Topolectures (Olivia Jack) — 2D cell grid + text snippets + audio-amplitude pulse

Math essence

Per cell (r, c): phase, cell_freq ∈ rand; amp = audio_low(t) + audio_mid(t) + audio_high(t) + 1Hz_kick(t). bright(r,c,t) = clip(0.5 + 0.4*sin(t * amp_freq * cell_freq + phase * phase_jitter) + 0.5*kick_pulse + 0.25*amp, 0, 1). canvas[y0:y1,x0:x1] = max(canvas[y0:y1,x0:x1], fg_color * bright * glyph_bitmap[word]).

Parameters

Reference

First 60 lines of reference.py. Full source: library_external/live_coding_synth/TopolecturesOliviaJack/reference.py

"""TopolecturesOliviaJack — Olivia Jack's 2D cell-grid + text snippets.

Topolectures (Olivia Jack) is a 2D grid of small cells. Each cell
displays a tiny snippet of text (one or two characters), and the
brightness of each cell pulses with an audio-amplitude signal —
synthetic here, but the structure matches the live-coding
performance: the performer reads aloud, the cell whose text
matches what is being said lights up, the rest stay dim.

The visual is built by rasterising each cell's text glyph into a
small bitmap (numpy), then compositing it onto the canvas with a
per-