RULE, W)
from ..render.glow import fit_scale
OX, OY, OS = CX, CY - 18, 700.0 # where the object lives, and how big
N_PROBE = 15
R_PROBE = 452
@lru_cache(maxsize=1)
def _probes():
out = []
for i in range(N_PROBE):
a = -math.pi / 2 + i * 2 * math.pi / N_PROBE
out.append((OX + math.cos(a) * R_PROBE * 1.68,
OY + math.sin(a) * R_PROBE * 0.94, a))
return tuple(out)
@lru_cache(maxsize=2)
def _targets(n=2600, seed=5):
"""A sample of the object, and which probe each incoming arrow comes from."""
xy, _ = points("sierpinski", 900_000)
rng = np.random.default_rng(seed)
idx = rng.choice(len(xy), n, replace=False)
pts = xy[idx]
ctr, scl = fit_scale(xy, (W, H), 0.62)
scr = np.column_stack([OX + (pts[:, 0] - ctr[0]) * scl,
OY - (pts[:, 1] - ctr[1]) * scl])
who = rng.integers(0, N_PROBE, n)
jit = rng.uniform(0, 1, n)
return scr, who, jit
def render(ctx, size):
fr = stage(ctx, size, dust_alpha=0.7)
k = fr.k
say = pulse(ctx.t, ctx.slots["y2"].start - 0.2,
ctx.slots["y4"].end + 0.2, 0.9) # the lemma, in words
build = clamp01((ctx.since("y5") - 0.3) / 3.2) # arrows arrive
hollow = smoother(clamp01((ctx.since("y6") - 0.2) / 2.4)) # the object leaves
close = pulse(ctx.t, ctx.slots["y7"].start - 0.2, ctx.dur + ctx.span.start, 0.9)
# the object itself, present until it is no longer needed
obj_a = (clamp01((ctx.since("y5") - 0.1) / 1.4) * (1 - hollow)
* (1 - say * 0.9) * (1 - close * 0.75))
if obj_a > 0.01:
xy, rgb = points("sierpinski", 1_000_000)
ctr, scl = fit_scale(xy, (size[0], size[1]), 0.62)
img = render_points(xy, rgb, size, ctr, scl,
center_override=None) if False else render_points(
xy, rgb, size, ctr, scl, exposure=2.0, bloom_strength=0.6)
fr.add(img, obj_a)
def draw(c):
# --- the lemma, said plainly ---------------------------------------
if say > 0.01:
draw_text(c, "the Yoneda lemma", CX, 250, size=34, color=INK_DIM,
alpha=say * 0.9, align="center", tracking=0.28,
reveal=clamp01((ctx.since("y2") - 0.2) / 1.4))
hairline(c, 296, CX - 220, CX + 220, alpha=say * 0.5,
t=clamp01((ctx.since("y2") - 1.0) / 1.0))
draw_paragraph(c, "a thing is completely determined by its "
"relationships to everything else",
CX, 452, 1320, size=62, color=INK, alpha=say,
align="center", leading=1.34, rise=12, glow=0.22,
reveal=clamp01((ctx.since("y3") - 0.1) / 2.6))
a4 = smooth((ctx.since("y4") - 0.1) / 0.9) * say
draw_text(c, "not approximately. completely.", CX, 700,
size=40, color=A_MINT, alpha=a4, align="center",
reveal=clamp01((ctx.since("y4") - 0.3) / 1.6), glow=0.2)
# --- every arrow into it -------------------------------------------
if build > 0.01:
scr, who, jit = _targets()
probes = _probes()
base = (0.055 + 0.085 * hollow) * (1 - close * 0.55)
pen = paint(INK, 1.0, width=1.0)
for i in range(0, len(scr), 1):
if jit[i] > build:
continue
px, py, _ = probes[who[i]]
col = GENERATORS[who[i] % 3]
a = base * (0.45 + 0.55 * jit[i])
pen.setColor(rgba(mix(col, INK, 0.45 * hollow), a))
c.drawLine(px, py, scr[i, 0], scr[i, 1], pen)
# the tips alone are the object
if hollow > 0.02:
for i in range(len(scr)):
if jit[i] > build:
continue
col = GENERATORS[who[i] % 3]
c.drawCircle(scr[i, 0], scr[i, 1], 1.35,
paint(col, 0.85 * hollow * (1 - close * 0.5)))
for j, (px, py, ang) in enumerate(probes):
a = clamp01((build - j * 0.045) / 0.3) * (1 - close * 0.6)
node(c, px, py, r=7.5, color=INK, alpha=a * 0.9, halo=0.8)
# --- the object's own outline, once it is gone ---------------------
if hollow > 0.02 and build > 0.5:
draw_text(c, "you never have to open the box", CX, 138, size=32,
color=INK_DIM, alpha=hollow * 0.85 * (1 - close),
align="center", tracking=0.22,
reveal=clamp01((ctx.since("y6") - 0.6) / 1.8))
# --- the closing lines ---------------------------------------------
if close > 0.01:
draw_text(c, "you are not what you are made of", CX, CY - 34,
size=56, color=INK, alpha=close, align="center",
reveal=clamp01((ctx.since("y8") - 0.1) / 1.6), glow=0.2)
draw_text(c, "you are how you connect", CX, CY + 58,
size=56, color=A_MINT, alpha=close, align="center",
reveal=clamp01((ctx.since("y8") - 1.5) / 1.6), glow=0.25)
fr.vector(draw)
return fr.finish(grain=0.010, seed=ctx.frame)
PY
uv run catfilm contact yoneda -n 8 2>&1 | tail -2
04:11:29
Read ← ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code/out/gallery/sheet_yoneda.png
04:11:29 · 🖼 image returned to Claude — [Image: original 2560x720, displayed at 2000x563. Multiply coordinates by 1.28 to map to original image.]
04:12:11The Yoneda "portrait made of arrows" works. Now the finale, credits, and the generative score:
04:12:39
Bash — Write finale and credits scenes
python3 - <<'PY'
p='src/catfilm/scenes/yoneda.py'
s=open(p).read()
s=s.replace(''' img = render_points(xy, rgb, size, ctr, scl,
center_override=None) if False else render_points(
xy, rgb, size, ctr, scl, exposure=2.0, bloom_strength=0.6)''',
''' img = render_points(xy, rgb, size, ctr, scl, exposure=2.0,
bloom_strength=0.6)''')
s=s.replace("base = (0.055 + 0.085 * hollow) * (1 - close * 0.55)","base = (0.075 + 0.105 * hollow) * (1 - close * 0.72)")
s=s.replace("c.drawCircle(scr[i, 0], scr[i, 1], 1.35,\n paint(col, 0.85 * hollow * (1 - close * 0.5)))",
"c.drawCircle(scr[i, 0], scr[i, 1], 1.45,\n paint(col, 0.95 * hollow * (1 - close * 0.62)))")
s=s.replace('draw_text(c, "you never have to open the box", CX, 138, size=32,\n color=INK_DIM, alpha=hollow * 0.85 * (1 - close),',
'draw_text(c, "you never have to open the box", CX, 126, size=33,\n color=INK, alpha=hollow * 0.80 * (1 - close),')
open(p,'w').write(s); print("ok")
PY
cat > src/catfilm/scenes/finale.py <<'PY'
"""Finale: one skeleton, every flesh it has."""
from __future__ import annotations
import math
from ._common import * # noqa: F403
from ..config import H, INK, INK_DIM, W
TOUR = ["sierpinski", "lattice", "pinwheel", "crown", "fold", "spiral", "frond",
"sierpinski"]
def render(ctx, size):
fr = stage(ctx, size, dust_alpha=0.6)
t0 = ctx.slots["z2"].start
t1 = ctx.slots["z4"].start + 1.2
leg = (t1 - t0) / (len(TOUR) - 1)
u = clamp01((ctx.t - t0) / max(t1 - t0, 1e-6)) * (len(TOUR) - 1)
i = min(int(u), len(TOUR) - 2)
show = clamp01((ctx.t - t0) / 1.4)
close = smoother(clamp01((ctx.t - (ctx.slots["z4"].start + 2.2)) / 2.6))
if show > 0.01:
img = morph_image(TOUR[i], TOUR[i + 1], smoother(u - i), size,
n=900_000, margin=0.70, exposure=2.3, bloom=0.68)
fr.add(img, show * (1 - close * 0.94) * ctx.envelope)
def draw(c):
a = ctx.envelope
# the source, always at the centre of what it makes
sig_a = a * (0.30 + 0.70 * clamp01(1 - show) + 0.55 * close)
sig_r = 118 - 46 * show + 34 * close
sigil(c, CX, CY - 10, r=sig_r, node_r=0.17 * sig_r, label_size=0.33 * sig_r,
alpha=min(1.0, sig_a), t=clamp01(ctx.since("z1") / 1.2),
label_off=1.28, width=2.4)
a3 = smooth((ctx.since("z3") - 0.1) / 1.2) * (1 - close * 0.4) * a
if a3 > 0.01:
draw_text(c, "none of this was drawn. it was composed.", CX,
H - 118, size=40, color=INK, alpha=a3, align="center",
reveal=clamp01((ctx.since("z3") - 0.2) / 2.0), glow=0.2)
a4 = smooth((ctx.since("z4") - 0.4) / 1.4) * a
if a4 > 0.01:
draw_text(c, "objects, and arrows", CX, 168, size=34, color=INK_DIM,
alpha=a4 * (1 - close * 0.3), align="center", tracking=0.24,
reveal=clamp01((ctx.since("z4") - 0.5) / 1.4))
draw_text(c, "arrows all the way down", CX, 218, size=34,
color=INK_DIM, alpha=a4 * (1 - close * 0.3), align="center",
tracking=0.24, reveal=clamp01((ctx.since("z4") - 1.9) / 1.4))
fr.vector(draw)
return fr.finish(grain=0.010, seed=ctx.frame)
PY
cat > src/catfilm/scenes/credits.py <<'PY'
"""Credits."""
from __future__ import annotations
from ._common import * # noqa: F403
from ..config import A_MINT, H, INK, INK_DIM, RULE, W
LINES = [
(68, "FUNCTOR", INK, 0.30, "serif"),
(30, "a short film about category theory", INK_DIM, 0.16, "serif"),
(0, None, None, 0, None),
(24, "THE MATHEMATICS", INK_DIM, 0.26, "serif"),
(30, "Samuel Eilenberg & Saunders Mac Lane — categories, functors,", INK, 0, "serif"),
(30, "natural transformations (1945)", INK, 0, "serif"),
(30, "Nobuo Yoneda — the lemma (c. 1954)", INK, 0, "serif"),
(30, "John Hutchinson & Michael Barnsley — attractors of", INK, 0, "serif"),
(30, "iterated function systems (1981, 1988)", INK, 0, "serif"),
(0, None, None, 0, None),
(24, "THE PICTURES", INK_DIM, 0.26, "serif"),
(28, "every image is the attractor of a functor from the free monoid", INK, 0, "serif"),
(28, "on {a, b, c} into the affine maps of the plane — computed, never drawn", INK, 0, "serif"),
(0, None, None, 0, None),
(24, "MADE WITH", INK_DIM, 0.26, "serif"),
(26, "python · numpy · skia · scipy · ffmpeg · uv · mise", A_MINT, 0.06, "mono"),
(0, None, None, 0, None),
(26, "the score is the same functor, read as pitch instead of position", INK_DIM, 0, "serif"),
]
def render(ctx, size):
fr = stage(ctx, size, dust_alpha=0.9)
bg = pulse(ctx.tl, 0.4, ctx.dur - 1.0, 1.4) * 0.16
if bg > 0.01:
fr.add(attractor_image("sierpinski", size[0], size[1], margin=0.52), bg)
scroll = ctx.tl / max(ctx.dur, 1e-6)
def draw(c):
a = ctx.envelope
y = H + 90 - scroll * (H + 1180)
for size_, text, col, tr, kind in LINES:
if text is None:
y += 46
continue
fade = clamp01((y - 60) / 160) * clamp01((H - 40 - y) / 200)
if fade > 0.01:
draw_text(c, text, CX, y, size=size_, color=col, alpha=a * fade,
align="center", tracking=tr, kind=kind)
y += size_ * 1.62
fr.vector(draw)
return fr.finish(grain=0.010, seed=ctx.frame)
PY
uv run catfilm contact finale -n 6 2>&1|tail -1; uv run catfilm contact credits -n 4 2>&1|tail -1
04:12:48
Read ← ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code/out/gallery/sheet_finale.png
04:12:48 · 🖼 image returned to Claude — [Image: original 2560x720, displayed at 2000x563. Multiply coordinates by 1.28 to map to original image.]
04:13:09Finale works. Now the score — the same three matrices, read as pitch instead of position:
04:13:58
Bash — Write the generative score and build the soundtrack
python3 -c "
p='src/catfilm/scenes/finale.py'
s=open(p).read().replace('margin=0.70','margin=0.80')
open(p,'w').write(s); print('ok')"
cat > src/catfilm/audio/score.py <<'PY'
"""The score is the same functor, read as pitch instead of position.
Nothing new is invented here. The three matrices that draw the Sierpiński
triangle are applied to a two-dimensional *musical* state — one axis pitch, the
other weight — and the orbit is played instead of plotted. When the picture
changes functor in the film, the music changes with it, because it is the same
change.
That is the claim the film makes, made audible: the structure was never in the
plane. The plane was just one place to put it.
"""
from __future__ import annotations
import numpy as np
from scipy.signal import oaconvolve
from ..config import AUDIO, SAMPLE_RATE as SR
from ..ifs import SYSTEMS, System
from .narration import read_wav, write_wav
# A minor pentatonic — the interval set that is hardest to make ugly.
SCALE = np.array([0, 3, 5, 7, 10])
ROOT = 45 # A2
# ---------------------------------------------------------------------------
# The functor, evaluated in music space
# ---------------------------------------------------------------------------
def orbit(system: System, n: int, seed: int = 3) -> np.ndarray:
"""Run the same three affine maps on a (pitch, weight) state."""
rng = np.random.default_rng(seed)
mats = np.stack([f.mat[:2, :2] for f in system.maps])
offs = np.stack([f.mat[:2, 2] for f in system.maps])
w = np.array(system.weights)
w = w / w.sum()
p = np.array([0.05, -0.05])
out = np.empty((n, 3))
draw = rng.choice(3, size=n + 30, p=w)
for i in range(30): # settle onto the attractor
p = mats[draw[i]] @ p + offs[draw[i]]
for i in range(n):
d = draw[i + 30]
p = mats[d] @ p + offs[d]
out[i] = (p[0], p[1], d)
return out
def notes(system: System, n: int, *, lo: int = 0, span: int = 20, seed: int = 3):
"""Turn an orbit into (degree, weight, letter) triples on the scale."""
o = orbit(system, n, seed)
x, y, d = o[:, 0], o[:, 1], o[:, 2].astype(int)
def _norm(v):
a, b = np.quantile(v, 0.02), np.quantile(v, 0.98)
return np.clip((v - a) / max(b - a, 1e-9), 0, 1)
deg = lo + np.floor(_norm(x) * span).astype(int)
wgt = 0.35 + 0.65 * _norm(y)
return deg, wgt, d
def midi(deg: np.ndarray) -> np.ndarray:
return ROOT + 12 * (deg // len(SCALE)) + SCALE[deg % len(SCALE)]
def hz(m):
return 440.0 * 2.0 ** ((np.asarray(m, dtype=np.float64) - 69) / 12.0)
# ---------------------------------------------------------------------------
# Synthesis
# ---------------------------------------------------------------------------
def bell(f: float, dur: float, amp: float = 1.0, bright: float = 1.0) -> np.ndarray:
n = int(dur * SR)
t = np.arange(n) / SR
y = np.zeros(n)
for k, (mult, a, dec) in enumerate((
(1.0, 1.00, 0.55), (2.0, 0.42, 0.95), (3.01, 0.20, 1.5),
(4.16, 0.10, 2.2), (5.43, 0.05, 3.0))):
env = np.exp(-t * dec / max(dur, 0.2) * 2.6)
y += a * (bright ** k) * np.sin(2 * np.pi * f * mult * t + k) * env
atk = np.minimum(1.0, t / 0.006)
y *= atk
y *= np.exp(-t * 0.35)
return (y * amp / 1.8).astype(np.float32)
def pad(f: float, dur: float, amp: float = 1.0, detune: float = 0.004) -> np.ndarray:
n = int(dur * SR)
t = np.arange(n) / SR
y = np.zeros(n)
for k, a in ((1.0, 1.0), (2.0, 0.30), (3.0, 0.12), (4.0, 0.05)):
for s in (-1, 1):
y += a * np.sin(2 * np.pi * f * k * (1 + s * detune) * t
+ s * k * 0.7)
y *= 1.0 + 0.16 * np.sin(2 * np.pi * 0.07 * t)
fade = np.minimum(np.minimum(t / 2.4, (dur - t) / 3.2), 1.0).clip(0, 1)
return (y * fade * amp / 3.4).astype(np.float32)
def _reverb_ir(seconds=2.8, decay=4.2, seed=1) -> np.ndarray:
rng = np.random.default_rng(seed)
n = int(seconds * SR)
t = np.arange(n) / SR
ir = rng.standard_normal(n) * np.exp(-t * decay)
ir[: int(0.012 * SR)] *= np.linspace(0, 1, int(0.012 * SR))
ir /= np.abs(ir).sum() / 12.0
return ir.astype(np.float32)
def reverb(x: np.ndarray, mix: float = 0.30) -> np.ndarray:
ir = _reverb_ir()
wet = oaconvolve(x, ir)[: len(x)]
return ((1 - mix) * x + mix * wet).astype(np.float32)
# ---------------------------------------------------------------------------
# Arrangement: every act gets the functor the picture is showing
# ---------------------------------------------------------------------------
PLAN = {
"opening": dict(sys="sierpinski", dens=0.34, lo=8, span=13, gain=0.55, pad=0.35),
"title": dict(sys="sierpinski", dens=0.55, lo=6, span=16, gain=0.85, pad=0.75),
"category": dict(sys="sierpinski", dens=0.30, lo=7, span=13, gain=0.48, pad=0.40),
"examples": dict(sys="lattice", dens=0.40, lo=6, span=15, gain=0.50, pad=0.40),
"monoid": dict(sys="sierpinski", dens=0.26, lo=10, span=11, gain=0.46, pad=0.42),
"functor": dict(sys="pinwheel", dens=0.36, lo=6, span=15, gain=0.52, pad=0.45),
"bloom": dict(sys="sierpinski", dens=0.60, lo=4, span=19, gain=0.92, pad=0.60),
"variants": dict(sys="spiral", dens=0.62, lo=4, span=19, gain=0.86, pad=0.55),
"natural": dict(sys="crown", dens=0.38, lo=6, span=16, gain=0.58, pad=0.48),
"yoneda": dict(sys="frond", dens=0.30, lo=9, span=14, gain=0.54, pad=0.52),
"finale": dict(sys="fold", dens=0.78, lo=3, span=21, gain=1.00, pad=0.72),
"credits": dict(sys="sierpinski", dens=0.46, lo=5, span=17, gain=0.80, pad=0.62),
}
def render_score(total: float, acts) -> np.ndarray:
buf = np.zeros((int(total * SR) + 4 * SR, 2), dtype=np.float32)
rng = np.random.default_rng(17)
for span in acts:
cfg = PLAN.get(span.act.scene, PLAN["category"])
sysm = SYSTEMS[cfg["sys"]]
dur = span.dur
n = max(4, int(dur * cfg["dens"]))
deg, wgt, letter = notes(sysm, n, lo=cfg["lo"], span=cfg["span"],
seed=7 + len(span.act.name))
ms = midi(deg)
# notes, laid on a loose pulse so it breathes rather than ticks
step = dur / n
for i in range(n):
t0 = span.start + i * step + rng.uniform(-0.12, 0.12) * step
if t0 < span.start or t0 > span.start + dur - 0.3:
continue
hold = float(np.clip(step * (1.6 + 2.4 * wgt[i]), 0.8, 5.5))
amp = cfg["gain"] * (0.16 + 0.30 * wgt[i]) * rng.uniform(0.85, 1.12)
y = bell(float(hz(ms[i])), hold, amp,
bright=0.72 + 0.30 * wgt[i])
pan = 0.5 + 0.34 * (deg[i] / max(cfg["span"], 1) - 0.5)
j = int(t0 * SR)
m = min(len(y), len(buf) - j)
buf[j:j + m, 0] += y[:m] * (1 - pan)
buf[j:j + m, 1] += y[:m] * pan
# a drone underneath, rooted on the act's lowest note
root = float(hz(ROOT + 12 * (cfg["lo"] // len(SCALE))))
for f, a in ((root, 1.0), (root * 1.5, 0.55), (root * 2, 0.30)):
y = pad(f, dur + 1.2, cfg["pad"] * 0.09 * a)
j = int(span.start * SR)
m = min(len(y), len(buf) - j)
buf[j:j + m, 0] += y[:m] * 0.97
buf[j:j + m, 1] += y[:m] * 1.03
out = np.stack([reverb(buf[:, 0], 0.34), reverb(buf[:, 1], 0.34)], axis=1)
peak = np.abs(out).max()
return (out / max(peak, 1e-6) * 0.72).astype(np.float32)
# ---------------------------------------------------------------------------
# Mix
# ---------------------------------------------------------------------------
def _envelope(x: np.ndarray, attack=0.04, release=0.55) -> np.ndarray:
"""A cheap follower, used to duck the score under the voice."""
a = np.abs(x)
k = int(0.02 * SR)
a = np.convolve(a, np.ones(k) / k, mode="same")
ca = np.exp(-1.0 / (attack * SR))
cr = np.exp(-1.0 / (release * SR))
out = np.empty_like(a)
y = 0.0
for i in range(0, len(a), 1):
c = ca if a[i] > y else cr
y = c * y + (1 - c) * a[i]
out[i] = y
return out
def _duck(score: np.ndarray, voice: np.ndarray, depth=0.62) -> np.ndarray:
step = 64 # follow at 690 Hz; plenty
e = _envelope(voice[::step])
e = np.interp(np.arange(len(voice)), np.arange(len(e)) * step, e)
e = e / max(e.max(), 1e-9)
g = (1.0 - depth * np.clip(e * 3.2, 0, 1))[:, None]
n = min(len(score), len(g))
out = score.copy()
out[:n] *= g[:n]
return out
def build_soundtrack() -> "Path":
from ..timeline import build as build_timeline
from .narration import voice_track
tl = build_timeline()
total = tl.total + 1.0
voice = voice_track(tl.schedule(), total)
score = render_score(total, tl.acts)
n = int(total * SR)
score = score[:n] if len(score) >= n else np.pad(score, ((0, n - len(score)), (0, 0)))
voice = voice[:n] if len(voice) >= n else np.pad(voice, (0, n - len(voice)))
score = _duck(score, voice)
v = voice * 1.32
mix = np.stack([v, v], axis=1) + score * 0.62
# a soft limiter, so nothing ever slams
peak = np.abs(mix).max()
mix = mix / max(peak, 1e-6) * 0.94
mix = np.tanh(mix * 1.12) / np.tanh(1.12)
out = AUDIO / "mix.wav"
write_wav(out, mix.astype(np.float32))
return out
PY
uv run python -c "
import time,numpy as np
from catfilm.audio.score import *
from catfilm.ifs import SYSTEMS
d,w,l = notes(SYSTEMS['sierpinski'], 24, lo=4, span=19)
print('degrees', d); print('midi ', midi(d)); print('weights', np.round(w,2))
t=time.time(); p=build_soundtrack(); print('mix', p, f'{time.time()-t:.1f}s')
" 2>&1 | tail -6
04:14:31Melody leaps are too wild. Let me derive it from a word-tree traversal so it inherits the fractal's nesting:
04:14:50
Bash — Rework melody from word-tree traversal and verify audio
python3 - <<'PY'
p='src/catfilm/audio/score.py'
s=open(p).read()
s=s.replace('''def notes(system: System, n: int, *, lo: int = 0, span: int = 20, seed: int = 3):
"""Turn an orbit into (degree, weight, letter) triples on the scale."""
o = orbit(system, n, seed)
x, y, d = o[:, 0], o[:, 1], o[:, 2].astype(int)
def _norm(v):
a, b = np.quantile(v, 0.02), np.quantile(v, 0.98)
return np.clip((v - a) / max(b - a, 1e-9), 0, 1)
deg = lo + np.floor(_norm(x) * span).astype(int)
wgt = 0.35 + 0.65 * _norm(y)
return deg, wgt, d''',
'''def _norm(v):
a, b = np.quantile(v, 0.02), np.quantile(v, 0.98)
return np.clip((v - a) / max(b - a, 1e-9), 0, 1)
def word_melody(system: System, depth: int = 5) -> np.ndarray:
"""Every word of a given length, played in an order that keeps its nesting.
``F(w)`` applied to the origin is a point of the plane; its two coordinates
become pitch and weight. Words are visited so that consecutive notes share
their *outermost* letters — which is exactly the ordering under which the
attractor's self-similarity becomes melodic repetition. The tune has the
same nested structure the picture does, for the same reason.
"""
from ..core import words
from ..ifs import LETTERS, MONOID
F = system.functor()
ws = sorted(words(LETTERS, depth), key=lambda w: tuple(reversed(w)))
pts = np.array([F(MONOID.source_of(w, "•")).apply(np.zeros((1, 2)))[0]
for w in ws])
letters = np.array([LETTERS.index(w[0]) for w in ws])
return pts, letters
@lru_cache(maxsize=32)
def _melody(name: str, depth: int):
return word_melody(SYSTEMS[name], depth)
def notes(system: System, n: int, *, lo: int = 0, span: int = 20, seed: int = 3,
name: str | None = None):
"""``n`` notes of the melody this functor makes."""
depth = 4 if n <= 90 else 5
pts, letters = (_melody(name, depth) if name
else word_melody(system, depth))
rng = np.random.default_rng(seed)
if len(pts) > n: # take one nested stretch of the tune
i0 = int(rng.integers(0, len(pts) - n))
pts, letters = pts[i0:i0 + n], letters[i0:i0 + n]
else:
reps = int(np.ceil(n / len(pts)))
pts = np.tile(pts, (reps, 1))[:n]
letters = np.tile(letters, reps)[:n]
deg = lo + np.floor(_norm(pts[:, 0]) * span).astype(int)
wgt = 0.35 + 0.65 * _norm(pts[:, 1])
return deg, wgt, letters''')
s=s.replace("from ..config import AUDIO, SAMPLE_RATE as SR","from functools import lru_cache\n\nfrom ..config import AUDIO, SAMPLE_RATE as SR")
s=s.replace(''' deg, wgt, letter = notes(sysm, n, lo=cfg["lo"], span=cfg["span"],
seed=7 + len(span.act.name))''',
''' deg, wgt, letter = notes(sysm, n, lo=cfg["lo"], span=cfg["span"],
seed=7 + len(span.act.name), name=cfg["sys"])''')
open(p,'w').write(s); print("ok")
PY
uv run python - <<'PY'
import numpy as np, time
from catfilm.audio.score import notes, midi
from catfilm.ifs import SYSTEMS
for k in ["sierpinski","spiral","frond"]:
d,w,l = notes(SYSTEMS[k], 40, lo=4, span=19, name=k)
m = midi(d)
print(f"{k:11s} leaps: mean {np.abs(np.diff(m)).mean():4.1f} max {np.abs(np.diff(m)).max():3d} semitones")
print(" ", " ".join(f"{v:3d}" for v in m[:24]))
t=time.time()
from catfilm.audio.score import build_soundtrack
p=build_soundtrack(); print(f"mix rebuilt {time.time()-t:.1f}s")
import wave
with wave.open(str(p)) as wv:
n=wv.getnframes(); a=np.frombuffer(wv.readframes(n),dtype=np.int16).reshape(-1,2)/32768
print(f"duration {n/44100/60:.2f} min peak {np.abs(a).max():.3f} rms {np.sqrt((a**2).mean()):.4f}")
# rough voice/score balance check: rms in a speech window vs a silent window
print("rms @ 0-2s (lead-in, score only):", round(float(np.sqrt((a[:2*44100]**2).mean())),4))
print("rms @ 60-70s (speech+score) :", round(float(np.sqrt((a[60*44100:70*44100]**2).mean())),4))
PY
04:15:12
Bash — Measure voice-to-score balance
uv run python - <<'PY'
import numpy as np
from catfilm.timeline import build
from catfilm.audio.narration import voice_track
from catfilm.audio.score import render_score, _duck
from catfilm.config import SAMPLE_RATE as SR
tl=build(); total=tl.total+1.0
v=voice_track(tl.schedule(), total); s=render_score(total, tl.acts)
n=int(total*SR); v=v[:n]; s=s[:n]
sd=_duck(s,v)
# during speech vs during silence
speech=np.zeros(n,bool)
for k,sl in tl.slots.items():
if sl.speech_end>sl.start: speech[int(sl.start*SR):int(sl.speech_end*SR)]=True
def rms(x,m):
x=x[m] if x.ndim==1 else x[m].mean(1)
return float(np.sqrt((x**2).mean())) if m.any() else 0
print(f"voice rms during speech {rms(v,speech):.4f}")
print(f"score rms during speech (duck){rms(sd,speech):.4f} ratio {rms(v,speech)/max(rms(sd,speech),1e-9):.1f}x")
print(f"score rms during silence {rms(sd,~speech):.4f}")
print(f"voice peak {np.abs(v).max():.3f} score peak {np.abs(sd).max():.3f}")
PY
04:15:37Balance is right (12 dB voice over music). Fixing mix headroom, then a smoke test across every act:
04:15:43
Bash — Fix mix levels and smoke-test every act
python3 - <<'PY'
p='src/catfilm/audio/score.py'
s=open(p).read()
s=s.replace(''' score = _duck(score, voice)
v = voice * 1.32
mix = np.stack([v, v], axis=1) + score * 0.62
# a soft limiter, so nothing ever slams
peak = np.abs(mix).max()
mix = mix / max(peak, 1e-6) * 0.94
mix = np.tanh(mix * 1.12) / np.tanh(1.12)''',
''' score = _duck(score, voice)
v = voice / max(np.abs(voice).max(), 1e-6) * 0.80
mix = np.stack([v, v], axis=1) + score * 0.66
# a soft limiter, so nothing ever slams
mix = np.tanh(mix * 1.15) / np.tanh(1.15)
mix = mix / max(np.abs(mix).max(), 1e-6) * 0.95''')
open(p,'w').write(s); print("ok")
PY
uv run catfilm plan && echo "--- smoke test: one frame per act ---" && uv run python - <<'PY'
import time, traceback
import numpy as np
from catfilm.timeline import build
from catfilm.build import render_frame
from catfilm.config import FPS
tl=build()
bad=0
for a in tl.acts:
for frac in (0.08, 0.45, 0.92):
t=a.start + a.dur*frac
try:
t0=time.time(); f=render_frame(tl,int(t*FPS),(960,540)); dt=time.time()-t0
assert f.shape==(540,960,3) and f.dtype==np.uint8
except Exception as e:
bad+=1; print(f" FAIL {a.act.scene} @{frac}: {type(e).__name__}: {e}"); traceback.print_exc(limit=2)
break
else:
print(f" ok {a.act.scene:10s} last-frame {dt*1000:5.0f} ms")
print("failures:", bad)
PY
04:15:59All twelve acts render clean. Launching the full render in the background:
04:16:01
Bash — Render the complete film
uv run catfilm build --crf 17 --preset medium 2>&1 | tail -45
04:16:05Render is running. While it works, let me build the standalone generative-art gallery:
04:16:23
Bash — Write gallery module and check render progress
cat > src/catfilm/gallery.py <<'PY'
"""The generative-art gallery.
Each plate is the attractor of a functor from the free monoid on {a, b, c} into
the affine maps of the plane. Nothing is drawn; the images are what the words
of that monoid converge to under one choice of three matrices, and the colour of
each point records which letters most recently acted on it.
"""
from __future__ import annotations
import numpy as np
from PIL import Image
from .config import BG, GALLERY, GENERATORS, INK, INK_DIM, RULE
from .ifs import LETTERS, SYSTEMS, Aff, _mk, chaos_game
from .render.canvas import Frame, draw_text, measure
from .render.glow import fit_scale, render_points
def _plate(system, w, h, *, n=6_000_000, margin=0.80, exposure=2.4, seed=7,
title=None, subtitle=None, matrices=True, caption=None):
fr = Frame(w, h)
xy, rgb = chaos_game(system, n, seed=seed)
ctr, scl = fit_scale(xy, (w, h), margin)
fr.add(render_points(xy, rgb, (w, h), ctr, scl, exposure=exposure,
bloom_strength=0.62, ss=2))
k = w / 1920
def draw(c):
c.save()
c.scale(1 / k, 1 / k) # annotate in device pixels
pad = int(58 * k)
if title:
draw_text(c, title, pad, pad + int(40 * k), size=int(44 * k),
color=INK, alpha=0.92, tracking=0.10)
if subtitle:
draw_text(c, subtitle, pad, pad + int(84 * k), size=int(25 * k),
color=INK_DIM, alpha=0.78, tracking=0.06)
if matrices:
y = h - pad - int(96 * k)
for i, (col, lab) in enumerate(zip(GENERATORS, LETTERS)):
m = system.maps[i].mat[:2]
row = (f"{lab} ↦ [{m[0,0]:+.2f} {m[0,1]:+.2f} {m[0,2]:+.2f}]"
f" [{m[1,0]:+.2f} {m[1,1]:+.2f} {m[1,2]:+.2f}]")
draw_text(c, row, pad, y + i * int(34 * k), size=int(20 * k),
kind="mono", color=col, alpha=0.80)
if caption:
draw_text(c, caption, w - pad, h - pad, size=int(21 * k),
color=INK_DIM, alpha=0.62, align="right", tracking=0.10)
c.restore()
fr.vector(draw)
return fr.finish(vignette=0.34, grain=0.006, seed=3)
def render_gallery(width: int = 2400) -> None:
h = int(width * 9 / 16) // 2 * 2
out = []
for key, sysm in SYSTEMS.items():
img = _plate(sysm, width, h, title=sysm.name, subtitle=sysm.subtitle,
caption="the free monoid on {a, b, c}, translated")
p = GALLERY / f"plate_{key}.png"
Image.fromarray(img).save(p)
out.append(p)
print(" ", p.name)
# a naturally isomorphic pair: the same functor, conjugated by one map
alpha = _mk(1.06, 0.86, 0.46, 0.34, 0.02, 0.0)
conj = SYSTEMS["sierpinski"].conjugate(alpha, "Sierpiński, conjugated")
img = _plate(conj, width, h, title="α · Sierpiński · α⁻¹",
subtitle="naturally isomorphic to the first plate — "
"every square commutes",
caption="different in every number · identical in every relationship")
p = GALLERY / "plate_conjugate.png"
Image.fromarray(img).save(p)
out.append(p)
print(" ", p.name)
# a contact sheet of the whole family
tiles = []
tw = width // 3 // 2 * 2
th = int(tw * 9 / 16) // 2 * 2
for key, sysm in SYSTEMS.items():
tiles.append(_plate(sysm, tw, th, n=2_200_000, title=sysm.name,
subtitle=None, matrices=False))
while len(tiles) % 3:
tiles.append(np.zeros_like(tiles[0]))
rows = [np.concatenate(tiles[i:i + 3], axis=1) for i in range(0, len(tiles), 3)]
p = GALLERY / "family.png"
Image.fromarray(np.concatenate(rows, axis=0)).save(p)
print(" ", p.name)
print(f"\n {len(out) + 1} plates in {GALLERY}")
PY
echo "--- render check ---" && sleep 1 && tail -4 /private/tmp/claude-501/-Users-bowiesmith-repos-llm-video-repos-category-theory-opus-5-max-claude-code/af4e5c83-3019-4c3a-8cd5-9aff1cfa8267/tasks/bd3ltoyxo.output
04:16:30
Bash — Check render progress
cat /private/tmp/claude-501/-Users-bowiesmith-repos-llm-video-repos-category-theory-opus-5-max-claude-code/af4e5c83-3019-4c3a-8cd5-9aff1cfa8267/tasks/bd3ltoyxo.output 2>/dev/null | tail -12; echo "---"; ls -la out/chunks/ 2>/dev/null | head -5
04:16:36Writing the README while the render runs:
04:17:17
Bash — Write README and executable law checks
cat > README.md <<'MD'
# Functor
**A short film about category theory, and the generative art it makes.**
Nine minutes, narrated, scored. Every picture in it — and every note — is
computed by evaluating a functor. Nothing is drawn.
mise run install # or: uv sync mise run film # narration + score + picture -> out/functor.mp4 mise run stills # the generative-art plates -> out/gallery/
---
## The idea
A category is three things: **objects**, **arrows** between them, and a rule for
**chaining arrows together**. Two laws: every object has a do-nothing arrow, and
chaining is associative. That is the entire definition — and it never says what
the objects *are*.
A **functor** translates one category into another. It sends objects to objects
and arrows to arrows, and obeys exactly one law:
F(g ∘ f) = F(g) ∘ F(f)
Combine then translate, or translate then combine — same answer. The film's
claim is that this one equation is load-bearing, and the art is the evidence.
## The art is the argument
Take the smallest interesting category: **one object, three arrows** called
`a`, `b`, `c`. Nowhere to go, so all you can do is compose. Its arrows are
therefore exactly the *words* in three letters — `ab`, `cca`, `bbbb`. There is
no geometry in it. There is no picture.
Now pick a functor out of it into the affine maps of the plane. The single
object has to go to the plane; the three arrows go to three matrices. That is
every decision you are allowed to make. Functoriality forces the rest: the word
`ab` *must* mean "do `a`, then do `b`".
Ask where the words go, and you get this:
<p align="center"><img src="out/gallery/plate_sierpinski.png" width="640" alt="Sierpiński"></p>
Nobody drew it. There is no triangle anywhere in the definition — there are
three matrices and a rule about composition. **The colour is grammar**: each
point is tinted by the letters that most recently acted on it, so blue marks
where `a` went last, amber `b`, violet `c`. The image is painted by its own
sentences.
Keep every word. Change only the three matrices — the same free monoid, a
different translation — and the same skeleton wears different flesh:
<p align="center"><img src="out/gallery/family.png" width="820" alt="the family"></p>
That is what "abstraction is powerful" means, concretely. Not that it is vague:
that a single fact upstairs, where there are no pictures, is a fact about every
world downstairs at once.
## The score is the same functor
The soundtrack is not accompaniment. The **same three matrices** are applied to
a two-dimensional *musical* state — one axis pitch, the other weight — and the
orbit is played instead of plotted. Words are visited in an order that preserves
their nesting, so the melody repeats at every scale, for the same reason the
picture does. When the film changes functor, the music changes with it, because
it is the same change.
The plane was never where the structure lived. It was just one place to put it.
## Natural transformations, honestly
Two functors are "the same" when a **natural transformation** connects them: one
arrow per object, such that every square commutes. The film demonstrates a real
one rather than asserting it. Conjugating a system by a single plane map `α`,
G(x) = α ∘ F(x) ∘ α⁻¹
gives a genuinely naturally isomorphic functor, and `NaturalTransformation
.check_naturality()` verifies the square commutes for every word up to length 4
before a frame is rendered. Its attractor is the first plate, standing
differently:
<p align="center"><img src="out/gallery/plate_conjugate.png" width="640" alt="conjugate"></p>
Different in every number. Identical in every relationship.
---
## The mathematics is executable
`src/catfilm/core.py` is not decoration. Categories, functors and natural
transformations are implemented with their laws as assertions, and the build
checks them:
```python
from catfilm.core import Category
from catfilm.ifs import SYSTEMS, naturality, _mk
Category(["A","B","C"], {"f":("A","B"), "g":("B","C")}).check_laws()
for s in SYSTEMS.values():
s.functor().check_functoriality(max_len=3) # F(g∘f) == F(g)∘F(f)
alpha = _mk(1.0, 1.0, 0.6, 0.35, 0.12, -0.05)
src = SYSTEMS["sierpinski"]
naturality(src, alpha, src.conjugate(alpha)).check_naturality(max_len=4)
Run them with uv run python -m catfilm.laws.
core.py |
categories, functors, natural transformations — with law checks |
ifs.py |
functors into the affine maps of the plane; the chaos game |
render/glow.py |
density accumulation and the log tone curve that makes light |
render/canvas.py |
float compositing, typography with math-font fallback |
render/diagram.py |
the visual grammar: dots, arrows, self-loops, squares |
script.py |
the screenplay, one Beat per spoken line |
timeline.py |
beat durations → absolute times; the Ctx scenes query |
scenes/ |
one module per act |
audio/ |
narration via say; the score, from the same functor |
build.py |
parallel chunked encoding straight into ffmpeg |
Brightness is a readout of how often the attractor visits a pixel — that is, how many words land there. Points are histogrammed into a supersampled buffer and passed through a logarithmic tone curve, so the depth in the image is genuine density, not shading.
The picture is cut to the voice. Each line is synthesised once, its true duration measured, and the timeline rebuilt from those measurements — so editing the script re-times every animation automatically.
Frames are never written to disk. The film is split into contiguous chunks, one
per core; each worker pipes raw frames into its own ffmpeg and the chunks are
concatenated. Nine minutes of 1080p costs a few hundred megabytes of temporary
video instead of thirty gigabytes of PNGs.
uv run catfilm plan # the timeline
uv run catfilm audio # narration + score
uv run catfilm render # picture only
uv run catfilm render --scene bloom # one act
uv run catfilm still 4:20 # one frame (seconds, mm:ss, or a beat key)
uv run catfilm contact natural # a contact sheet of one act
uv run catfilm gallery # the art plates
uv run catfilm build # everything
Samuel Eilenberg & Saunders Mac Lane, General Theory of Natural Equivalences (1945) — categories were invented to make one adjective precise. Nobuo Yoneda, for the lemma that says a thing is its relationships. John Hutchinson (1981) and Michael Barnsley (1988), for attractors of iterated function systems: the fact that three contractions determine a unique compact set is what makes the pictures exist at all.
Built with Python, numpy, Skia, scipy, ffmpeg, uv and mise. Narration is macOS
say; the score is numpy.
MD
cat > src/catfilm/laws.py <<'PY'
"""Run every law the film relies on. uv run python -m catfilm.laws"""
from future import annotations
import numpy as np
from .core import Category, free_monoid from .ifs import SYSTEMS, Aff, _mk, blend_systems, naturality
def main() -> int: print("category laws") C = Category(["A", "B", "C", "D"], {"f": ("A", "B"), "g": ("B", "C"), "h": ("C", "D"), "k": ("A", "C")}) C.check_laws(max_len=3) free_monoid(list("abc")).check_laws(max_len=3) print(" identity, associativity ok")
print("functoriality F(g∘f) = F(g)∘F(f)")
for name, s in SYSTEMS.items():
s.functor().check_functoriality(max_len=3)
assert all(f.contraction < 1.0 for f in s.maps), f"{name} is not contractive"
print(f" {name:11s} contractions "
f"{[round(f.contraction, 2) for f in s.maps]} ok")
print("naturality α ∘ F(w) = G(w) ∘ α")
alpha = _mk(1.06, 0.86, 0.46, 0.34, 0.02, 0.0)
for name, s in SYSTEMS.items():
naturality(s, alpha, s.conjugate(alpha)).check_naturality(max_len=4)
print(f" {name:11s} every square commutes ok")
print("every frame of every morph is itself a functor")
keys = list(SYSTEMS)
for a, b in zip(keys, keys[1:] + keys[:1]):
for t in np.linspace(0, 1, 25):
m = blend_systems(SYSTEMS[a], SYSTEMS[b], float(t))
m.functor().check_functoriality(max_len=2)
assert all(f.contraction < 0.97 for f in m.maps)
print(" all interpolation paths stay contractive ok")
print("\nall laws hold.")
return 0
if name == "main": raise SystemExit(main()) PY uv run python -m catfilm.laws 2>&1 | tail -22
<sub>`04:17:25`</sub>
**Bash** — Check render progress
```bash
ls out/chunks/*.mp4 2>/dev/null | wc -l; ls -la out/*.mp4 2>/dev/null; echo "--- proc ---"; ps aux | grep -c "[c]atfilm"
04:17:38
Bash — Verify soundtrack duration matches timeline
ffprobe -v error -show_entries format=duration,size -show_entries stream=codec_name,sample_rate,channels -of default=nw=1 out/audio/mix.wav; echo "--- expected ---"; uv run python -c "
from catfilm.timeline import build; tl=build(); print(f'film {tl.total:.2f}s frames {tl.frames}')"
04:17:44
Bash — Wait and check render progress
sleep 90; ls out/chunks/*.mp4 2>/dev/null | wc -l; ls -la out/*.mp4 2>/dev/null
04:17:48
ToolSearch — {"query": "select:Monitor", "max_results": 1}
04:17:54
Bash — Wait for the film to finish rendering
until [ -f out/functor.mp4 ]; do sleep 5; done; echo "FILM READY"; ls -la out/functor.mp4
04:17:58
Bash — Check chunk count
ls out/chunks/*.mp4 2>/dev/null | wc -l
04:18:06
Bash — Check worker CPU and chunk growth
ps aux | grep "[P]ython" | awk '{print $3, $4}' | head -12; echo "--- chunk sizes ---"; ls -la out/chunks/ | awk '{print $5, $9}' | tail -11
04:18:16
Bash — Check for running python processes and task output
ps aux | grep -ci "[p]ython"; ps aux | grep -i "[p]ython" | awk '{printf "%s %s %s\n",$3,$4,$11}' | head -12; echo "--- task output ---"; cat /private/tmp/claude-501/-Users-bowiesmith-repos-llm-video-repos-category-theory-opus-5-max-claude-code/af4e5c83-3019-4c3a-8cd5-9aff1cfa8267/tasks/bd3ltoyxo.output
04:18:27
Bash — Measure frames encoded per chunk
for f in out/chunks/part00{0,4,9}.mp4; do echo -n "$f "; ffprobe -v error -count_frames -select_streams v:0 -show_entries stream=nb_read_frames -of csv=p=0 "$f" 2>/dev/null; done; echo "expected per chunk: $((15277/30))"; ps aux | grep -c "[f]fmpeg"
04:18:47Render is at ~30% CPU per worker with 10 concurrent x264 encoders — it's saturated. Let me wait for it:
04:18:49
Bash — Wait for render to reach final round
until [ "$(ls out/chunks/*.mp4 2>/dev/null | wc -l)" -ge 21 ]; do sleep 10; done; echo "round 3 started: $(ls out/chunks/*.mp4 | wc -l) chunks"
04:22:36
Bash — Wait for final mux and inspect the film
until [ -f out/functor.mp4 ]; do sleep 5; done; ls -la out/functor.mp4; ffprobe -v error -show_entries format=duration,bit_rate -show_entries stream=codec_name,width,height,r_frame_rate,nb_frames -of default=nw=1 out/functor.mp4
04:32:42
Bash — Read render log and inspect the final film
cat /private/tmp/claude-501/-Users-bowiesmith-repos-llm-video-repos-category-theory-opus-5-max-claude-code/af4e5c83-3019-4c3a-8cd5-9aff1cfa8267/tasks/bd3ltoyxo.output | tail -12; echo "=== FILM ==="; ls -la out/functor.mp4 && ffprobe -v error -show_entries format=duration,bit_rate -show_entries stream=codec_name,width,height,nb_frames -of default=nw=1 out/functor.mp4
04:33:01
Bash — Read the full render log
cat /private/tmp/claude-501/-Users-bowiesmith-repos-llm-video-repos-category-theory-opus-5-max-claude-code/af4e5c83-3019-4c3a-8cd5-9aff1cfa8267/tasks/bd3ltoyxo.output
04:33:16Found it — getPosTan returns None on a zero-length arc, which happens when the commuting mark is just barely fading in. Let me harden the primitives and add a real preflight:
04:33:40
Bash — Harden path primitives, add resilient workers and preflight
python3 - <<'PY'
p='src/catfilm/render/diagram.py'
s=open(p).read()
# _trim: a zero-length path yields no position/tangent
s=s.replace('''def _trim(path: skia.Path, t0: float, t1: float) -> tuple[skia.Path, tuple, tuple]:
pm = skia.PathMeasure(path, False)
L = pm.getLength()
out = skia.Path()
pm.getSegment(L * clamp01(t0), L * clamp01(t1), out, True)
pos, tan = pm.getPosTan(L * clamp01(t1))
return out, (pos.x(), pos.y()), (tan.x(), tan.y())''',
'''def _trim(path: skia.Path, t0: float, t1: float) -> tuple[skia.Path, tuple, tuple]:
pm = skia.PathMeasure(path, False)
L = pm.getLength()
out = skia.Path()
if L <= 1e-6: # a degenerate path has nowhere to point
return out, (0.0, 0.0), (1.0, 0.0)
pm.getSegment(L * clamp01(t0), L * clamp01(t1), out, True)
got = pm.getPosTan(L * clamp01(t1))
if got is None:
return out, (0.0, 0.0), (1.0, 0.0)
pos, tan = got
return out, (pos.x(), pos.y()), (tan.x(), tan.y())''')
# commuting_mark: skip while the arc is still shorter than a pixel
s=s.replace(''' a = alpha * smooth(t)
path = skia.Path()
path.addArc(skia.Rect.MakeLTRB(x - r, y - r, x + r, y + r), -60, 300 * smoother(t))
c.drawPath(path, paint(color, a * 0.9, width=2.0))
pm = skia.PathMeasure(path, False)
pos, tan = pm.getPosTan(pm.getLength())
arrowhead(c, (pos.x(), pos.y()), (tan.x(), tan.y()), 9.0 * smooth((t - .5) / .5),
color, a)''',
''' sweep = 300 * smoother(t)
if sweep < 1.0:
return
a = alpha * smooth(t)
path = skia.Path()
path.addArc(skia.Rect.MakeLTRB(x - r, y - r, x + r, y + r), -60, sweep)
c.drawPath(path, paint(color, a * 0.9, width=2.0))
pm = skia.PathMeasure(path, False)
got = pm.getPosTan(pm.getLength())
if got is None:
return
pos, tan = got
arrowhead(c, (pos.x(), pos.y()), (tan.x(), tan.y()), 9.0 * smooth((t - .5) / .5),
color, a)''')
# self_loop / arrow label lookups can hit the same degenerate case
s=s.replace(''' if label:
pm = skia.PathMeasure(path, False)
L = pm.getLength()
mp, mt = pm.getPosTan(L * 0.5)
nx, ny = -mt.y(), mt.x()''',''' if label:
pm = skia.PathMeasure(path, False)
L = pm.getLength()
got = pm.getPosTan(L * 0.5)
if got is None:
return
mp, mt = got
nx, ny = -mt.y(), mt.x()''')
open(p,'w').write(s)
# make a lost frame cost one frame, not the whole render — but say so loudly
p='src/catfilm/build.py'
s=open(p).read()
s=s.replace('''def _work(job):
idx, f0, f1, size, crf, preset = job
path = CHUNKS / f"part{idx:03d}.mp4"
proc = _ffmpeg_writer(path, size, crf=crf, preset=preset)
t0 = time.time()
for i in range(f0, f1):
frame = render_frame(_TL, i, size)
proc.stdin.write(frame.tobytes())
proc.stdin.close()
proc.wait()
return idx, f1 - f0, time.time() - t0''',
'''def _work(job):
idx, f0, f1, size, crf, preset = job
path = CHUNKS / f"part{idx:03d}.mp4"
proc = _ffmpeg_writer(path, size, crf=crf, preset=preset)
t0 = time.time()
last = np.zeros((size[1], size[0], 3), dtype=np.uint8)
errs: list[str] = []
for i in range(f0, f1):
try:
last = render_frame(_TL, i, size)
except Exception as exc: # keep the reel rolling
errs.append(f"frame {i}: {type(exc).__name__}: {exc}")
proc.stdin.write(last.tobytes())
proc.stdin.close()
proc.wait()
return idx, f1 - f0, time.time() - t0, errs''')
s=s.replace(''' for idx, cnt, dt in pool.imap_unordered(_work, jobs):
done += cnt''',''' failures: list[str] = []
for idx, cnt, dt, errs in pool.imap_unordered(_work, jobs):
done += cnt
failures += errs''')
s=s.replace(''' lst = CHUNKS / "list.txt"''',''' if failures:
print(f"\\n !! {len(failures)} frames failed to render:")
for line in failures[:12]:
print(" " + line)
if len(failures) > 12:
print(f" … and {len(failures) - 12} more")
lst = CHUNKS / "list.txt"''')
open(p,'w').write(s)
# preflight: sweep the whole film cheaply before committing to an encode
s=open(p).read()
s=s.replace('''def still(frame_index: int, path: Path, size=(W, H)) -> Path:''',
'''def preflight(step: int = 5, size=(480, 270)) -> list[str]:
"""Render every ``step``-th frame small, to find crashes before encoding."""
tl = build_timeline()
bad = []
for i in range(0, tl.frames, step):
try:
render_frame(tl, i, size)
except Exception as exc:
bad.append(f"frame {i} (t={i/FPS:6.1f}s, {tl.at(i/FPS).act.scene}): "
f"{type(exc).__name__}: {exc}")
return bad
def still(frame_index: int, path: Path, size=(W, H)) -> Path:''')
open(p,'w').write(s)
p='src/catfilm/cli.py'
s=open(p).read()
s=s.replace(''' b = sub.add_parser("build", help="audio + picture + mux")''',
''' pf = sub.add_parser("preflight", help="sweep every Nth frame for crashes")
pf.add_argument("--step", type=int, default=5)
b = sub.add_parser("build", help="audio + picture + mux")''')
s=s.replace(''' if ns.cmd == "build":''',''' if ns.cmd == "preflight":
from .build import preflight
import multiprocessing as mp
bad = preflight(ns.step)
print(f" {len(bad)} failing frames")
for line in bad[:30]:
print(" " + line)
return 1 if bad else 0
if ns.cmd == "build":''')
open(p,'w').write(s); print("patched")
PY
echo "--- preflight (every 3rd frame, ~5100 frames) ---"
time uv run catfilm preflight --step 3 2>&1 | tail -20
04:35:28Preflight is clean. Re-rendering with resilient workers and a faster encoder preset:
04:35:29
Bash — Re-render the complete film
rm -rf out/chunks && uv run catfilm build --crf 16 --preset fast 2>&1 | tail -40
04:35:34
Bash — Wait for the film
until [ -f out/functor.mp4 ]; do sleep 10; done; echo READY
04:35:41While it renders, let me set up the docs images so the README renders on GitHub:
04:35:48
Bash — Wire gallery to emit web-sized docs images
python3 - <<'PY'
p='src/catfilm/gallery.py'
s=open(p).read()
s=s.replace('from .config import BG, GALLERY, GENERATORS, INK, INK_DIM, RULE',
'from .config import BG, GALLERY, GENERATORS, INK, INK_DIM, ROOT, RULE')
s=s.replace(''' # a contact sheet of the whole family''',''' # web-sized copies, so the README has something to show
docs = ROOT / "docs"
docs.mkdir(exist_ok=True)
for src in (GALLERY / "plate_sierpinski.png", GALLERY / "plate_conjugate.png"):
im = Image.open(src)
im.resize((1280, int(1280 * im.height / im.width)), Image.LANCZOS).save(
docs / src.name, optimize=True)
# a contact sheet of the whole family''')
s=s.replace(''' p = GALLERY / "family.png"
Image.fromarray(np.concatenate(rows, axis=0)).save(p)
print(" ", p.name)''',''' p = GALLERY / "family.png"
fam = Image.fromarray(np.concatenate(rows, axis=0))
fam.save(p)
fam.resize((1640, int(1640 * fam.height / fam.width)), Image.LANCZOS).save(
docs / "family.png", optimize=True)
print(" ", p.name)''')
open(p,'w').write(s)
p='README.md'
s=open(p).read()
s=s.replace('out/gallery/plate_sierpinski.png','docs/plate_sierpinski.png')
s=s.replace('out/gallery/plate_conjugate.png','docs/plate_conjugate.png')
s=s.replace('out/gallery/family.png','docs/family.png')
open(p,'w').write(s)
p='.gitignore'
s=open(p).read().replace('out/frames/','out/frames/\nout/gallery/\nout/cache/\nout/chunks/')
open(p,'w').write(s)
print("ok")
PY
cat .gitignore && grep -n 'docs/' README.md
04:35:53
Bash — Check render progress
ls out/chunks/*.mp4 2>/dev/null | wc -l; du -sh out/chunks 2>/dev/null
04:36:05
Bash — Wait for render to near completion
until [ "$(ls out/chunks/*.mp4 2>/dev/null | wc -l)" -ge 25 ]; do sleep 15; done; echo "chunks: $(ls out/chunks/*.mp4 | wc -l)"
04:42:44
Bash — Wait for mux and inspect the film
until [ -f out/functor.mp4 ]; do sleep 8; done; sleep 2; echo "=== DONE ==="; tail -6 /private/tmp/claude-501/-Users-bowiesmith-repos-llm-video-repos-category-theory-opus-5-max-claude-code/af4e5c83-3019-4c3a-8cd5-9aff1cfa8267/tasks/bne1z90o6.output; ls -la out/functor.mp4; ffprobe -v error -show_entries format=duration,bit_rate -show_entries stream=codec_type,codec_name,width,height,nb_frames,sample_rate -of default=nw=1 out/functor.mp4
04:50:52
Bash — Wait for mux and read the log
until [ -f out/functor.mp4 ]; do sleep 8; done; cat /private/tmp/claude-501/-Users-bowiesmith-repos-llm-video-repos-category-theory-opus-5-max-claude-code/af4e5c83-3019-4c3a-8cd5-9aff1cfa8267/tasks/bne1z90o6.output | tail -12
04:53:54
Bash — Check for the finished film and read log
ls -la out/functor.mp4 2>/dev/null; tail -14 /private/tmp/claude-501/-Users-bowiesmith-repos-llm-video-repos-category-theory-opus-5-max-claude-code/af4e5c83-3019-4c3a-8cd5-9aff1cfa8267/tasks/bne1z90o6.output
04:54:09Rendered clean, but 2.9 GB — the per-frame film grain is incompressible. Let me measure the tradeoff:
04:54:18
Bash — Measure grain and CRF impact on file size
cd "$CLAUDE_JOB_DIR/tmp" 2>/dev/null || cd ~/.claude/jobs/e7f5c640/tmp
cat > enc_test.py <<'PY'
import subprocess, os, sys, time
sys.path.insert(0,'~/repos/llm-video-repos/category-theory-opus-5-max-claude-code/src')
import numpy as np
from catfilm.timeline import build
from catfilm.build import render_frame
import catfilm.render.canvas as canvas
tl = build()
F0 = int(4*60*20*30/30) # ~ inside the bloom hold
F0 = int(262*30)
N = 120
orig_finish = canvas.Frame.finish
def make(grain):
def finish(self, vignette=0.42, gr=0.010, lift=0.0, seed=0, **kw):
return orig_finish(self, vignette=vignette, grain=grain, lift=lift, seed=seed)
return finish
for grain in (0.010, 0.006, 0.003):
canvas.Frame.finish = make(grain)
frames = [render_frame(tl, F0+i, (1920,1080)) for i in range(N)]
for crf, preset in ((16,'fast'),(20,'fast'),(22,'slow'),(20,'slow')):
out=f"g{grain}_crf{crf}_{preset}.mp4"
p=subprocess.Popen(["ffmpeg","-hide_banner","-loglevel","error","-y","-f","rawvideo",
"-pix_fmt","rgb24","-s","1920x1080","-r","30","-i","-","-an","-c:v","libx264",
"-preset",preset,"-crf",str(crf),"-pix_fmt","yuv420p","-g","60",
"-x264-params","keyint=60:min-keyint=60:scenecut=0",out],stdin=subprocess.PIPE)
for f in frames: p.stdin.write(f.tobytes())
p.stdin.close(); p.wait()
mb=os.path.getsize(out)/1e6
print(f"grain {grain:.3f} crf {crf} {preset:5s}: {mb:6.1f} MB / {N/30:.0f}s -> {mb/(N/30)*509:6.0f} MB for the film")
canvas.Frame.finish = orig_finish
PY
uv run --project ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code python enc_test.py
04:56:27
Bash — Check partial encode-test results
cd ~/.claude/jobs/e7f5c640/tmp && ls -la *.mp4 2>/dev/null | awk '{printf "%-32s %8.1f MB\n", $9, $5/1e6}'
04:56:47CRF is the dominant lever. Let me also make the grain temporally coherent — a small cycling bank instead of pure per-frame noise, which compresses vastly better:
04:56:58
Bash — Test cycling grain bank against CRF on the busiest section
python3 - <<'PY'
p='src/catfilm/render/canvas.py'
s=open(p).read()
s=s.replace(''' if grain > 0:
rng = np.random.default_rng(seed * 2654435761 % (2**32))
n = rng.standard_normal((self.h, self.w, 1)).astype(np.float32)
img = np.clip(img + n * grain * (0.30 + 0.70 * (1 - img)), 0, 1)
return (img * 255.0 + 0.5).astype(np.uint8)''',
''' if grain > 0:
# A small bank of fixed fields, cycled — grain on the print rather
# than noise in the signal. It breaks up banding in the dark
# gradients without costing the encoder a fortune in bitrate.
n = _grain(self.w, self.h, seed % GRAIN_BANK)
img = np.clip(img + n * grain * (0.30 + 0.70 * (1 - img)), 0, 1)
return (img * 255.0 + 0.5).astype(np.uint8)''')
s=s.replace('''@lru_cache(maxsize=8)
def _vignette''','''GRAIN_BANK = 4
@lru_cache(maxsize=GRAIN_BANK)
def _grain(w: int, h: int, i: int) -> np.ndarray:
rng = np.random.default_rng(0xC47 + i * 7919)
return rng.standard_normal((h, w, 1)).astype(np.float32)
@lru_cache(maxsize=8)
def _vignette''')
open(p,'w').write(s); print("ok")
PY
cd ~/.claude/jobs/e7f5c640/tmp && cat > enc2.py <<'PY'
import subprocess, os, sys
sys.path.insert(0,'~/repos/llm-video-repos/category-theory-opus-5-max-claude-code/src')
from catfilm.timeline import build
from catfilm.build import render_frame
tl = build()
F0 = int(283*30) # inside the variants morph — the busiest motion in the film
N = 90
frames=[render_frame(tl,F0+i,(1920,1080)) for i in range(N)]
for crf,preset in ((16,'medium'),(19,'medium'),(20,'medium'),(21,'medium')):
out=f"v_crf{crf}.mp4"
p=subprocess.Popen(["ffmpeg","-hide_banner","-loglevel","error","-y","-f","rawvideo",
"-pix_fmt","rgb24","-s","1920x1080","-r","30","-i","-","-an","-c:v","libx264",
"-preset",preset,"-crf",str(crf),"-pix_fmt","yuv420p","-g","60",
"-x264-params","keyint=60:min-keyint=60:scenecut=0",out],stdin=subprocess.PIPE)
for f in frames: p.stdin.write(f.tobytes())
p.stdin.close(); p.wait()
mb=os.path.getsize(out)/1e6
print(f"cycling grain, crf {crf} {preset}: {mb:5.2f} MB / {N/30:.0f}s -> ~{mb/(N/30)*509:5.0f} MB film")
PY
uv run --project ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code python enc2.py
04:57:46Let me verify CRF 20 doesn't visibly hurt this content before committing:
04:57:50
Bash — Compare CRF levels visually and by PSNR
cd ~/.claude/jobs/e7f5c640/tmp && for c in 16 20 21; do ffmpeg -hide_banner -loglevel error -y -i v_crf$c.mp4 -vf "select=eq(n\,45),crop=760:560:820:280" -frames:v 1 crop$c.png; done && uv run --project ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code python -c "
from PIL import Image; import numpy as np
a=[np.array(Image.open(f'crop{c}.png').convert('RGB')) for c in (16,20,21)]
print('PSNR 16 vs 20:', round(10*np.log10(255**2/((a[0].astype(float)-a[1])**2).mean()),1),'dB')
print('PSNR 16 vs 21:', round(10*np.log10(255**2/((a[0].astype(float)-a[2])**2).mean()),1),'dB')
Image.fromarray(np.concatenate(a,axis=1)).save('~/repos/llm-video-repos/category-theory-opus-5-max-claude-code/out/gallery/crf.png')"
04:57:55
Read ← ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code/out/gallery/crf.png
04:57:56 · 🖼 image returned to Claude — [Image: original 2280x560, displayed at 2000x491. Multiply coordinates by 1.14 to map to original image.]
04:58:08CRF 20 is visually indistinguishable at 100%. Locking that in and cleaning up the code:
04:58:25
Bash — Apply CRF/grain settings, clean dead code, verify
python3 - <<'PY'
import re, glob
# grain: the cycling bank means less is needed
for f in glob.glob('src/catfilm/scenes/*.py'):
s=open(f).read()
s2=s.replace('grain=0.010','grain=0.007').replace('grain=0.009','grain=0.007').replace('grain=0.006, seed=ctx.frame','grain=0.007, seed=ctx.frame')
if s2!=s: open(f,'w').write(s2)
s=open('src/catfilm/cli.py').read()
s=s.replace('r.add_argument("--crf", type=int, default=16)','r.add_argument("--crf", type=int, default=20)')
s=s.replace('b.add_argument("--crf", type=int, default=16)','b.add_argument("--crf", type=int, default=20)')
open('src/catfilm/cli.py','w').write(s)
s=open('src/catfilm/build.py').read().replace('crf=16, preset="medium"','crf=20, preset="medium"')
open('src/catfilm/build.py','w').write(s)
# bloom: say what it does, without the leftovers
p='src/catfilm/scenes/bloom.py'
s=open(p).read()
s=s.replace('''@lru_cache(maxsize=8)
def _tris(depth: int):
"""Every word of length ``depth``, as a triangle and the colour of its word."""
out = []
for w in words(LETTERS, depth):
arr = SYS.functor()(SYSTEMS["sierpinski"].functor().source.source_of(w, "•"))
out.append((arr.apply(UNIT_TRIANGLE), word_color(w)))
return tuple(out)''',
'''@lru_cache(maxsize=8)
def _tris(depth: int):
"""Every word of length ``depth``, as a triangle and the colour of its word.
``F(w)`` is evaluated by the functor itself — the triangles are not laid out
by a recursion written here, they are the images of the words.
"""
return tuple(
(FUN(MONOID.source_of(w, "•")).apply(UNIT_TRIANGLE), word_color(w))
for w in words(LETTERS, depth)
)''')
s=s.replace(''' F = SYS.functor()
M = SYS.source_maps if False else SYS.maps
base = UNIT_TRIANGLE''',''' M = SYS.maps
base = UNIT_TRIANGLE''')
s=s.replace(''' col = mix(GENERATORS[0], GENERATORS[1], k1)
polyline(c, to_screen(cur, xs, ys, S), color=col, alpha=0.98,
width=2.6, close=True, glow=0.45)
_w = "ab"
draw_text''',''' col = mix(GENERATORS[0], GENERATORS[1], k1)
polyline(c, to_screen(cur, xs, ys, S), color=col, alpha=0.98,
width=2.6, close=True, glow=0.45)
draw_text''')
s=s.replace('from ..ifs import LETTERS, SYSTEMS, UNIT_TRIANGLE, chaos_game',
'from ..ifs import LETTERS, MONOID, SYSTEMS, UNIT_TRIANGLE, chaos_game')
open(p,'w').write(s)
# natural: let the code prove the square commutes at the moment it draws it
p='src/catfilm/scenes/natural.py'
s=open(p).read()
s=s.replace('''@lru_cache(maxsize=8)
def _corner(kind: str, w: int, h: int):
"""The four pictures of the naturality square, in a shared frame."""
xy, rgb = _cloud()
T = {"tl": None, "tr": FW, "bl": ALPHA,
"br": ALPHA.then(Aff.identity()) if False else None}[kind]
if kind == "br":
pts = ALPHA.apply(FW.apply(xy)) # = G(w) applied to α — same thing
elif T is None:
pts = xy
else:
pts = T.apply(xy)''',
'''@lru_cache(maxsize=8)
def _corner(kind: str, w: int, h: int):
"""The four pictures of the naturality square, in a shared frame.
The bottom-right corner is reachable two ways, and the assertion below is
the whole point of the scene: going across then down gives the same picture,
pixel for pixel, as going down then across.
"""
xy, rgb = _cloud()
if kind == "tl":
pts = xy
elif kind == "tr":
pts = FW.apply(xy) # F(w)
elif kind == "bl":
pts = ALPHA.apply(xy) # α
else:
across_then_down = ALPHA.apply(FW.apply(xy)) # α ∘ F(w)
down_then_across = GW.apply(ALPHA.apply(xy)) # G(w) ∘ α
assert np.allclose(across_then_down, down_then_across, atol=1e-9)
pts = across_then_down''')
open(p,'w').write(s); print("ok")
PY
uv run python -m catfilm.laws 2>&1 | tail -3 && echo "--- preflight ---" && uv run catfilm preflight --step 4 2>&1 | tail -6
04:59:46
Bash — Final render at CRF 20
rm -f out/functor.mp4 out/picture.mp4 && rm -rf out/chunks && uv run catfilm build 2>&1 | tail -30
04:59:54
Bash — Wait for the final render
until [ -f out/functor.mp4 ]; do sleep 15; done; sleep 3; ls -la out/functor.mp4; tail -6 /private/tmp/claude-501/-Users-bowiesmith-repos-llm-video-repos-category-theory-opus-5-max-claude-code/e7f5c640-4511-40bd-95f5-fa35e413aa34/tasks/besa1tqki.output
05:10:00
Bash — Check render progress
tail -3 /private/tmp/claude-501/-Users-bowiesmith-repos-llm-video-repos-category-theory-opus-5-max-claude-code/e7f5c640-4511-40bd-95f5-fa35e413aa34/tasks/besa1tqki.output; du -sh out/chunks
05:10:26
Bash — Compute matching framing between bloom and variants
uv run python -c "
from catfilm.scenes._common import _fit
from catfilm.config import W,H
c,s = _fit('sierpinski', W, H, 0.74)
xs = W/2 - c[0]*s; ys = H/2 + c[1]*s
print(f'variants framing in design space: xs={xs:.1f} ys={ys:.1f} S={s:.1f}')
print('bloom BIG currently: (960, 558, 862)')
"
05:10:52Two seam issues to fix (bloom→variants has a brightness dip and a scale pop). Letting the render finish first so I can batch all fixes after a QC pass:
05:10:56
Bash — Wait for render completion
until [ -f out/functor.mp4 ]; do sleep 20; done; sleep 5; ls -la out/functor.mp4; grep -E "picture:|✦|!!" /private/tmp/claude-501/-Users-bowiesmith-repos-llm-video-repos-category-theory-opus-5-max-claude-code/e7f5c640-4511-40bd-95f5-fa35e413aa34/tasks/besa1tqki.output
05:17:50247 MB, zero failed frames. Now a QC pass on the actual encoded film:
05:17:54
Bash — Extract QC frames from the encoded film
ffprobe -v error -show_entries format=duration -show_entries stream=index,codec_type,codec_name,width,height,r_frame_rate,sample_rate,channels -of default=nw=1 out/functor.mp4
echo "--- extracting QC strip from the encoded film ---"
mkdir -p out/qc && rm -f out/qc/*.png
for i in $(seq 0 23); do
T=$(python3 -c "print(f'{6 + $i*(503-6)/23:.2f}')")
ffmpeg -hide_banner -loglevel error -y -ss $T -i out/functor.mp4 -frames:v 1 -vf scale=640:-2 out/qc/q$(printf %02d $i).png
done
uv run python -c "
from PIL import Image; import numpy as np, glob
fs=sorted(glob.glob('out/qc/q*.png'))
a=[np.array(Image.open(f).convert('RGB')) for f in fs]
rows=[np.concatenate(a[i:i+4],1) for i in range(0,24,4)]
Image.fromarray(np.concatenate(rows,0)).save('out/qc/strip1.png')
Image.fromarray(np.concatenate(rows[:3],0)).save('out/qc/stripA.png')
Image.fromarray(np.concatenate(rows[3:],0)).save('out/qc/stripB.png')
print('ok', len(a))"
05:18:04
Read ← ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code/out/qc/stripA.png
05:18:04 · 🖼 image returned to Claude — [Image: original 2560x1080, displayed at 2000x844. Multiply coordinates by 1.28 to map to original image.]
05:18:09
Read ← ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code/out/qc/stripB.png
05:18:09 · 🖼 image returned to Claude — [Image: original 2560x1080, displayed at 2000x844. Multiply coordinates by 1.28 to map to original image.]
05:18:37The film reads well end to end. Let me check the one composition problem I can see — the category act:
05:18:39
Bash — Extract category and finale frames at full res
ffmpeg -hide_banner -loglevel error -y -ss 88 -i out/functor.mp4 -frames:v 1 out/qc/cat.png && ffmpeg -hide_banner -loglevel error -y -ss 470 -i out/functor.mp4 -frames:v 1 out/qc/fin.png && uv run python -c "
from PIL import Image; import numpy as np
a=[np.array(Image.open(f'out/qc/{k}.png').convert('RGB'))[::2,::2] for k in ('cat','fin')]
Image.fromarray(np.concatenate(a,0)).save('out/qc/cmp.png')"
05:18:46
Read ← ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code/out/qc/cmp.png
05:19:04Two fixes needed: the category act is top-heavy, and the Yoneda closing text is fighting the burst. Applying all fixes:
05:19:15
Bash — Apply composition and seam fixes, verify
python3 - <<'PY'
# 1. category: bring the chain toward the optical centre
p='src/catfilm/scenes/category.py'
s=open(p).read().replace("Y = CY - 96","Y = CY - 44")
s=s.replace('draw_text(c, "( h ∘ g ) ∘ f = h ∘ ( g ∘ f )", CX, Y + 320,','draw_text(c, "( h ∘ g ) ∘ f = h ∘ ( g ∘ f )", CX, Y + 300,')
open(p,'w').write(s)
# 2. bloom: end on exactly the framing the next act opens with, so the cut is a cut
p='src/catfilm/scenes/bloom.py'
s=open(p).read().replace("BIG = (CX, CY + 18, 862.0) # plane, once it takes the frame",
"BIG = (CX, 534.7, 941.5) # matches how `variants` frames it")
open(p,'w').write(s)
# 3. variants: the picture is already on screen — don't fade it up from black
p='src/catfilm/scenes/variants.py'
s=open(p).read().replace(" fr.add(img, ctx.envelope)",
" # the previous act ends on this exact picture, so there is no fade in here\n fr.add(img, ctx.fade_out(0.9))")
open(p,'w').write(s)
# 4. yoneda: let the last line breathe
p='src/catfilm/scenes/yoneda.py'
s=open(p).read()
s=s.replace("base = (0.075 + 0.105 * hollow) * (1 - close * 0.72)","base = (0.075 + 0.105 * hollow) * (1 - close * 0.88)")
s=s.replace("paint(col, 0.95 * hollow * (1 - close * 0.62)))","paint(col, 0.95 * hollow * (1 - close * 0.88)))")
s=s.replace("a = clamp01((build - j * 0.045) / 0.3) * (1 - close * 0.6)","a = clamp01((build - j * 0.045) / 0.3) * (1 - close * 0.85)")
open(p,'w').write(s)
# 5. finale: the tour moves fast, so give each frame more light to work with
p='src/catfilm/scenes/finale.py'
s=open(p).read().replace("n=900_000, margin=0.80, exposure=2.3, bloom=0.68",
"n=1_300_000, margin=0.80, exposure=2.5, bloom=0.70")
open(p,'w').write(s)
print("ok")
PY
uv run catfilm still 1:28 -o out/qc/cat2.png && uv run catfilm still y8 -o out/qc/yon2.png && uv run python -c "
from PIL import Image; import numpy as np
a=[np.array(Image.open(f'out/qc/{k}.png').convert('RGB'))[::2,::2] for k in ('cat2','yon2')]
Image.fromarray(np.concatenate(a,0)).save('out/qc/cmp.png')"
05:19:22
Read ← ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code/out/qc/cmp.png
05:19:32Both fixed. Let me verify the bloom→variants seam is now continuous:
05:19:37
Bash — Check the bloom-to-variants seam
uv run python - <<'PY'
from PIL import Image
import numpy as np
from catfilm.timeline import build
from catfilm.build import render_frame
from catfilm.config import FPS
tl=build()
b=[a for a in tl.acts if a.act.scene=="bloom"][0]
print(f"bloom ends / variants begins at {b.end:.2f}s (frame {int(b.end*FPS)})")
fs=[int(b.end*FPS)+d for d in (-12,-1,0,1,12,30)]
ims=[render_frame(tl,f,(640,360)) for f in fs]
Image.fromarray(np.concatenate([np.concatenate(ims[:3],1),np.concatenate(ims[3:],1)],0)).save("out/qc/seam.png")
print("mean luminance across the cut:", [round(float(i.mean()),1) for i in ims])
PY
05:19:44
Read ← ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code/out/qc/seam.png
05:19:51Seam is now seamless — the triangle holds position and brightness across the cut while the rail fades in over it. Final render:
05:19:52
Bash — Preflight and final film render
uv run catfilm preflight --step 4 2>&1 | tail -3 && rm -f out/functor.mp4 out/picture.mp4 && rm -rf out/chunks && uv run catfilm build 2>&1 | tail -6
05:20:02
Bash — Wait for the final render
until [ -f out/functor.mp4 ]; do sleep 20; done; sleep 4; ls -la out/functor.mp4; grep -E "✦|!!|failing" /private/tmp/claude-501/-Users-bowiesmith-repos-llm-video-repos-category-theory-opus-5-max-claude-code/e7f5c640-4511-40bd-95f5-fa35e413aa34/tasks/bq1i56ma1.output
05:20:15
Bash — Check whether the render actually started
cat /private/tmp/claude-501/-Users-bowiesmith-repos-llm-video-repos-category-theory-opus-5-max-claude-code/e7f5c640-4511-40bd-95f5-fa35e413aa34/tasks/bq1i56ma1.output 2>/dev/null | tail -5; echo "--- chunks ---"; ls out/chunks/*.mp4 2>/dev/null | wc -l; ls -la out/functor.mp4 2>/dev/null
05:20:32
Bash — Inspect file state and running processes
stat -f '%N size=%z mtime=%Sm' out/functor.mp4 out/picture.mp4 2>/dev/null; echo "--- log ---"; wc -c /private/tmp/claude-501/-Users-bowiesmith-repos-llm-video-repos-category-theory-opus-5-max-claude-code/e7f5c640-4511-40bd-95f5-fa35e413aa34/tasks/bq1i56ma1.output; echo "--- running ---"; ps aux | grep -ci "[c]atfilm\|[p]ython3" ; ps aux|grep -c "[f]fmpeg"; du -sh out/chunks
05:20:44
Bash — Identify running processes for this project
ps aux | grep "[c]ategory-theory" | awk '{printf "%5s %5s %s\n",$3,$4,substr($0,index($0,$11),110)}' | head -8; echo "--- task status ---"; ls -la /private/tmp/claude-501/-Users-bowiesmith-repos-llm-video-repos-category-theory-opus-5-max-claude-code/e7f5c640-4511-40bd-95f5-fa35e413aa34/tasks/ | tail -5
05:20:55Preflight is still running (single-threaded). Waiting on the actual file change this time:
05:20:58
Bash — Wait for the film file to be rewritten
OLD=$(stat -f %m out/functor.mp4); until [ "$(stat -f %m out/functor.mp4 2>/dev/null || echo 0)" != "$OLD" ]; do sleep 20; done; sleep 5; stat -f '%N size=%z mtime=%Sm' out/functor.mp4; grep -E "✦|!!|failing" /private/tmp/claude-501/-Users-bowiesmith-repos-llm-video-repos-category-theory-opus-5-max-claude-code/e7f5c640-4511-40bd-95f5-fa35e413aa34/tasks/bq1i56ma1.output
05:21:31Preflight clean (0 failing frames). Waiting for the render:
05:21:33
Bash — Wait for the final film
until [ -f out/functor.mp4 ]; do sleep 20; done; sleep 5; stat -f '%N %z bytes' out/functor.mp4; grep -E "✦|!!" /private/tmp/claude-501/-Users-bowiesmith-repos-llm-video-repos-category-theory-opus-5-max-claude-code/e7f5c640-4511-40bd-95f5-fa35e413aa34/tasks/bq1i56ma1.output
05:31:39
Bash — Check render progress
ls out/chunks/*.mp4 2>/dev/null | wc -l; du -sh out/chunks 2>/dev/null; tail -2 /private/tmp/claude-501/-Users-bowiesmith-repos-llm-video-repos-category-theory-opus-5-max-claude-code/e7f5c640-4511-40bd-95f5-fa35e413aa34/tasks/bq1i56ma1.output
05:31:45
Bash — Wait for final film
until [ -f out/functor.mp4 ]; do sleep 25; done; sleep 6; stat -f '%N %z bytes' out/functor.mp4; grep -E "✦|!!" /private/tmp/claude-501/-Users-bowiesmith-repos-llm-video-repos-category-theory-opus-5-max-claude-code/e7f5c640-4511-40bd-95f5-fa35e413aa34/tasks/bq1i56ma1.output
05:39:51The film is done — 246 MB, zero failed frames. Now the gallery plates:
05:39:52
Bash — Render the generative-art gallery plates
rm -rf out/chunks out/picture.mp4 out/qc && uv run catfilm gallery --size 2400 2>&1 | tail -14 && ls -la docs/
05:40:10
Read ← ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code/docs/plate_sierpinski.png
05:40:22The matrix rows collide with the triangle. Let me offset the composition:
05:40:35
Bash — Offset plate composition and re-render gallery
python3 - <<'PY'
p='src/catfilm/gallery.py'
s=open(p).read()
s=s.replace('''def _plate(system, w, h, *, n=6_000_000, margin=0.80, exposure=2.4, seed=7,
title=None, subtitle=None, matrices=True, caption=None):
fr = Frame(w, h)
xy, rgb = chaos_game(system, n, seed=seed)
ctr, scl = fit_scale(xy, (w, h), margin)
fr.add(render_points(xy, rgb, (w, h), ctr, scl, exposure=exposure,
bloom_strength=0.62, ss=2))''',
'''def _plate(system, w, h, *, n=6_000_000, margin=0.80, exposure=2.4, seed=7,
title=None, subtitle=None, matrices=True, caption=None, shift=0.0):
fr = Frame(w, h)
xy, rgb = chaos_game(system, n, seed=seed)
ctr, scl = fit_scale(xy, (w, h), margin)
ctr = (ctr[0] - shift * w / scl, ctr[1]) # leave the annotation column clear
fr.add(render_points(xy, rgb, (w, h), ctr, scl, exposure=exposure,
bloom_strength=0.62, ss=2))''')
s=s.replace(''' img = _plate(sysm, width, h, title=sysm.name, subtitle=sysm.subtitle,
caption="the free monoid on {a, b, c}, translated")''',
''' img = _plate(sysm, width, h, margin=0.74, shift=0.055,
title=sysm.name, subtitle=sysm.subtitle,
caption="the free monoid on {a, b, c}, translated")''')
s=s.replace(''' img = _plate(conj, width, h, title="α · Sierpiński · α⁻¹",''',
''' img = _plate(conj, width, h, margin=0.74, shift=0.055,
title="α · Sierpiński · α⁻¹",''')
s=s.replace(''' y = h - pad - int(96 * k)''',''' y = h - pad - int(88 * k)''')
open(p,'w').write(s); print("ok")
PY
uv run catfilm gallery --size 2400 2>&1 | tail -3
05:40:52
Read ← ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code/docs/plate_conjugate.png
05:41:29The conjugate plate reveals a precision problem in my own narration: conjugating scalar maps leaves the linear parts untouched, so "different in every number" overclaims. Let me check the family sheet, then fix the language:
05:41:30
Read ← ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code/docs/family.png
05:41:42The family sheet is strong. Let me fix the overclaim, tighten the grid, and do the last render:
05:41:55
Bash — Fix the overclaim in narration, on-screen text, and docs
python3 - <<'PY'
# The linear parts of the Sierpiński maps are scalar, so conjugation moves the
# translations only. Say what is actually true — it is just as strong a line.
p='src/catfilm/script.py'
s=open(p).read()
s=s.replace('B("n10", "Apply that one map on both sides of every arrow, "\n "and you get a new functor — three completely different matrices.", hold=1.2),',
'B("n10", "Apply that one map on both sides of every arrow, "\n "and you get a new functor — a different set of three matrices.", hold=1.2),')
s=s.replace('B("n13", "Different in every number. Identical in every relationship.", hold=1.8),',
'B("n13", "Different matrices. And not one relationship disturbed.", hold=1.8),')
open(p,'w').write(s)
p='src/catfilm/scenes/natural.py'
s=open(p).read().replace('draw_text(c, "different in every number · identical in every "\n "relationship", CX, H - 48,',
'draw_text(c, "different matrices · not one relationship disturbed",\n CX, H - 48,')
s=s.replace(''' alpha=a13, align="center",
reveal=clamp01((ctx.since("n13") - 0.4) / 2.4))''',
''' size=33, color=INK, alpha=a13, align="center",
reveal=clamp01((ctx.since("n13") - 0.4) / 2.4))''')
s=s.replace('''CX, H - 48, size=33, color=INK,
size=33, color=INK,''','''CX, H - 48,
size=33, color=INK,''')
open(p,'w').write(s)
p='src/catfilm/gallery.py'
s=open(p).read()
s=s.replace('caption="different in every number · identical in every relationship")',
'caption="a different set of matrices · not one relationship disturbed")')
s=s.replace(''' # a contact sheet of the whole family
tiles = []
tw = width // 3 // 2 * 2''',''' # a contact sheet of the whole family, with the conjugate as its eighth face
tiles = []
tw = width // 4 // 2 * 2''')
s=s.replace(''' for key, sysm in SYSTEMS.items():
tiles.append(_plate(sysm, tw, th, n=2_200_000, title=sysm.name,
subtitle=None, matrices=False))
while len(tiles) % 3:
tiles.append(np.zeros_like(tiles[0]))
rows = [np.concatenate(tiles[i:i + 3], axis=1) for i in range(0, len(tiles), 3)]''',
''' for sysm in list(SYSTEMS.values()) + [conj]:
tiles.append(_plate(sysm, tw, th, n=2_200_000, title=sysm.name,
subtitle=None, matrices=False))
while len(tiles) % 4:
tiles.append(np.zeros_like(tiles[0]))
rows = [np.concatenate(tiles[i:i + 4], axis=1) for i in range(0, len(tiles), 4)]''')
s=s.replace('conj = SYSTEMS["sierpinski"].conjugate(alpha, "Sierpiński, conjugated")',
'conj = SYSTEMS["sierpinski"].conjugate(alpha, "α · Sierpiński · α⁻¹")')
s=s.replace(' img = _plate(conj, width, h, margin=0.74, shift=0.055,\n title="α · Sierpiński · α⁻¹",',
' img = _plate(conj, width, h, margin=0.74, shift=0.055,\n title=conj.name,')
open(p,'w').write(s)
p='README.md'
s=open(p).read().replace('Different in every number. Identical in every relationship.',
'A different set of matrices. Not one relationship disturbed.')
open(p,'w').write(s)
print("ok")
PY
sed -n '/n13/p;/n10/p' src/catfilm/script.py && grep -n "different matrices" src/catfilm/scenes/natural.py
05:42:01
Bash — Verify the edited draw_text block
sed -n '186,196p' src/catfilm/scenes/natural.py
05:42:08
Bash — Regenerate audio and do the final render
uv run catfilm audio 2>&1 | tail -4 && uv run catfilm plan | tail -3 && uv run catfilm preflight --step 6 2>&1 | tail -2 && rm -f out/functor.mp4 && uv run catfilm build 2>&1 | tail -4
05:42:17While the final render runs, let me review the code for leftovers:
05:42:20
Bash — Scan for dead code and unused imports
cd src/catfilm && grep -rn "if False\|TODO\|FIXME\|XXX\|noop\|leftover\|print(" --include=*.py . | grep -v "cli.py\|laws.py\|gallery.py\|build.py\|narration.py" ; echo "--- unused imports (rough) ---"; for f in $(find . -name '*.py'); do
for m in $(grep -oE '^from \.\.?[a-z_.]* import .*' $f | sed 's/.*import //' | tr ',' '\n' | sed 's/ //g' | grep -vE '^\*$'); do
n=$(grep -c "\b$m\b" $f); [ "$n" -le 1 ] && echo "$f: $m";
done
done 2>/dev/null | head -20
05:42:26
Bash — Run ruff for unused imports and variables
cd ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code && uv run --with ruff ruff check src/ --select F401,F811,F841,E711,E712 2>&1 | tail -30
05:42:4485 lint findings, mostly from the import * re-export pattern. I'll fix those after the render (editing scene files mid-render would race with worker imports):
05:42:46
Bash — Check render progress
tail -4 /private/tmp/claude-501/-Users-bowiesmith-repos-llm-video-repos-category-theory-opus-5-max-claude-code/e7f5c640-4511-40bd-95f5-fa35e413aa34/tasks/b39ur1rs4.output; ls out/chunks/*.mp4 2>/dev/null | wc -l
05:42:52
Bash — Wait for the final film
until [ -f out/functor.mp4 ]; do sleep 25; done; sleep 6; stat -f '%N %z bytes %Sm' out/functor.mp4; grep -E "✦|!!|failing" /private/tmp/claude-501/-Users-bowiesmith-repos-llm-video-repos-category-theory-opus-5-max-claude-code/e7f5c640-4511-40bd-95f5-fa35e413aa34/tasks/b39ur1rs4.output
05:43:06
Bash — Wait for the film to be rewritten
OLD=245902515; until [ -f out/functor.mp4 ] && [ "$(stat -f %z out/functor.mp4)" != "$OLD" ]; do sleep 25; done; sleep 6; stat -f '%N %z bytes %Sm' out/functor.mp4; grep -E "✦|!!|failing" /private/tmp/claude-501/-Users-bowiesmith-repos-llm-video-repos-category-theory-opus-5-max-claude-code/e7f5c640-4511-40bd-95f5-fa35e413aa34/tasks/b39ur1rs4.output
05:53:13
Bash — Check render progress
ls out/chunks/*.mp4 2>/dev/null | wc -l; du -sh out/chunks 2>/dev/null; tail -3 /private/tmp/claude-501/-Users-bowiesmith-repos-llm-video-repos-category-theory-opus-5-max-claude-code/e7f5c640-4511-40bd-95f5-fa35e413aa34/tasks/b39ur1rs4.output
05:53:18
Bash — Wait for final mux
OLD=245902515; until [ -f out/functor.mp4 ] && [ "$(stat -f %z out/functor.mp4)" != "$OLD" ]; do sleep 20; done; sleep 6; stat -f '%N %z bytes' out/functor.mp4; grep -E "✦|!!" /private/tmp/claude-501/-Users-bowiesmith-repos-llm-video-repos-category-theory-opus-5-max-claude-code/e7f5c640-4511-40bd-95f5-fa35e413aa34/tasks/b39ur1rs4.output
05:59:30Final film is done. Now the gallery, lint cleanup, and verification:
05:59:34
Bash — Regenerate gallery and clean up lint
rm -rf out/chunks out/picture.mp4 && uv run catfilm gallery --size 2400 2>&1 | tail -3
cat >> pyproject.toml <<'EOF'
[tool.ruff.lint]
select = ["E", "F", "W", "I"]
ignore = ["E501", "E741"]
[tool.ruff.lint.per-file-ignores]
# scenes/_common.py is a deliberate re-export hub: the scenes pull their whole
# vocabulary from it with `import *`, so its imports look unused where they sit.
"src/catfilm/scenes/_common.py" = ["F401"]
"src/catfilm/scenes/*.py" = ["F403", "F405"]
EOF
uv run --with ruff ruff check src/ --fix 2>&1 | tail -20
05:59:54
Bash — List remaining lint findings concisely
uv run --with ruff ruff check src/ --output-format concise 2>&1 | tail -32
06:00:09
Bash — Fix real lint issues and verify nothing broke
python3 - <<'PY'
p='src/catfilm/audio/score.py'
s=open(p).read()
s=s.replace("from functools import lru_cache\n","from functools import lru_cache\nfrom pathlib import Path\n")
s=s.replace('def build_soundtrack() -> "Path":','def build_soundtrack() -> Path:')
open(p,'w').write(s)
p='src/catfilm/scenes/finale.py'
s=open(p).read().replace(" leg = (t1 - t0) / (len(TOUR) - 1)\n","")
open(p,'w').write(s)
p='src/catfilm/scenes/yoneda.py'
s=open(p).read().replace(" fr = stage(ctx, size, dust_alpha=0.7)\n k = fr.k\n"," fr = stage(ctx, size, dust_alpha=0.7)\n")
open(p,'w').write(s)
p='pyproject.toml'
s=open(p).read().replace('ignore = ["E501", "E741"]',
'ignore = [\n "E501", # long lines are fine at this line-length\n "E741",\n "E701", # compact one-line guards are deliberate in the easing helpers\n "E702", # and in the CLI dispatch table\n]')
open(p,'w').write(s); print("ok")
PY
uv run --with ruff ruff check src/ --output-format concise 2>&1 | tail -4
echo "--- laws ---" && uv run python -m catfilm.laws 2>&1 | tail -2
echo "--- preflight ---" && uv run catfilm preflight --step 9 2>&1 | tail -2
06:00:57All green. Final verification — comparing a freshly rendered frame against the encoded film:
06:01:00
Bash — Verify code still produces the rendered film
mkdir -p out/qc && ffmpeg -hide_banner -loglevel error -y -ss 398 -i out/functor.mp4 -frames:v 1 out/qc/from_film.png && uv run catfilm still 398 -o out/qc/from_code.png >/dev/null && uv run python -c "
from PIL import Image; import numpy as np
a=np.array(Image.open('out/qc/from_film.png').convert('RGB')).astype(float)
b=np.array(Image.open('out/qc/from_code.png').convert('RGB')).astype(float)
print('encoded vs freshly-rendered frame @398s — PSNR', round(10*np.log10(255**2/((a-b)**2).mean()),1),'dB (encode-only difference)')
Image.fromarray(np.concatenate([a,b],0)[::3,::3].astype(np.uint8)).save('out/qc/verify.png')"
06:01:07
Read ← ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code/out/qc/verify.png
06:01:24Code reproduces the film exactly. Let me do one thorough QC sweep to catch everything before a final render — the α matrix is colliding with the triangle apex:
06:01:28
Bash — Dense QC sweep of the final film
rm -f out/qc/*.png; for T in 20 34 52 63 78 95 110 130 148 160 172 190 205 218 232 248 262 275 292 308 322 340 356 372 390 404 418 432 446 458 470 484 496; do
ffmpeg -hide_banner -loglevel error -y -ss $T -i out/functor.mp4 -frames:v 1 -vf scale=560:-2 out/qc/t$(printf %03d $T).png; done
uv run python -c "
from PIL import Image; import numpy as np, glob
fs=sorted(glob.glob('out/qc/t*.png')); a=[np.array(Image.open(f).convert('RGB')) for f in fs]
while len(a)%5: a.append(np.zeros_like(a[0]))
rows=[np.concatenate(a[i:i+5],1) for i in range(0,len(a),5)]
for j,g in enumerate([rows[:4],rows[4:]]):
Image.fromarray(np.concatenate(g,0)).save(f'out/qc/sweep{j}.png')
print(len(fs),'frames')"
06:01:38
Read ← ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code/out/qc/sweep0.png
06:01:38 · 🖼 image returned to Claude — [Image: original 2800x1264, displayed at 2000x903. Multiply coordinates by 1.40 to map to original image.]
06:01:51
Read ← ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code/out/qc/sweep1.png
06:01:51 · 🖼 image returned to Claude — [Image: original 2800x948, displayed at 2000x677. Multiply coordinates by 1.40 to map to original image.]
06:02:07Two real issues: the α matrix collides with the apex, and the finale morph clips at frame edges. Let me check them at full res:
06:02:09
Bash — Render the alpha and naturality-square shots at full res
uv run catfilm still n10 -o out/qc/a1.png >/dev/null && uv run catfilm still n12 -o out/qc/a2.png >/dev/null && uv run python -c "
from PIL import Image; import numpy as np
a=[np.array(Image.open(f'out/qc/a{i}.png').convert('RGB'))[::2,::2] for i in (1,2)]
Image.fromarray(np.concatenate(a,0)).save('out/qc/cmp.png')"
06:02:18
Read ← ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code/out/qc/cmp.png
06:02:41Both confirmed. Applying the final fixes:
06:02:53
Bash — Fix alpha placement, enlarge the square, contain the finale
python3 - <<'PY'
p='src/catfilm/scenes/natural.py'
s=open(p).read()
# α's matrix was sitting on the apex of its own picture
s=s.replace('matrix_block(c, ALPHA.mat[:2], CX, 214, size=30, color=A_ROSE,\n alpha=a, label="α ↦", label_color=A_ROSE)',
'matrix_block(c, ALPHA.mat[:2], CX - 556, CY - 30, size=30, color=A_ROSE,\n alpha=a, label="α ↦", label_color=A_ROSE)')
# give the picture-square more of the frame
s=s.replace('PW, PH = 556, 322 # corner picture size',
'PW, PH = 600, 350 # corner picture size')
s=s.replace('CELLS = {"tl": (CX - 410, CY - 214), "tr": (CX + 410, CY - 214),\n "bl": (CX - 410, CY + 194), "br": (CX + 410, CY + 194)}',
'CELLS = {"tl": (CX - 430, CY - 224), "tr": (CX + 430, CY - 224),\n "bl": (CX - 430, CY + 186), "br": (CX + 430, CY + 186)}')
s=s.replace('gap=(PW / 2 - 20, PW / 2 - 8) if j in (0, 3)\n else (PH / 2 - 26, PH / 2 - 18), glow=0.32)',
'gap=(PW / 2 - 25, PW / 2 - 10) if j in (0, 3)\n else (PH / 2 - 30, PH / 2 - 22), glow=0.32)')
s=s.replace('commuting_mark(c, CX, CY - 10, r=24, color=A_MINT, alpha=a, t=com)',
'commuting_mark(c, CX, CY - 19, r=22, color=A_MINT, alpha=a, t=com)')
open(p,'w').write(s)
# the diagram module draws the mark thin; give it presence
p='src/catfilm/render/diagram.py'
s=open(p).read().replace('c.drawPath(path, paint(color, a * 0.9, width=2.0))',
'c.drawPath(path, paint(color, a * 0.95, width=2.6, blur=0.0))\n c.drawPath(path, paint(color, a * 0.35, width=7.0, blur=5.0))')
open(p,'w').write(s)
# the finale tour swings wide mid-morph; keep every frame inside the gate
p='src/catfilm/scenes/finale.py'
s=open(p).read().replace('n=1_300_000, margin=0.80, exposure=2.5, bloom=0.70',
'n=1_300_000, margin=0.68, exposure=2.5, bloom=0.70')
open(p,'w').write(s)
print("ok")
PY
uv run catfilm still n12 -o out/qc/b1.png >/dev/null && uv run catfilm still n10 -o out/qc/b2.png >/dev/null && uv run catfilm still 7:58 -o out/qc/b3.png >/dev/null && uv run python -c "
from PIL import Image; import numpy as np
a=[np.array(Image.open(f'out/qc/b{i}.png').convert('RGB'))[::2,::2] for i in (2,1)]
Image.fromarray(np.concatenate(a,0)).save('out/qc/cmp.png')"
06:03:04
Read ← ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code/out/qc/cmp.png
06:03:14α is now legible and the square is bigger. Final render:
06:03:16
Bash — Final render of the film
uv run catfilm preflight --step 7 2>&1 | tail -2 && rm -f out/functor.mp4 && uv run catfilm build 2>&1 | tail -4
06:03:23
Bash — Stage files and review the tree
git add -A && git status --short | head -30 && echo "--- files ---" && find src docs -type f | sort && wc -l src/catfilm/*.py src/catfilm/*/*.py | tail -1
06:03:35
Bash — Clean gitignore and re-stage
git reset -q && rm -rf out/qc && python3 - <<'PY'
s = """.venv/
__pycache__/
*.pyc
.uv-cache/
.DS_Store
# Everything the build produces. The film, the plates and the audio are
# artefacts of running the code, not part of it; docs/ holds the web-sized
# stills the README needs.
out/
"""
open('.gitignore','w').write(s)
PY
git add -A && git status --short && echo "--- staged file count ---" && git diff --cached --name-only | wc -l
06:03:46
Bash — Wait for the final render
OLD=246306061; until [ -f out/functor.mp4 ] && [ "$(stat -f %z out/functor.mp4)" != "$OLD" ]; do sleep 25; done; sleep 6; stat -f '%N %z bytes' out/functor.mp4; grep -E "✦|!!|failing" /private/tmp/claude-501/-Users-bowiesmith-repos-llm-video-repos-category-theory-opus-5-max-claude-code/e7f5c640-4511-40bd-95f5-fa35e413aa34/tasks/bpt50c8db.output
06:13:56
Bash — Check render progress
ls out/chunks/*.mp4 2>/dev/null | wc -l; tail -2 /private/tmp/claude-501/-Users-bowiesmith-repos-llm-video-repos-category-theory-opus-5-max-claude-code/e7f5c640-4511-40bd-95f5-fa35e413aa34/tasks/bpt50c8db.output
06:14:04
Bash — Wait for final mux
OLD=246306061; until [ -f out/functor.mp4 ] && [ "$(stat -f %z out/functor.mp4)" != "$OLD" ]; do sleep 20; done; sleep 8; stat -f '%N %z bytes' out/functor.mp4; grep -E "✦|!!" /private/tmp/claude-501/-Users-bowiesmith-repos-llm-video-repos-category-theory-opus-5-max-claude-code/e7f5c640-4511-40bd-95f5-fa35e413aa34/tasks/bpt50c8db.output
06:19:58The film is final. Last verification pass, then commit:
06:20:03
Bash — Verify the final encoded film
rm -rf out/chunks out/picture.mp4
echo "=== FILM ==="
ffprobe -v error -show_entries format=duration,size,bit_rate -show_entries stream=codec_type,codec_name,width,height,r_frame_rate,channels -of default=nw=1 out/functor.mp4
echo; echo "=== spot-check the two fixed shots in the encoded film ==="
mkdir -p out/qc
ffmpeg -hide_banner -loglevel error -y -ss 381 -i out/functor.mp4 -frames:v 1 -vf scale=900:-2 out/qc/f1.png
ffmpeg -hide_banner -loglevel error -y -ss 394 -i out/functor.mp4 -frames:v 1 -vf scale=900:-2 out/qc/f2.png
ffmpeg -hide_banner -loglevel error -y -ss 478 -i out/functor.mp4 -frames:v 1 -vf scale=900:-2 out/qc/f3.png
ffmpeg -hide_banner -loglevel error -y -ss 484 -i out/functor.mp4 -frames:v 1 -vf scale=900:-2 out/qc/f4.png
uv run python -c "
from PIL import Image; import numpy as np
a=[np.array(Image.open(f'out/qc/f{i}.png').convert('RGB')) for i in (1,2,3,4)]
Image.fromarray(np.concatenate([np.concatenate(a[:2],1),np.concatenate(a[2:],1)],0)).save('out/qc/final.png')"
06:20:10
Read ← ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code/out/qc/final.png
06:20:25Let me check one transition that looks thin — around 394s:
06:20:29
Bash — Inspect the transition around 394s
uv run python -c "
from catfilm.timeline import build
tl=build()
for k in ['n9','n10','n11','n12','n13']:
s=tl.slots[k]; print(f'{k}: {s.start:7.2f} → speech {s.speech_end:7.2f} → end {s.end:7.2f}')
"
for T in 388 392 394 396 399 403; do ffmpeg -hide_banner -loglevel error -y -ss $T -i out/functor.mp4 -frames:v 1 -vf scale=600:-2 out/qc/g$T.png; done
uv run python -c "
from PIL import Image; import numpy as np, glob
fs=sorted(glob.glob('out/qc/g*.png')); a=[np.array(Image.open(f).convert('RGB')) for f in fs]
print('mean luminance:', [round(float(x.mean()),2) for x in a])
Image.fromarray(np.concatenate([np.concatenate(a[:3],1),np.concatenate(a[3:],1)],0)).save('out/qc/gap.png')"
06:20:53That dip is a deliberate beat before the reveal (luminance 5.7 → 11, not a black frame) — the narrator is saying "let me show you one." Finalizing the README and committing:
06:21:08
Bash — Finalize README and commit
rm -rf out/qc && python3 - <<'PY'
p='README.md'
s=open(p).read()
s=s.replace("Nine minutes, narrated, scored. Every picture in it — and every note — is\ncomputed by evaluating a functor. Nothing is drawn.",
"Eight and a half minutes, narrated, scored. Every picture in it — and every\nnote — is computed by evaluating a functor. Nothing is drawn.")
s=s.replace("Nine minutes of 1080p costs a few hundred megabytes of temporary\nvideo instead of thirty gigabytes of PNGs.",
"The finished film is 1920x1080 at 30fps, 243 MB; rendering it costs a few\nhundred megabytes of temporary video instead of thirty gigabytes of PNGs.")
s=s.replace("""uv run catfilm contact natural # a contact sheet of one act""",
"""uv run catfilm contact natural # a contact sheet of one act
uv run catfilm preflight # sweep every Nth frame for crashes""")
s=s.replace("""```
mise run install # or: uv sync
mise run film # narration + score + picture -> out/functor.mp4
mise run stills # the generative-art plates -> out/gallery/
```""","""```
mise run install # or: uv sync
mise run film # narration + score + picture -> out/functor.mp4 (~20 min)
mise run stills # the generative-art plates -> out/gallery/
Narration uses the macOS say command, so the film builds end-to-end on a Mac
with no API keys and nothing to download. Everything else is portable.""")
open(p,'w').write(s); print("ok")
PY
git add -A && git -c user.name="Bowie Smith" -c user.email="r.bowie.smith@gmail.com" commit -q -F - <<'MSG'
Functor: a short film about category theory
An eight-and-a-half-minute narrated film, and the generative art it makes.
The argument the film makes is that a functor's one law is load-bearing, and the pictures are the evidence. The source category is fixed throughout: one object, three arrows called a, b and c, whose arrows are therefore just the words in three letters. Choosing three affine maps of the plane picks a functor out of it, and functoriality forces everything else. What the words converge to is the picture. Keep the words, change the three matrices, and the same skeleton wears different flesh.
The mathematics is executable, not decorative. Categories, functors and natural
transformations live in core.py with their laws as assertions; catfilm.laws
checks associativity, identity, functoriality, naturality of a real conjugation,
and that every frame of every morph is itself a contractive functor. The scene
that draws the naturality square asserts both routes agree before rendering it.
Notes on the build:
Co-Authored-By: Claude Opus 5 noreply@anthropic.com MSG git log --stat --oneline | head -3; echo "…"; git log -1 --format="%H %an <%ae>"
<sub>`06:21:16`</sub>
**Bash** — Final inventory and checks
```bash
echo "=== deliverables ==="; ls -la out/functor.mp4; ls out/gallery/*.png | sed 's|^| |'; echo; echo "=== repo ==="; git log --oneline; git status --short | head -3; echo "(clean)"; echo; echo "=== checks ==="; uv run python -m catfilm.laws 2>&1 | tail -1; uv run --with ruff ruff check src/ 2>&1 | tail -1
06:21:24
Bash — Remove development scratch images from the gallery
cd out/gallery && rm -f bloom.png cmp.png crf.png diag.png loops.png probe.png tune.png type.png s_*.png sheet_*.png still_*.png && ls | sed 's|^| |'
06:21:45Done. Here's what's in the repo.
out/functor.mp48:29, 1920×1080/30, narrated and scored, 243 MB. Twelve acts: cold open → what a category is → five categories that were already there → the one-object monoid → functors → the first bloom → change the functor → natural transformations (Eilenberg & Mac Lane, 1945) → Yoneda → finale → credits.
Run it again with mise run film (~20 min on 10 cores).
The film keeps one source category fixed throughout: one object, three arrows called a, b, c. Nowhere to go, so all you can do is compose — its arrows are exactly the words in three letters. No geometry, no picture.
Pick a functor out of it into the affine maps of the plane and you get exactly three decisions: what a does, what b does, what c does. Functoriality forces everything else — ab must mean "do a, then b". Ask where the words go and the Sierpiński triangle falls out. Nobody drew it.
Then keep every word and change only the three matrices. The film morphs continuously between functors, and every intermediate frame is itself a valid functor, so it isn't a dissolve between two images — it's one category translated slightly differently every thirtieth of a second.
Two things I'd point out:
a went last, amber b, violet c. The image is painted by its own sentences, and brightness is a direct readout of how many words land on a pixel.core.py isn't decoration. uv run python -m catfilm.laws checks associativity and identity, functoriality for all seven systems, naturality of a genuine conjugation G = α∘F∘α⁻¹ for every word up to length 4, and that every frame of every morph stays contractive. The scene that draws the naturality square computes the bottom-right corner both ways round and asserts they agree before rendering it.
out/gallery/, mise run stillsEight plates at 2400px plus a contact sheet, each annotated with the three matrices that produced it.
Two things worth flagging that I changed along the way:
One thing I did not do: I never listened to the audio. Narration levels are set by measurement (voice sits ~12 dB over the ducked score) and the sync is structural — the timeline is built from the measured duration of each generated line — but the actual sound of Daniel's delivery and the synthesized bells is unverified by ear.
13:41:59The voice in the film doesn't sound natural. Can you fix that?
13:42:30The voice is macOS say with "Daniel" — a legacy concatenative engine, which is exactly why it sounds synthetic. Let me see what better options this machine can reach.
13:42:33
Bash — Check for higher-quality macOS voices on disk
echo "=== installed voice assets (size = quality tier) ==="; ls -la /System/Library/Speech/Voices/ 2>/dev/null | head -20; echo "--- user/downloaded ---"; ls -la ~/Library/Speech/Voices/ 2>/dev/null | head; ls /Library/Speech/Voices/ 2>/dev/null | head; echo "--- AVSpeech premium/enhanced on disk ---"; find /System/Library/Speech /Library/Speech ~/Library/Speech -iname "*.SpeechVoice" -o -iname "*premium*" -o -iname "*enhanced*" 2>/dev/null | head -20
13:42:35
Bash — Check network and Siri voice availability
echo "=== network reachable? ==="; curl -s -o /dev/null -w "pypi:%{http_code} " https://pypi.org/simple/ --max-time 8; curl -s -o /dev/null -w "hf:%{http_code}\n" https://huggingface.co --max-time 8; echo "=== siri-class voices exposed to say? ==="; say -v '?' 2>/dev/null | grep -icE "siri"; say -v '?' 2>/dev/null | awk '{print $NF}' | head -0; say -v '?' 2>/dev/null | wc -l
13:42:52No premium voices installed, but PyPI and HuggingFace are reachable — so a local neural TTS is the fix. Let me try Kokoro (82M params, ONNX, runs on CPU):
13:42:54
Bash — Test kokoro-onnx installability
cd ~/.claude/jobs/e7f5c640/tmp && timeout 300 uv run --no-project --python 3.13 --with kokoro-onnx --with soundfile python -c "
import kokoro_onnx, inspect
print('kokoro-onnx OK', kokoro_onnx.__file__)
print([n for n in dir(kokoro_onnx) if not n.startswith('_')])
" 2>&1 | tail -8
13:43:10
Bash — Install and probe kokoro-onnx API
cd ~/.claude/jobs/e7f5c640/tmp && uv run --no-project --python 3.13 --with kokoro-onnx --with soundfile python -c "
import kokoro_onnx
print('kokoro-onnx OK')
print([n for n in dir(kokoro_onnx) if not n.startswith('_')])
import inspect; from kokoro_onnx import Kokoro
print(inspect.signature(Kokoro.__init__))
print([m for m in dir(Kokoro) if not m.startswith('_')])
" 2>&1 | tail -10
13:43:29kokoro-onnx installs cleanly (onnxruntime is only 20 MB). Let me check its phonemizer dependency and fetch the model:
13:43:34
Bash — Check espeak bundling and model availability
cd ~/.claude/jobs/e7f5c640/tmp && uv run --no-project --python 3.13 --with kokoro-onnx python -c "
import importlib
for m in ('espeakng_loader','phonemizer','phonemizer_fork','misaki'):
try:
mod=importlib.import_module(m); print(m,'OK',getattr(mod,'__file__',''))
except Exception as e: print(m,'--',type(e).__name__)
try:
import espeakng_loader
print('espeak lib :', espeakng_loader.get_library_path())
print('espeak data:', espeakng_loader.get_data_path())
except Exception as e: print('loader err', e)
" 2>&1 | tail -8
echo "=== model file sizes on the release ==="
for f in kokoro-v1.0.onnx voices-v1.0.bin kokoro-v1.0.fp16.onnx; do
URL="https://github.com/thewh1teagle/kokoro-onnx/releases/download/model-files-v1.0/$f"
SZ=$(curl -sIL "$URL" --max-time 20 | grep -i '^content-length' | tail -1 | tr -d '\r' | awk '{print $2}')
echo " $f ${SZ:-?} bytes"
done
13:44:07espeak-ng ships bundled — no system dependency. Let me wire up Kokoro and fetch the model:
13:44:10
Bash — Add kokoro dependency and download model weights
python3 - <<'PY'
p='pyproject.toml'
s=open(p).read()
s=s.replace(''' "scipy>=1.14",
]''',''' "scipy>=1.14",
"kokoro-onnx>=0.4",
]''')
open(p,'w').write(s); print("deps updated")
PY
uv sync 2>&1 | tail -4
mkdir -p out/cache/tts && cd out/cache/tts
for f in kokoro-v1.0.onnx voices-v1.0.bin; do
[ -f "$f" ] || curl -sL --retry 2 --max-time 900 -o "$f" \
"https://github.com/thewh1teagle/kokoro-onnx/releases/download/model-files-v1.0/$f"
done
ls -la
13:44:40
Bash — Load Kokoro and list available voices
cd ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code && uv run python - <<'PY'
import time, os
import espeakng_loader
os.environ.setdefault("ESPEAK_DATA_PATH", str(espeakng_loader.get_data_path()))
from kokoro_onnx import Kokoro, EspeakConfig
t=time.time()
k = Kokoro("out/cache/tts/kokoro-v1.0.onnx", "out/cache/tts/voices-v1.0.bin",
espeak_config=EspeakConfig(lib_path=str(espeakng_loader.get_library_path()),
data_path=str(espeakng_loader.get_data_path())))
print(f"loaded in {time.time()-t:.1f}s")
vs = sorted(k.get_voices())
print(f"{len(vs)} voices")
for pre,lab in (("bm_","British male"),("bf_","British female"),("am_","American male"),("af_","American female")):
print(f" {lab:17s}", " ".join(v for v in vs if v.startswith(pre)))
t=time.time()
audio, sr = k.create("A category is made of three things, and nothing else.", voice="bm_george", speed=1.0, lang="en-gb")
print(f"synth {len(audio)/sr:.2f}s of audio in {time.time()-t:.2f}s @ {sr} Hz")
PY
13:44:553× realtime, 24 kHz. Before picking a voice, let me verify it pronounces the proper nouns correctly — something I can check objectively via phonemes:
13:44:58
Bash — Check phonemization of proper nouns and jargon
uv run python - <<'PY'
import os, espeakng_loader
os.environ.setdefault("ESPEAK_DATA_PATH", str(espeakng_loader.get_data_path()))
from phonemizer.backend.espeak.wrapper import EspeakWrapper
EspeakWrapper.set_library(str(espeakng_loader.get_library_path()))
from phonemizer.backend import EspeakBackend
for lang in ("en-gb","en-us"):
be = EspeakBackend(lang, preserve_punctuation=True, with_stress=True)
tests = ["Eilenberg","Saunders Mac Lane","Yoneda","Yoneda lemma","functor","morphism",
"Sierpinski","monoid","associative","nineteen forty-five","isomorphic"]
print(f"--- {lang} ---")
for t in tests:
print(f" {t:22s} {be.phonemize([t])[0].strip()}")
PY
13:45:22Found a real problem: Yoneda phonemizes as jˈəʊndə ("YOH-nduh") — a syllable short of the correct "yoh-NEH-dah". Let me sweep the whole script for mispronunciations:
13:45:29
Bash — Phonemize every unusual word in the narration
uv run python - <<'PY'
import os, re, espeakng_loader
os.environ.setdefault("ESPEAK_DATA_PATH", str(espeakng_loader.get_data_path()))
from phonemizer.backend.espeak.wrapper import EspeakWrapper
EspeakWrapper.set_library(str(espeakng_loader.get_library_path()))
from phonemizer.backend import EspeakBackend
from catfilm.script import all_beats
be = EspeakBackend("en-gb", preserve_punctuation=True, with_stress=True)
words = sorted({w.strip(".,;:—“”’?!").lower() for b in all_beats() if b.text
for w in b.text.split()} - {""})
print(f"{len(words)} distinct words in the narration")
# flag the unusual ones: proper nouns, jargon, hyphenates
sus = [w for w in words if (w[:1].isupper() or "-" in w or len(w) > 9
or w in {"functor","functors","yoneda","lemma","monoid","arrow","arrows","commutes","matrices"})]
sus = sorted(set(sus + [w for b in all_beats() if b.text for w in b.text.split()
if w[:1].isupper() and w.lower() not in {"a","the","in","if","and","so","to","it","we","you","not","let","every","here","there","this","that","take","give","add","now","which","when","because","even","apply","different","objects","translate","combine","prove","nobody","three","two","one","or","as","across","go","but","remember","across,"}]))
for w in sus:
c = w.strip(".,;:—“”’?!")
print(f" {c:22s} {be.phonemize([c])[0].strip()}")
PY
13:45:48Everything phonemizes correctly except Yoneda — and "None" looks suspicious too. Let me find respellings and verify them objectively:
13:45:54
Bash — Test respellings for Yoneda and check None in context
uv run python - <<'PY'
import os, espeakng_loader
os.environ.setdefault("ESPEAK_DATA_PATH", str(espeakng_loader.get_data_path()))
from phonemizer.backend.espeak.wrapper import EspeakWrapper
EspeakWrapper.set_library(str(espeakng_loader.get_library_path()))
from phonemizer.backend import EspeakBackend
be = EspeakBackend("en-gb", preserve_punctuation=True, with_stress=True)
def ph(t): return be.phonemize([t])[0].strip()
print("TARGET Yoneda = /jəʊnˈɛdə/ 'yoh-NEH-dah'")
for c in ["Yoneda","Yonehda","Yo-neh-da","yonneda","Yonneda","Yon-eh-dah","yoh-neh-dah",
"Yonaida","Yonedda","yo neh da","Yonneh-da","Yonn-eh-da"]:
print(f" {c:16s} {ph(c)}")
print()
print("IN CONTEXT — 'None of this was drawn.'")
for c in ["None of this was drawn.","None of this was drawn. It was composed.",
"Nun of this was drawn.","none of this was drawn."]:
print(f" {c[:34]:36s} {ph(c)}")
print()
print("IN CONTEXT — the Yoneda lines")
for c in ["The Yoneda lemma.", "The Yonn-eh-da lemma.", "The Yonneh-da lemma."]:
print(f" {c:24s} {ph(c)}")
PY
13:46:16"None" is genuinely mispronounced as "non" too. Let me search respellings systematically and check whether Kokoro accepts raw phonemes:
13:46:24
Bash — Search for a correct Yoneda respelling and check the phoneme API
uv run python - <<'PY'
import os, inspect, itertools, espeakng_loader
os.environ.setdefault("ESPEAK_DATA_PATH", str(espeakng_loader.get_data_path()))
from phonemizer.backend.espeak.wrapper import EspeakWrapper
EspeakWrapper.set_library(str(espeakng_loader.get_library_path()))
from phonemizer.backend import EspeakBackend
from kokoro_onnx import Kokoro
print("Kokoro.create signature:", inspect.signature(Kokoro.create))
be = EspeakBackend("en-gb", preserve_punctuation=True, with_stress=True)
def ph(t): return be.phonemize([t])[0].strip()
TARGET = "jəʊnˈɛdə"
print(f"\nsearching for a spelling that yields {TARGET}")
first = ["Yo","Yoh","Yow","Jo","Yoe","You","Yō"]
mid = ["ned","nedd","ned'","nnedd","neh","nedh","nehd"]
last = ["a","ah","uh","er","a.",""]
best=[]
for a,b,c in itertools.product(first,mid,last):
w=a+b+c
try: p=ph(w)
except Exception: continue
best.append((p==TARGET, p.replace("ˌ",""), w))
hits=[x for x in best if x[0]]
print("exact hits:", [h[2] for h in hits][:10] or "none")
# near misses: right vowels, any stress
import re
def bare(s): return re.sub(r"[ˈˌ]","",s)
near=[(p,w) for ok,p,w in best if bare(p)==bare(TARGET)]
print("right phonemes, any stress:", near[:12])
PY
13:46:51"Yohneda" gives the right phonemes. But Kokoro accepts raw phonemes, so I can do it exactly — let me build a proper pronunciation lexicon and generate an audition of candidate voices:
13:47:00
Bash — Generate voice audition samples
mkdir -p out/audition && uv run python - <<'PY'
import os, time
import numpy as np, espeakng_loader
os.environ.setdefault("ESPEAK_DATA_PATH", str(espeakng_loader.get_data_path()))
from kokoro_onnx import Kokoro, EspeakConfig
from catfilm.audio.narration import write_wav
from catfilm.config import SAMPLE_RATE
k = Kokoro("out/cache/tts/kokoro-v1.0.onnx", "out/cache/tts/voices-v1.0.bin",
espeak_config=EspeakConfig(lib_path=str(espeakng_loader.get_library_path()),
data_path=str(espeakng_loader.get_data_path())))
TEXT = ("This is a thing. It doesn't matter what it is — that isn't a limitation, "
"that is the point. And this is an arrow: a way of getting from the first "
"one to the second. Category theory is the study of the shape of "
"relationships, with the things themselves deliberately left out.")
CANDS = [("bm_george","en-gb"),("bm_fable","en-gb"),("bm_lewis","en-gb"),("bm_daniel","en-gb"),
("bf_emma","en-gb"),("bf_alice","en-gb"),
("am_michael","en-us"),("am_puck","en-us"),("am_fenrir","en-us"),("am_onyx","en-us"),
("af_heart","en-us"),("af_bella","en-us"),("af_nicole","en-us")]
from scipy.signal import resample_poly
clips=[]
for v,lang in CANDS:
t=time.time()
a,sr = k.create(TEXT, voice=v, speed=0.95, lang=lang)
a = resample_poly(a, SAMPLE_RATE, sr).astype(np.float32)
a = a/max(np.abs(a).max(),1e-9)*0.82
write_wav(f"out/audition/{v}.wav", a)
clips.append((v, a))
print(f" {v:12s} {len(a)/SAMPLE_RATE:5.2f}s ({time.time()-t:.1f}s to synth)")
gap = np.zeros(int(0.9*SAMPLE_RATE), dtype=np.float32)
write_wav("out/audition/_all_in_order.wav", np.concatenate([c for _,a in clips for c in (a,gap)]))
print("\norder in _all_in_order.wav:", " → ".join(v for v,_ in clips))
PY
ls -la out/audition/ | tail -15
13:48:1813 auditions ready in out/audition/. While you listen, let me build the backend — starting with a pronunciation lexicon that fixes both words exactly:
13:48:48
Bash — Write the neural TTS backend with pronunciation lexicon
cat > src/catfilm/audio/tts.py <<'PY'
"""Neural narration.
The film was first narrated with the macOS ``say`` command, whose voices are
concatenative and sound it. This module drives Kokoro-82M instead — a small
neural TTS that runs locally on the CPU — and adds the one thing a general
purpose voice cannot know: how this film pronounces its proper nouns.
The model weights are not in the repository; ``ensure_model()`` fetches them on
first use. If they are unavailable the caller falls back to ``say``, so the
project still builds on a machine with no network.
"""
from __future__ import annotations
import os
import re
import shutil
import subprocess
from dataclasses import dataclass
from functools import lru_cache
from pathlib import Path
import numpy as np
from ..config import CACHE, SAMPLE_RATE
TTS_DIR = CACHE / "tts"
MODEL = TTS_DIR / "kokoro-v1.0.onnx"
VOICES = TTS_DIR / "voices-v1.0.bin"
BASE = "https://github.com/thewh1teagle/kokoro-onnx/releases/download/model-files-v1.0"
SIZES = {MODEL.name: 325_532_387, VOICES.name: 28_214_398}
# Words espeak-ng gets wrong, given as phonemes so the fix is exact rather than
# a respelling that only approximately lands.
# Yoneda — espeak drops a syllable: jˈəʊndə, "YOH-nduh"
# none — espeak's en-gb gives nˈɒn, "non", instead of "nun"
LEXICON = {
"yoneda": "jəʊnˈɛdə",
"none": "nˈʌn",
}
_LEX_RE = re.compile(r"\b(" + "|".join(map(re.escape, LEXICON)) + r")\b", re.I)
MAX_PHONEMES = 480 # the model's context, with headroom
@dataclass(frozen=True)
class VoiceSpec:
name: str = "bm_george"
speed: float = 0.95
lang: str = "en-gb"
@staticmethod
def for_voice(name: str, speed: float = 0.95) -> "VoiceSpec":
return VoiceSpec(name, speed, "en-gb" if name[0] == "b" else "en-us")
# ---------------------------------------------------------------------------
# Model files
# ---------------------------------------------------------------------------
def model_present() -> bool:
return all(p.exists() and p.stat().st_size == SIZES[p.name] for p in (MODEL, VOICES))
def ensure_model(quiet: bool = False) -> bool:
"""Fetch the weights if they are missing. Returns whether they are usable."""
if model_present():
return True
if shutil.which("curl") is None:
return False
TTS_DIR.mkdir(parents=True, exist_ok=True)
for p in (MODEL, VOICES):
if p.exists() and p.stat().st_size == SIZES[p.name]:
continue
if not quiet:
print(f" fetching {p.name} ({SIZES[p.name]/1e6:.0f} MB)…", flush=True)
r = subprocess.run(["curl", "-sL", "--retry", "2", "--max-time", "1800",
"-o", str(p), f"{BASE}/{p.name}"])
if r.returncode != 0 or not p.exists() or p.stat().st_size != SIZES[p.name]:
p.unlink(missing_ok=True)
return False
return True
# ---------------------------------------------------------------------------
# Front end: text -> phonemes, with our corrections spliced in
# ---------------------------------------------------------------------------
@lru_cache(maxsize=4)
def _backend(lang: str):
import espeakng_loader
from phonemizer.backend import EspeakBackend
from phonemizer.backend.espeak.wrapper import EspeakWrapper
os.environ.setdefault("ESPEAK_DATA_PATH", str(espeakng_loader.get_data_path()))
EspeakWrapper.set_library(str(espeakng_loader.get_library_path()))
return EspeakBackend(lang, preserve_punctuation=True, with_stress=True)
def phonemize(text: str, lang: str = "en-gb") -> str:
"""Phonemes for a line, with the lexicon words replaced wholesale.
The text either side of a lexicon word is phonemised normally and the two
are spliced, so a corrected word can never collide with a coincidentally
identical phoneme run elsewhere in the sentence.
"""
be = _backend(lang)
out: list[str] = []
pos = 0
for m in _LEX_RE.finditer(text):
head = text[pos:m.start()]
if head.strip():
out.append(be.phonemize([head])[0].strip())
out.append(LEXICON[m.group(1).lower()])
pos = m.end()
tail = text[pos:]
if tail.strip():
out.append(be.phonemize([tail])[0].strip())
return " ".join(s for s in out if s)
def _split_phonemes(ph: str, limit: int = MAX_PHONEMES) -> list[str]:
"""Break an over-long line at clause boundaries the model can breathe on."""
if len(ph) <= limit:
return [ph]
parts, cur = [], ""
for piece in re.split(r"(?<=[.!?;:,])\s+", ph):
if cur and len(cur) + len(piece) + 1 > limit:
parts.append(cur)
cur = piece
else:
cur = f"{cur} {piece}".strip()
if cur:
parts.append(cur)
return parts
# ---------------------------------------------------------------------------
# Synthesis
# ---------------------------------------------------------------------------
@lru_cache(maxsize=1)
def _kokoro():
import espeakng_loader
from kokoro_onnx import EspeakConfig, Kokoro
return Kokoro(str(MODEL), str(VOICES), espeak_config=EspeakConfig(
lib_path=str(espeakng_loader.get_library_path()),
data_path=str(espeakng_loader.get_data_path())))
def speak(text: str, spec: VoiceSpec) -> np.ndarray:
"""One line of narration, at the film's sample rate."""
from scipy.signal import resample_poly
k = _kokoro()
chunks = _split_phonemes(phonemize(text, spec.lang))
pieces = []
for i, ph in enumerate(chunks):
a, sr = k.create(ph, voice=spec.name, speed=spec.speed, lang=spec.lang,
is_phonemes=True)
pieces.append(np.asarray(a, dtype=np.float32))
if i + 1 < len(chunks):
pieces.append(np.zeros(int(0.16 * sr), dtype=np.float32))
audio = np.concatenate(pieces)
if sr != SAMPLE_RATE:
audio = resample_poly(audio, SAMPLE_RATE, sr).astype(np.float32)
return audio
def available_voices() -> list[str]:
return sorted(_kokoro().get_voices())
PY
uv run python - <<'PY'
from catfilm.audio.tts import phonemize, speak, VoiceSpec, model_present
print("model present:", model_present())
for t in ["The Yoneda lemma. Written out properly it takes a page.",
"None of this was drawn. It was composed.",
"In nineteen forty-five, Samuel Eilenberg and Saunders Mac Lane were trying to pin down a word."]:
print(f"\n{t}\n -> {phonemize(t)}")
a = speak("A thing is completely determined by its relationships to everything else.",
VoiceSpec.for_voice("bm_george"))
print(f"\nsynth ok: {len(a)/44100:.2f}s @44100, peak {abs(a).max():.2f}")
PY
13:49:07Both corrections land exactly. Wiring it into the narration pipeline:
13:49:40
Bash — Wire neural TTS into narration and add audition command
python3 - <<'PY'
p='src/catfilm/config.py'
s=open(p).read()
s=s.replace('''# --- Audio ------------------------------------------------------------------
SAMPLE_RATE = 44100
NARRATOR_VOICE = "Daniel"
NARRATOR_WPM = 172''','''# --- Audio ------------------------------------------------------------------
SAMPLE_RATE = 44100
# Narration is Kokoro-82M, run locally. The weights land in out/cache/tts on
# first build; if they cannot be fetched the pipeline falls back to macOS `say`,
# whose concatenative voices are serviceable but plainly synthetic.
NARRATOR_VOICE = "bm_george"
NARRATOR_SPEED = 0.95
NARRATOR_TARGET_RMS = 0.115 # per-line levelling, so no line sits under the score
# Fallback only.
SAY_VOICE = "Daniel"
SAY_WPM = 172''')
open(p,'w').write(s)
p='src/catfilm/audio/narration.py'
s=open(p).read()
s=s.replace('''from ..config import AUDIO, NARRATOR_VOICE, NARRATOR_WPM, SAMPLE_RATE
from ..script import all_beats''','''from ..config import (AUDIO, NARRATOR_SPEED, NARRATOR_TARGET_RMS, NARRATOR_VOICE,
SAMPLE_RATE, SAY_VOICE, SAY_WPM)
from ..script import all_beats
from . import tts''')
s=s.replace('''def _say(text: str, out: Path) -> None:
subprocess.run(
["say", "-v", NARRATOR_VOICE, "-r", str(NARRATOR_WPM),
"--data-format=LEI16@%d" % SAMPLE_RATE, "-o", str(out), text],
check=True, capture_output=True,
)''','''def _say(text: str, out: Path) -> None:
"""Fallback voice: macOS `say`. Used only when the neural weights are absent."""
subprocess.run(
["say", "-v", SAY_VOICE, "-r", str(SAY_WPM),
"--data-format=LEI16@%d" % SAMPLE_RATE, "-o", str(out), text],
check=True, capture_output=True,
)''')
s=s.replace('''"""Narration: synthesise every line, then let its measured length set the cut.
The film is edited to the voice. Each beat is rendered to its own wav once,
its true duration is measured and cached, and the timeline is rebuilt from
that cache — so a change to the script re-times the pictures automatically.
"""''','''"""Narration: synthesise every line, then let its measured length set the cut.
The film is edited to the voice. Each beat is rendered to its own wav once,
its true duration is measured and cached, and the timeline is rebuilt from that
cache — so a change to the script, or a change of voice, re-times every
animation in the film automatically.
"""''')
s=s.replace('''def synthesize(force: bool = False) -> dict[str, float]:
VOICE_DIR.mkdir(parents=True, exist_ok=True)
cache = json.loads(DURATIONS.read_text()) if DURATIONS.exists() and not force else {}
out: dict[str, float] = {}
for b in all_beats():
if b.text is None:
out[b.key] = 0.0
continue
wav = VOICE_DIR / f"{b.key}.wav"
stamp = f"{NARRATOR_VOICE}|{NARRATOR_WPM}|{b.text}"
if not force and wav.exists() and cache.get(b.key + ".stamp") == stamp:
out[b.key] = cache[b.key]
continue
raw = VOICE_DIR / f"{b.key}.raw.wav"
_say(b.text, raw)
a = _trim_tail(read_wav(raw))
write_wav(wav, a)
raw.unlink(missing_ok=True)
out[b.key] = len(a) / SAMPLE_RATE
cache[b.key + ".stamp"] = stamp
print(f" voice {b.key:5s} {out[b.key]:6.2f}s {b.text[:56]}")
merged = {**cache, **out}
DURATIONS.write_text(json.dumps(merged, indent=1))
return out''',
'''def _level(a: np.ndarray, target: float = NARRATOR_TARGET_RMS) -> np.ndarray:
"""Match each line to a common loudness, with a ceiling so nothing clips.
Neural TTS varies a little line to line; levelling here means the duck
against the score behaves the same way in every act.
"""
rms = float(np.sqrt((a.astype(np.float64) ** 2).mean())) if len(a) else 0.0
if rms < 1e-6:
return a
g = min(target / rms, 0.94 / max(float(np.abs(a).max()), 1e-6))
return (a * g).astype(np.float32)
def synthesize(force: bool = False, voice: str | None = None,
speed: float | None = None) -> dict[str, float]:
VOICE_DIR.mkdir(parents=True, exist_ok=True)
name = voice or NARRATOR_VOICE
spd = NARRATOR_SPEED if speed is None else speed
neural = tts.ensure_model()
if neural:
spec = tts.VoiceSpec.for_voice(name, spd)
engine = f"kokoro:{spec.name}@{spec.speed}"
else:
spec = None
engine = f"say:{SAY_VOICE}@{SAY_WPM}"
print(" ! neural weights unavailable — falling back to macOS `say`")
cache = json.loads(DURATIONS.read_text()) if DURATIONS.exists() and not force else {}
out: dict[str, float] = {}
for b in all_beats():
if b.text is None:
out[b.key] = 0.0
continue
wav = VOICE_DIR / f"{b.key}.wav"
stamp = f"{engine}|{b.text}"
if not force and wav.exists() and cache.get(b.key + ".stamp") == stamp:
out[b.key] = cache[b.key]
continue
if spec is not None:
a = tts.speak(b.text, spec)
else:
raw = VOICE_DIR / f"{b.key}.raw.wav"
_say(b.text, raw)
a = read_wav(raw)
raw.unlink(missing_ok=True)
a = _level(_trim_tail(a))
write_wav(wav, a)
out[b.key] = len(a) / SAMPLE_RATE
cache[b.key + ".stamp"] = stamp
print(f" voice {b.key:5s} {out[b.key]:6.2f}s {b.text[:56]}")
merged = {**cache, **out}
DURATIONS.write_text(json.dumps(merged, indent=1))
return out''')
open(p,'w').write(s)
p='src/catfilm/cli.py'
s=open(p).read()
s=s.replace(''' a = sub.add_parser("audio", help="synthesise narration + score")
a.add_argument("--force", action="store_true")''',
''' a = sub.add_parser("audio", help="synthesise narration + score")
a.add_argument("--force", action="store_true")
a.add_argument("--voice", default=None, help="Kokoro voice, e.g. bm_george")
a.add_argument("--speed", type=float, default=None)
au = sub.add_parser("audition", help="sample candidate narrator voices")
au.add_argument("--voices", default=None, help="comma-separated; default is a shortlist")
au.add_argument("--speed", type=float, default=0.95)''')
s=s.replace(''' print("narration…"); synthesize(force=ns.force)''',
''' print("narration…"); synthesize(force=ns.force, voice=ns.voice, speed=ns.speed)''')
s=s.replace(''' if ns.cmd == "render":''',''' if ns.cmd == "audition":
from .audition import audition
audition(ns.voices.split(",") if ns.voices else None, ns.speed); return 0
if ns.cmd == "render":''')
open(p,'w').write(s)
print("ok")
PY
cat > src/catfilm/audition.py <<'PY'
"""Sample candidate narrator voices on a line from the film."""
from __future__ import annotations
import numpy as np
from .audio.narration import write_wav
from .audio.tts import VoiceSpec, ensure_model, speak
from .config import OUT, SAMPLE_RATE
LINE = ("This is a thing. It doesn't matter what it is — that isn't a limitation, "
"that is the point. And this is an arrow: a way of getting from the first "
"one to the second. Category theory is the study of the shape of "
"relationships, with the things themselves deliberately left out.")
SHORTLIST = ["bm_george", "bm_fable", "bm_lewis", "bm_daniel", "bf_emma", "bf_alice",
"am_michael", "am_puck", "am_fenrir", "am_onyx",
"af_heart", "af_bella", "af_nicole"]
def audition(voices: list[str] | None = None, speed: float = 0.95) -> None:
if not ensure_model():
raise SystemExit("neural weights unavailable")
d = OUT / "audition"
d.mkdir(parents=True, exist_ok=True)
clips = []
for v in (voices or SHORTLIST):
a = speak(LINE, VoiceSpec.for_voice(v.strip(), speed))
a = a / max(float(np.abs(a).max()), 1e-9) * 0.82
write_wav(d / f"{v.strip()}.wav", a)
clips.append((v.strip(), a))
print(f" {v.strip():12s} {len(a)/SAMPLE_RATE:5.2f}s")
gap = np.zeros(int(0.9 * SAMPLE_RATE), dtype=np.float32)
write_wav(d / "_all_in_order.wav",
np.concatenate([c for _, a in clips for c in (a, gap)]))
print(f"\n {d}\n order: " + " → ".join(v for v, _ in clips))
PY
uv run --with ruff ruff check src/ 2>&1 | tail -2 && uv run catfilm audition --voices bm_george 2>&1 | tail -3
13:49:53
Bash — Fix lint and generate an old-vs-new comparison
uv run --with ruff ruff check src/ --fix 2>&1 | tail -2; uv run --with ruff ruff check src/ 2>&1 | tail -1
echo "--- comparison: old say vs new neural, same line ---"
say -v Daniel -r 172 --data-format=LEI16@44100 -o out/audition/_OLD_say_daniel.wav "This is a thing. It doesn't matter what it is — that isn't a limitation, that is the point. And this is an arrow: a way of getting from the first one to the second. Category theory is the study of the shape of relationships, with the things themselves deliberately left out." 2>&1
ls -la out/audition/ | awk '{print $5, $9}' | grep -v '^ *$'
13:50:02The pipeline is swapped over and everything's ready — I just can't judge voices by ear, so this is your call:
13:50:15say with Kokoro-82M (local neural TTS) and auditioned 13 voices on a line from the film. They're in out/audition/ — _all_in_order.wav plays them back to back, _OLD_say_daniel.wav is the current robotic one for comparison. Which voice should narrate?14:27:33Your questions have been answered: "I've replaced macOS
saywith Kokoro-82M (local neural TTS) and auditioned 13 voices on a line from the film. They're inout/audition/—_all_in_order.wavplays them back to back,_OLD_say_daniel.wavis the current robotic one for comparison. Which voice should narrate?"="af_heart — American female" selected preview: out/audition/af_heart.wav
American female. Graded 'A' on the model card — the most natural-sounding option.
Nearby: af_bella (A-), af_nicole (B-), "Kokoro at speed 1.0 is fairly brisk; I auditioned at 0.95. Slower pacing suits a contemplative film but lengthens the runtime (currently 8:29). How should I pace it?"="0.95 — as auditioned". You can now continue with these answers in mind.
14:27:50af_heart at 0.95 — that's American English, so the pronunciation lexicon needs re-verifying against en-us phonemes:
14:27:59
Bash — Verify en-us phonemization for the American voice
uv run python - <<'PY'
import os, espeakng_loader
os.environ.setdefault("ESPEAK_DATA_PATH", str(espeakng_loader.get_data_path()))
from phonemizer.backend.espeak.wrapper import EspeakWrapper
EspeakWrapper.set_library(str(espeakng_loader.get_library_path()))
from phonemizer.backend import EspeakBackend
from catfilm.script import all_beats
be = EspeakBackend("en-us", preserve_punctuation=True, with_stress=True)
def ph(t): return be.phonemize([t])[0].strip()
print("=== en-us: the words that matter ===")
checks = {
"Yoneda":"joʊnˈɛdə (yoh-NEH-dah)",
"None of this was drawn.":"nˈʌn … (nun, not 'non')",
"Eilenberg":"ˈaɪlənbɜːɡ",
"Saunders Mac Lane":"sˈɔːndɚz mˈæk lˈeɪn",
"functor":"fˈʌŋktɚ",
"nineteen forty-five":"—",
"matrices":"mˈeɪtɹɪsiːz",
"a-then-b":"ay-then-bee",
"g-after-f":"gee-after-ef",
"monoid":"—", "commutes":"—", "isomorphic":"—", "associative":"—",
}
for t,want in checks.items():
print(f" {t:26s} {ph(t):46s} want {want}")
print("\n=== full en-us sweep of unusual words ===")
words = sorted({w.strip('.,;:—“”’?!').lower() for b in all_beats() if b.text for w in b.text.split()} - {""})
odd=[w for w in words if len(w)>8 or '-' in w or w in
{"arrow","arrows","functor","lemma","none","yoneda","matrices","commutes","plane","word","words"}]
for w in odd: print(f" {w:22s} {ph(w)}")
PY
14:28:20none is correct in American English; only Yoneda needs fixing, with a different vowel. Making the lexicon language-aware and switching the voice:
14:28:31
Bash — Make lexicon language-aware, switch voice, re-synthesize
python3 - <<'PY'
p='src/catfilm/audio/tts.py'
s=open(p).read()
s=s.replace('''# Words espeak-ng gets wrong, given as phonemes so the fix is exact rather than
# a respelling that only approximately lands.
# Yoneda — espeak drops a syllable: jˈəʊndə, "YOH-nduh"
# none — espeak's en-gb gives nˈɒn, "non", instead of "nun"
LEXICON = {
"yoneda": "jəʊnˈɛdə",
"none": "nˈʌn",
}
_LEX_RE = re.compile(r"\\b(" + "|".join(map(re.escape, LEXICON)) + r")\\b", re.I)''',
'''# Words espeak-ng gets wrong, given as phonemes so the fix is exact rather than
# a respelling that only approximately lands. The corrections differ by accent,
# so the table is keyed by language.
#
# Yoneda — espeak drops a syllable in both accents (jˈəʊndə / jˈoʊndə,
# "YOH-nduh"); it is yoh-NEH-dah, stress on the second.
# none — espeak's en-gb alone gives nˈɒn, "non", instead of "nun".
LEXICON: dict[str, dict[str, str]] = {
"en-gb": {"yoneda": "jəʊnˈɛdə", "none": "nˈʌn"},
"en-us": {"yoneda": "joʊnˈɛdə"},
}
@lru_cache(maxsize=4)
def _lex_re(lang: str):
words = LEXICON.get(lang, {})
if not words:
return None
return re.compile(r"\\b(" + "|".join(map(re.escape, words)) + r")\\b", re.I)''')
s=s.replace(''' be = _backend(lang)
out: list[str] = []
pos = 0
for m in _LEX_RE.finditer(text):
head = text[pos:m.start()]
if head.strip():
out.append(be.phonemize([head])[0].strip())
out.append(LEXICON[m.group(1).lower()])
pos = m.end()''',''' be = _backend(lang)
rx = _lex_re(lang)
if rx is None:
return be.phonemize([text])[0].strip()
words = LEXICON[lang]
out: list[str] = []
pos = 0
for m in rx.finditer(text):
head = text[pos:m.start()]
if head.strip():
out.append(be.phonemize([head])[0].strip())
out.append(words[m.group(1).lower()])
pos = m.end()''')
open(p,'w').write(s)
p='src/catfilm/config.py'
s=open(p).read().replace('NARRATOR_VOICE = "bm_george"','NARRATOR_VOICE = "af_heart"')
open(p,'w').write(s)
print("ok")
PY
uv run python -c "
from catfilm.audio.tts import phonemize
for lang in ('en-us','en-gb'):
print(lang)
print(' ', phonemize('The Yoneda lemma. Written out properly it takes a page.', lang))
print(' ', phonemize('None of this was drawn. It was composed.', lang))
"
echo "=== re-synthesising all 76 lines with af_heart ==="
uv run catfilm audio 2>&1 | tail -8
14:30:04
Bash — Check new timeline and audio balance
uv run catfilm plan
echo "=== level & balance check on the new mix ==="
uv run python - <<'PY'
import numpy as np
from catfilm.timeline import build
from catfilm.audio.narration import voice_track, read_wav
from catfilm.audio.score import render_score, _duck
from catfilm.config import SAMPLE_RATE as SR, AUDIO
tl=build(); n=int((tl.total+1.0)*SR)
v=voice_track(tl.schedule(), tl.total+1.0)[:n]
s=render_score(tl.total+1.0, tl.acts)[:n]
sd=_duck(s,v)
speech=np.zeros(n,bool)
for k,sl in tl.slots.items():
if sl.speech_end>sl.start: speech[int(sl.start*SR):int(sl.speech_end*SR)]=True
r=lambda x,m:(float(np.sqrt(((x[m] if x.ndim==1 else x[m].mean(1))**2).mean())) if m.any() else 0)
print(f" voice rms in speech {r(v,speech):.4f}")
print(f" score rms in speech {r(sd,speech):.4f} ratio {r(v,speech)/max(r(sd,speech),1e-9):.1f}x ({20*np.log10(r(v,speech)/max(r(sd,speech),1e-9)):.0f} dB)")
print(f" voice peak {np.abs(v).max():.3f}")
# per-line level consistency (this is what the new _level() is for)
import glob, os
rms=[]
for f in sorted(glob.glob(str(AUDIO/'voice'/'*.wav'))):
a=read_wav(f);
if len(a)>1000: rms.append(float(np.sqrt((a**2).mean())))
rms=np.array(rms)
print(f" per-line rms: mean {rms.mean():.4f} spread {rms.min():.4f}–{rms.max():.4f} (sd {rms.std():.4f})")
PY
14:30:33Runtime holds at 8:31 and the balance is unchanged. Let me verify the visual choreography still lands with the new beat timings:
14:30:36
Bash — Preflight and check choreography against new timings
uv run catfilm preflight --step 8 2>&1 | tail -2
for s in bloom natural yoneda opening; do uv run catfilm contact $s -n 8 >/dev/null 2>&1; done
uv run python -c "
from PIL import Image; import numpy as np
a=[np.array(Image.open(f'out/gallery/sheet_{s}.png').convert('RGB')) for s in ('opening','bloom')]
h=min(x.shape[0] for x in a); Image.fromarray(np.concatenate([x[:h] for x in a],0)[::2,::2]).save('out/gallery/chk1.png')
b=[np.array(Image.open(f'out/gallery/sheet_{s}.png').convert('RGB')) for s in ('natural','yoneda')]
h=min(x.shape[0] for x in b); Image.fromarray(np.concatenate([x[:h] for x in b],0)[::2,::2]).save('out/gallery/chk2.png')"
14:31:24
Read ← ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code/out/gallery/chk2.png
14:31:42Choreography still lands. Updating the credits and README to reflect the new engine, then re-rendering:
14:31:53
Bash — Update credits and README for the new narration engine
python3 - <<'PY'
p='src/catfilm/scenes/credits.py'
s=open(p).read()
s=s.replace(' (26, "python · numpy · skia · scipy · ffmpeg · uv · mise", A_MINT, 0.06, "mono"),',
' (26, "python · numpy · skia · scipy · onnx · ffmpeg · uv · mise", A_MINT, 0.06, "mono"),')
s=s.replace(' (26, "the score is the same functor, read as pitch instead of position", INK_DIM, 0, "serif"),',
''' (0, None, None, 0, None),
(24, "THE VOICE", INK_DIM, 0.26, "serif"),
(28, "Kokoro-82M, run locally on the processor that drew the pictures", INK, 0, "serif"),
(0, None, None, 0, None),
(26, "the score is the same functor, read as pitch instead of position", INK_DIM, 0, "serif"),''')
open(p,'w').write(s)
p='README.md'
s=open(p).read()
s=s.replace("""Narration uses the macOS `say` command, so the film builds end-to-end on a Mac
with no API keys and nothing to download. Everything else is portable.""",
"""Narration is **Kokoro-82M**, a small neural TTS run locally on the CPU. The
weights (~350 MB) are fetched into `out/cache/tts/` on the first build and are
not in the repository; if they cannot be fetched the pipeline falls back to the
macOS `say` command. Either way there are no API keys and nothing leaves the
machine.
Preview the narrator before committing to a nine-minute render:
uv run catfilm audition # 13 candidate voices -> out/audition/ uv run catfilm audio --voice bf_emma # re-narrate with a different one
s=s.replace("""| `audio/` | narration via `say`; the score, from the same functor |""",
"""| `audio/tts.py` | neural narration, with a phoneme lexicon for the proper nouns |
| `audio/` | narration timing; the score, from the same functor |""")
s=s.replace("""Built with Python, numpy, Skia, scipy, ffmpeg, uv and mise. Narration is macOS
`say`; the score is numpy.""",
"""Built with Python, numpy, Skia, scipy, onnxruntime, ffmpeg, uv and mise.
Narration is Kokoro-82M; the score is numpy.""")
s=s.replace("""uv run catfilm audio # narration + score""",
"""uv run catfilm audition # sample candidate narrator voices
uv run catfilm audio # narration + score""")
open(p,'w').write(s)
print("ok")
PY
grep -n "Kokoro\|audition" README.md | head -8
echo; echo "=== a note on pronunciation, for the record ==="
uv run python -c "
from catfilm.audio.tts import LEXICON
for lang, words in LEXICON.items():
print(f' {lang}: ' + ', '.join(f'{w} -> {p}' for w,p in words.items()))"
14:32:00
Bash — Re-render the film with the new narration
rm -f out/functor.mp4 out/picture.mp4 && rm -rf out/chunks && uv run catfilm build 2>&1 | tail -5
14:32:07
Bash — Wait for the re-render
until [ -f out/functor.mp4 ]; do sleep 25; done; sleep 8; stat -f '%N %z bytes' out/functor.mp4; grep -E "✦|!!" /private/tmp/claude-501/-Users-bowiesmith-repos-llm-video-repos-category-theory-opus-5-max-claude-code/e7f5c640-4511-40bd-95f5-fa35e413aa34/tasks/brzdd19n8.output
14:42:18
Bash — Wait for the film
until [ -f out/functor.mp4 ]; do sleep 25; done; sleep 8; stat -f '%N %z bytes' out/functor.mp4; grep -E "✦|!!" /private/tmp/claude-501/-Users-bowiesmith-repos-llm-video-repos-category-theory-opus-5-max-claude-code/e7f5c640-4511-40bd-95f5-fa35e413aa34/tasks/brzdd19n8.output
14:47:12
Bash — Verify the final film and check A/V sync objectively
rm -rf out/chunks out/picture.mp4
echo "=== final film ==="
ffprobe -v error -show_entries format=duration,size -show_entries stream=codec_type,codec_name,width,height,r_frame_rate,sample_rate,channels -of default=nw=1 out/functor.mp4
echo
echo "=== A/V sync spot-check: does the narration land where the timeline says? ==="
uv run python - <<'PY'
import subprocess, wave, numpy as np
from catfilm.timeline import build
tl = build()
# pull the film's audio and check speech energy sits inside the scheduled windows
subprocess.run(["ffmpeg","-hide_banner","-loglevel","error","-y","-i","out/functor.mp4",
"-ac","1","-ar","8000","-f","wav","/tmp/chk8k.wav"],check=True)
with wave.open("/tmp/chk8k.wav") as w:
a=np.frombuffer(w.readframes(w.getnframes()),dtype=np.int16).astype(np.float32)/32768
SR=8000
env=np.convolve(np.abs(a), np.ones(int(0.05*SR))/(0.05*SR), mode="same")
inside=outside=0.0
mask=np.zeros(len(a),bool)
for k,s in tl.slots.items():
if s.speech_end>s.start: mask[int(s.start*SR):int(s.speech_end*SR)]=True
inside=env[mask].mean(); outside=env[~mask].mean()
print(f" mean level inside scheduled speech windows : {inside:.4f}")
print(f" mean level outside them (score only) : {outside:.4f}")
print(f" ratio {inside/max(outside,1e-9):.1f}x — speech is where the timeline puts it")
PY
14:47:28Sync confirmed — speech energy sits 3.7× higher inside the scheduled windows. Final checks and commit:
14:47:38
Bash — Run final checks and commit the narration change
uv run --with ruff ruff check src/ 2>&1 | tail -1
uv run python -m catfilm.laws 2>&1 | tail -1
echo "--- git ---"
git add -A && git status --short
git -c user.name="Bowie Smith" -c user.email="r.bowie.smith@gmail.com" commit -q -F - <<'MSG'
Narrate with a local neural TTS instead of macOS `say`
The `say` voices are concatenative, which is why the narration sounded
synthetic. Swapped in Kokoro-82M, run locally on the CPU through onnxruntime —
no API keys, nothing leaves the machine. Weights are fetched to out/cache/tts
on first build and are not in the repo; if they cannot be fetched the pipeline
falls back to `say`, so the project still builds offline.
Narrator is af_heart at speed 0.95, chosen from a 13-voice audition
(`catfilm audition`). Runtime is unchanged at 8:31 — the timeline is derived
from measured line durations, so changing the voice re-timed every animation in
the film by itself.
Also adds a pronunciation lexicon, because a general-purpose voice cannot know
how this film says its proper nouns. espeak-ng gets two words wrong:
Yoneda jˈoʊndə — a syllable short; it is yoh-NEH-dah, stress on the second
none nˈɒn — en-gb only, "non" rather than "nun"
Both are corrected as phonemes rather than respellings, spliced in around the
word so a correction can never collide with an identical phoneme run elsewhere
in the sentence. The table is keyed by language: with an American voice only
Yoneda needs fixing, and it needs a different vowel. Every other unusual word
in the script was checked against espeak's output and is correct as written.
Narration lines are now levelled to a common loudness (per-line rms sd 0.0115),
so the score ducks identically in every act. Voice sits 12 dB over the score,
and speech energy measures 3.7x higher inside its scheduled windows than
outside — the picture is still cut to the voice.
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
MSG
git log --oneline
14:47:58Fixed and re-rendered — out/functor.mp4, 8:31, 244 MB.
macOS say uses concatenative synthesis — it stitches recorded fragments, which is why it sounded like a machine reading. No amount of rate or pause tuning fixes that.
Kokoro-82M, a small neural TTS running locally on the CPU via onnxruntime. No API keys, nothing leaves the machine. The weights (~350 MB) land in out/cache/tts/ on first build and aren't in the repo; if they can't be fetched the pipeline falls back to say, so the project still builds offline.
You picked af_heart at 0.95 from the 13-voice audition — that's what's in the film. uv run catfilm audition regenerates the samples, and uv run catfilm audio --voice bf_emma re-narrates with any other if you change your mind.
Runtime is unchanged at 8:31. I didn't have to re-time anything by hand: the timeline is built from measured line durations, so swapping the voice re-cut every animation in the film automatically.
A general-purpose voice doesn't know how this film says its proper nouns, so I checked every unusual word in the script against espeak's phoneme output. Two were wrong:
jˈoʊndə, a syllable short — "YOH-nduh" instead of yoh-NEH-dahnˈɒn, "non" rather than "nun" (British English only)Both are corrected as phonemes rather than respellings, spliced in around the word so a fix can't collide with an identical phoneme run elsewhere in a sentence. The table is keyed by language, which turned out to matter: with an American voice only Yoneda needs fixing, and it needs a different vowel than the British one would. Everything else — Eilenberg, Mac Lane, functor, matrices, "g-after-f" — was already correct.
I also levelled each line to a common loudness (per-line RMS spread is now sd 0.0115), so the score ducks the same way in every act. Voice sits 12 dB over the music.
Sync is confirmed objectively: speech energy in the finished mp4 measures 3.7× higher inside its scheduled windows than outside. Laws pass, preflight is clean at 0 failing frames, ruff is clean.
I still haven't heard it. The voice choice is yours and the pronunciation is verified at the phoneme level, but the actual delivery — phrasing, where it breathes, whether any line reads oddly — is something only you can judge. If a specific line lands badly, uv run catfilm audio --force after editing script.py will re-time the film around it.
15:02:15Write the full script of this session to script.md. Write notes about this session to notes.md. Include things that may affect output, such as a downgrade in model version due to a safeguard, a change to restore the model, a change in effort, memory/persistence used by the client/harness, a single agent running serially vs concurrent/parallel agents, etc. Write a metadata.toml file including the following information about the artifact(s) generated (assuming directory name is of form <title>-<model-version>-<effort>-<harness>, i.e. algorithmic-complexity-fable-5-max-claude-code):
15:02:45I need accurate pricing for this, and there may be an exact usage record on disk. Let me check both.
15:02:45
Skill — claude-api — Claude Opus 5 pricing per MTok: input, output, cache write, cache read
15:02:47 · 📎 skill loaded
(the claude-api skill was loaded into the turn)
15:02:54Opus 5: $5.00/MTok input, $25.00/MTok output; cache write ~1.25× input, cache read ~0.1×. Now let me find the exact usage record on disk.
15:02:55
Bash — Locate the session transcript
D=~/.claude/projects/-Users-bowiesmith-repos-llm-video-repos-category-theory-opus-5-max-claude-code
ls -la "$D" 2>/dev/null | head -20
echo "--- jsonl files ---"
find "$D" -name '*.jsonl' -exec ls -la {} \; 2>/dev/null | head
15:03:08Both session files are here. Let me extract exact usage from them:
15:03:15
Bash — Parse transcripts for exact token usage
cd ~/.claude/jobs/e7f5c640/tmp && cat > parse.py <<'PY'
import json, glob, os, datetime as dt
from collections import defaultdict
D=os.path.expanduser("~/.claude/projects/-Users-bowiesmith-repos-llm-video-repos-category-theory-opus-5-max-claude-code")
for f in sorted(glob.glob(D+"/*.jsonl")):
n=0; kinds=defaultdict(int); models=defaultdict(int); ts=[]
u=defaultdict(int); usage_rows=0
with open(f, errors="replace") as fh:
for line in fh:
line=line.strip()
if not line: continue
n+=1
try: o=json.loads(line)
except Exception: continue
kinds[o.get("type","?")]+=1
if o.get("timestamp"): ts.append(o["timestamp"])
m=o.get("message") or {}
if isinstance(m,dict):
if m.get("model"): models[m["model"]]+=1
us=m.get("usage")
if isinstance(us,dict):
usage_rows+=1
for k,v in us.items():
if isinstance(v,int): u[k]+=v
print(f"\n=== {os.path.basename(f)} ===")
print(f" lines {n} usage-bearing {usage_rows}")
print(f" types {dict(kinds)}")
print(f" models {dict(models)}")
if ts:
a,b=min(ts),max(ts)
pa=dt.datetime.fromisoformat(a.replace('Z','+00:00')); pb=dt.datetime.fromisoformat(b.replace('Z','+00:00'))
print(f" first {a}\n last {b}\n span {(pb-pa).total_seconds():.0f}s = {(pb-pa).total_seconds()/3600:.2f}h")
print(" usage totals:")
for k,v in sorted(u.items(), key=lambda x:-x[1]):
print(f" {k:34s} {v:,}")
PY
uv run --no-project --python 3.13 python parse.py
15:03:42Two transcripts sharing a start timestamp — I need to check whether one contains the other before summing. Let me inspect the record structure:
15:03:48
Bash — Check transcript overlap and available timing fields
cd ~/.claude/jobs/e7f5c640/tmp && cat > probe.py <<'PY'
import json, glob, os
D=os.path.expanduser("~/.claude/projects/-Users-bowiesmith-repos-llm-video-repos-category-theory-opus-5-max-claude-code")
fs=sorted(glob.glob(D+"/*.jsonl"))
def uuids(f):
s=set()
with open(f,errors="replace") as fh:
for l in fh:
try: o=json.loads(l)
except Exception: continue
if o.get("type")=="assistant" and o.get("uuid"): s.add(o["uuid"])
return s
a,b=uuids(fs[0]),uuids(fs[1])
print(f"assistant uuids: A={len(a)} B={len(b)} shared={len(a&b)} A-only={len(a-b)} B-only={len(b-a)}")
print("=> B is a superset of A" if a<=b else "=> disjoint or forked")
# what fields does an assistant record carry?
with open(fs[1],errors="replace") as fh:
for l in fh:
o=json.loads(l)
if o.get("type")=="assistant":
print("\ntop-level keys:", sorted(o.keys()))
m=o["message"]
print("message keys:", sorted(m.keys()))
print("usage keys:", sorted((m.get("usage") or {}).keys()))
for k in ("durationMs","ttftMs","requestId","costUSD","stop_reason"):
if k in o or k in m: print(f" {k}:", o.get(k, m.get(k)))
break
PY
uv run --no-project --python 3.13 python probe.py
15:04:04B is a resumed continuation holding 212 of A's 216 turns — so the union, not the sum. Let me do the full accounting, including effort and service tier:
15:04:16
Bash — Compute union token totals and timing
cd ~/.claude/jobs/e7f5c640/tmp && cat > acct.py <<'PY'
import json, glob, os, datetime as dt
from collections import defaultdict, Counter
D=os.path.expanduser("~/.claude/projects/-Users-bowiesmith-repos-llm-video-repos-category-theory-opus-5-max-claude-code")
fs=sorted(glob.glob(D+"/*.jsonl"))
recs={} # uuid -> record (union, B wins on conflict)
order=[]
for f in fs:
with open(f,errors="replace") as fh:
for l in fh:
try:o=json.loads(l)
except Exception:continue
if o.get("type")!="assistant":continue
u=o.get("uuid")
if u and u not in recs:
recs[u]=o; order.append(u)
elif u: recs[u]=o
print(f"union of assistant turns: {len(recs)}")
U=defaultdict(int); eff=Counter(); tier=Counter(); speed=Counter(); geo=Counter()
stop=Counter(); models=Counter(); vers=Counter()
rows=[]
for u,o in recs.items():
m=o["message"]; us=m.get("usage") or {}
for k in ("input_tokens","output_tokens","cache_creation_input_tokens","cache_read_input_tokens"):
U[k]+=us.get(k,0) or 0
cc=us.get("cache_creation") or {}
for k,v in cc.items():
if isinstance(v,int): U["cc:"+k]+=v
eff[o.get("effort")]+=1; tier[us.get("service_tier")]+=1
speed[us.get("speed")]+=1; geo[us.get("inference_geo")]+=1
stop[m.get("stop_reason")]+=1; models[m.get("model")]+=1; vers[o.get("version")]+=1
rows.append((o.get("timestamp"),u))
print("\n--- token totals (union) ---")
for k,v in sorted(U.items(),key=lambda x:-x[1]): print(f" {k:34s} {v:,}")
print("\n--- request attributes ---")
for lbl,c in (("effort",eff),("service_tier",tier),("speed",speed),("inference_geo",geo),
("stop_reason",stop),("model",models),("cli version",vers)):
print(f" {lbl:14s} {dict(c)}")
# timing
rows.sort()
t=[dt.datetime.fromisoformat(r[0].replace('Z','+00:00')) for r in rows if r[0]]
span=(t[-1]-t[0]).total_seconds()
gaps=[(t[i+1]-t[i]).total_seconds() for i in range(len(t)-1)]
big=[g for g in gaps if g>300]
print(f"\n--- timing ---")
print(f" first turn {t[0].isoformat()}")
print(f" last turn {t[-1].isoformat()}")
print(f" wall span {span:,.0f}s = {span/3600:.2f}h")
print(f" gaps >5min: {len(big)} totalling {sum(big):,.0f}s = {sum(big)/3600:.2f}h")
print(f" span minus those gaps: {span-sum(big):,.0f}s = {(span-sum(big))/3600:.2f}h")
print(f" median inter-turn gap {sorted(gaps)[len(gaps)//2]:.1f}s mean {sum(gaps)/len(gaps):.1f}s")
print(f" sum of gaps <=300s: {sum(g for g in gaps if g<=300):,.0f}s")
PY
uv run --no-project --python 3.13 python acct.py
15:04:42All 423 turns are claude-opus-5 at effort max, standard tier, no fast mode, no refusals. Let me measure model latency precisely and separate idle from working time:
15:04:55
Bash — Measure model latency and classify idle gaps
cd ~/.claude/jobs/e7f5c640/tmp && cat > lat.py <<'PY'
import json, glob, os, datetime as dt
D=os.path.expanduser("~/.claude/projects/-Users-bowiesmith-repos-llm-video-repos-category-theory-opus-5-max-claude-code")
def P(s): return dt.datetime.fromisoformat(s.replace('Z','+00:00'))
# walk B (the surviving continuation) in file order, pairing each assistant with the
# preceding user/tool-result record; add A-only turns the same way.
def turns(f):
seq=[]
with open(f,errors="replace") as fh:
for l in fh:
try:o=json.loads(l)
except Exception:continue
if o.get("type") in ("user","assistant") and o.get("timestamp"):
seq.append(o)
return seq
fs=sorted(glob.glob(D+"/*.jsonl"))
seen=set(); lat=[]; human=[]
for f in (fs[1],fs[0]):
seq=turns(f); prev=None
for o in seq:
if o["type"]=="user": prev=o; continue
u=o.get("uuid")
if not u or u in seen: prev=o; continue
seen.add(u)
if prev is not None and prev["type"]=="user":
d=(P(o["timestamp"])-P(prev["timestamp"])).total_seconds()
if 0<=d<3600:
# a real human message has no tool_result content block
c=prev.get("message",{}).get("content")
is_tool = isinstance(c,list) and any(
isinstance(x,dict) and x.get("type")=="tool_result" for x in c)
(lat if is_tool or not isinstance(c,str) else human).append(d)
prev=o
lat_all=sorted(lat)
print(f"paired model latencies: {len(lat)}")
print(f" sum {sum(lat):,.0f}s = {sum(lat)/3600:.2f}h")
print(f" median {lat_all[len(lat_all)//2]:.1f}s")
print(f" mean {sum(lat)/len(lat):.1f}s")
print(f" p90 {lat_all[int(len(lat_all)*0.9)]:.1f}s max {lat_all[-1]:.1f}s")
print(f"\nturns following a typed human message: {len(human)} -> {sum(human):.0f}s")
# the >5 min gaps: were they tool-blocked or waiting on the human?
seq=turns(fs[1]); big=[]
for i in range(len(seq)-1):
d=(P(seq[i+1]["timestamp"])-P(seq[i]["timestamp"])).total_seconds()
if d>300:
c=seq[i+1].get("message",{}).get("content")
kind = "human-typed" if (seq[i+1]["type"]=="user" and isinstance(c,str)) else \
("tool-result" if seq[i+1]["type"]=="user" else "assistant")
big.append((d,kind,seq[i]["timestamp"][11:19]))
tot=sum(d for d,_,_ in big)
print(f"\ngaps > 300s: {len(big)}, total {tot:,.0f}s = {tot/3600:.2f}h")
for d,k,ts in sorted(big,reverse=True):
print(f" {d:8.0f}s at {ts}Z next={k}")
by={}
for d,k,_ in big: by[k]=by.get(k,0)+d
print(" by kind:", {k:f"{v:,.0f}s ({v/3600:.2f}h)" for k,v in by.items()})
PY
uv run --no-project --python 3.13 python lat.py
15:05:24
Bash — Refine model latency measurement and get wall-clock anchors
cd ~/.claude/jobs/e7f5c640/tmp && cat > lat2.py <<'PY'
import json, glob, os, datetime as dt
D=os.path.expanduser("~/.claude/projects/-Users-bowiesmith-repos-llm-video-repos-category-theory-opus-5-max-claude-code")
def P(s): return dt.datetime.fromisoformat(s.replace('Z','+00:00'))
fs=sorted(glob.glob(D+"/*.jsonl"))
seen=set(); d_all=[]
for f in (fs[1],fs[0]):
prev=None
with open(f,errors="replace") as fh:
for l in fh:
try:o=json.loads(l)
except Exception:continue
if not o.get("timestamp"): continue
if o.get("type")=="assistant":
u=o.get("uuid")
if u and u not in seen:
seen.add(u)
if prev is not None:
d=(P(o["timestamp"])-P(prev)).total_seconds()
if d>=0: d_all.append(d)
prev=o["timestamp"]
d_all.sort()
n=len(d_all)
def s(x): return f"{x:,.0f}s ({x/3600:.2f}h)"
print(f"assistant turns with a measurable predecessor: {n} of 423")
print(f" total {s(sum(d_all))}")
for cap in (60,120,300):
k=[d for d in d_all if d<=cap]
print(f" <= {cap:3d}s only : {s(sum(k))} over {len(k)} turns (excludes {n-len(k)} longer)")
print(f" median {d_all[n//2]:.1f}s mean {sum(d_all)/n:.1f}s p90 {d_all[int(n*.9)]:.1f}s p99 {d_all[int(n*.99)]:.1f}s")
PY
uv run --no-project --python 3.13 python lat2.py
echo "=== wall-clock anchors (local) ==="
git log --format=' commit %h %ad %s' --date=iso | tail -5
stat -f ' first source file %Sm %N' mise.toml 2>/dev/null
stat -f ' final film %Sm %N' out/functor.mp4
15:05:56Model time is 3,945s of a 41,172s wall span. Let me compute cost and build the transcript from the JSONL:
15:06:03
Bash — Compute exact API cost breakdown
git log --format=' %h %ad %s' --date=iso | tail -3 && stat -f ' %Sm %N' mise.toml out/functor.mp4 README.md
cd ~/.claude/jobs/e7f5c640/tmp && uv run --no-project --python 3.13 python - <<'PY'
inp, cw, cr, out = 846, 2_573_595, 101_978_914, 742_876
R = {"uncached_input":5.00, "cache_write_1h":10.00, "cache_read":0.50, "output":25.00}
c = {"uncached_input":inp/1e6*R["uncached_input"], "cache_write_1h":cw/1e6*R["cache_write_1h"],
"cache_read":cr/1e6*R["cache_read"], "output":out/1e6*R["output"]}
tot=sum(c.values()); toks=inp+cw+cr+out
print("component tokens $/MTok cost")
for k in c: print(f" {k:18s} {locals()['inp'] if 0 else '':0s}{ {'uncached_input':inp,'cache_write_1h':cw,'cache_read':cr,'output':out}[k]:>13,} {R[k]:>7.2f} ${c[k]:>7.2f}")
print(f" {'TOTAL':18s} {toks:>13,} {tot/toks*1e6:>7.3f} ${tot:>7.2f}")
print(f"\ntokens-in (all input incl. cache) = {inp+cw+cr:,}")
print(f"tokens-out = {out:,}")
print(f"effective blended $/MTok = {tot/toks*1e6:.4f}")
print(f"cache hit rate = {cr/(cr+cw+inp)*100:.1f}%")
PY
15:06:10Now let me build the transcript faithfully from the JSONL rather than from memory:
15:06:24
Bash — Extract conversation events for the transcript
cd ~/.claude/jobs/e7f5c640/tmp && cat > mkscript.py <<'PY'
import json, glob, os, datetime as dt
D=os.path.expanduser("~/.claude/projects/-Users-bowiesmith-repos-llm-video-repos-category-theory-opus-5-max-claude-code")
fs=sorted(glob.glob(D+"/*.jsonl"))
def P(s): return dt.datetime.fromisoformat(s.replace('Z','+00:00'))
# Rebuild the conversation in order: prefer the surviving continuation (fs[1]),
# then append any turns that only exist in the earlier session file.
events=[]; seen=set()
for f in (fs[1], fs[0]):
with open(f, errors="replace") as fh:
for l in fh:
try: o=json.loads(l)
except Exception: continue
if o.get("type") not in ("user","assistant"): continue
u=o.get("uuid")
if u in seen: continue
seen.add(u)
events.append(o)
events.sort(key=lambda o: o.get("timestamp") or "")
def blocks(c):
if isinstance(c,str): return [{"type":"text","text":c}]
return c if isinstance(c,list) else []
out=[]; nturn=0; thinking_seen=0
for o in events:
m=o.get("message") or {}
bs=blocks(m.get("content"))
ts=(o.get("timestamp") or "")[11:19]
if o["type"]=="user":
texts=[b.get("text","") for b in bs if b.get("type")=="text"]
tools=[b for b in bs if b.get("type")=="tool_result"]
body="\n".join(t for t in texts if t.strip())
if body.strip():
# skip harness-injected reminders / local command echoes
if body.lstrip().startswith("<local-command") or body.lstrip().startswith("Caveat:"):
continue
out.append(("human", ts, body))
elif tools:
out.append(("result", ts, f"[{len(tools)} tool result{'s' if len(tools)>1 else ''}]"))
else:
for b in bs:
t=b.get("type")
if t=="thinking":
if (b.get("thinking") or "").strip(): thinking_seen+=1
elif t=="text" and b.get("text","").strip():
out.append(("claude", ts, b["text"]))
elif t=="tool_use":
nm=b.get("name"); inp=b.get("input") or {}
if nm=="Bash":
d=inp.get("description") or ""
cmd=(inp.get("command") or "").strip()
out.append(("tool", ts, f"**Bash** — {d}\n```bash\n{cmd}\n```"))
elif nm in ("Write","Edit"):
out.append(("tool", ts, f"**{nm}** — `{inp.get('file_path','')}`"))
elif nm=="Read":
out.append(("tool", ts, f"**Read** — `{inp.get('file_path','')}`"))
elif nm=="AskUserQuestion":
qs=inp.get("questions") or []
lines=[]
for q in qs:
lines.append(f"- *{q.get('question','')}*")
for op in q.get("options",[]):
lines.append(f" - **{op.get('label','')}** — {op.get('description','')}")
out.append(("tool", ts, "**AskUserQuestion**\n"+"\n".join(lines)))
elif nm=="Skill":
out.append(("tool", ts, f"**Skill** — `{inp.get('skill','')}` {inp.get('args','')}"))
else:
out.append(("tool", ts, f"**{nm}** — `{json.dumps(inp)[:200]}`"))
nturn=sum(1 for k,_,_ in out if k=="claude")
print(f"events {len(events)} rendered {len(out)} claude-text {nturn} nonempty-thinking {thinking_seen}")
json.dump(out, open("script_events.json","w"))
PY
uv run --no-project --python 3.13 python mkscript.py
15:06:41
Bash — Render script.md
cd ~/.claude/jobs/e7f5c640/tmp && cat > render.py <<'PY'
import json, datetime as dt
ev=json.load(open("script_events.json"))
P="~/repos/llm-video-repos/category-theory-opus-5-max-claude-code/script.md"
L=[]
L.append("# Session transcript — *Functor*, a short film about category theory\n")
L.append("Claude Opus 5 · effort `max` · Claude Code 2.1.239 · 2026-08-22 (UTC timestamps)\n")
L.append("""
**How to read this.** Every human turn and every word Claude wrote to the user
appear verbatim. Tool calls are listed in order with their command or target;
their outputs are not reproduced — the raw session log is 23 MB and much of it
is rendered PNGs, ffmpeg logs and multi-megabyte command output. Where a tool
result mattered to what happened next, Claude's following message says so.
The model returned no visible reasoning: this session ran with thinking
`display: "omitted"`, so all 423 assistant turns carried empty thinking blocks.
Nothing has been removed from the visible conversation.
""")
L.append("\n---\n")
cur=None
for kind, ts, body in ev:
if kind=="human":
L.append(f"\n## 👤 Human · `{ts}`\n\n{body}\n")
elif kind=="claude":
L.append(f"\n### 🤖 Claude · `{ts}`\n\n{body}\n")
elif kind=="tool":
L.append(f"\n<sub>`{ts}` · tool</sub>\n\n{body}\n")
# 'result' events omitted — they carry no readable content
open(P,"w").write("\n".join(L))
import os
print(f"{P}\n {os.path.getsize(P):,} bytes {open(P).read().count(chr(10)):,} lines")
PY
uv run --no-project --python 3.13 python render.py && head -32 ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code/script.md
15:06:51
Bash — Clean the command echo and count transcript sections
cd ~/repos/llm-video-repos/category-theory-opus-5-max-claude-code
python3 - <<'PY'
p='script.md'; s=open(p).read()
# strip the harness's slash-command echo block, keep the effort line as a note
s=s.replace("""## 👤 Human · `03:34:33`
*(slash command)* `/effort` — set the session's effort level to **max**.
""","""## 👤 Human · `03:34:33`
*(slash command)* `/effort` → set effort level to **max** for this session.
""")
open(p,'w').write(s)
PY
grep -c "^## 👤 Human" script.md; grep -c "^### 🤖 Claude" script.md; grep -c "· tool" script.md; wc -c script.md
15:07:04
Bash — Inspect what the human turns actually contain
grep -n "^## 👤 Human" script.md | while IFS=: read -r n rest; do
echo "--- line $n: $rest"; sed -n "$((n+2)),$((n+3))p" script.md | head -2
done 2>/dev/null | head -70
This file was generated from the session's own log while the session was still
running, so it necessarily stops here — at the tool calls that produced it. The
three deliverables written immediately after this point are script.md (this
file), notes.md, and metadata.toml.
$/MTok uncached-input $5.00 cache-write-1h $10.00 cache-read $0.50 output $25.00 effective-blended $0.87
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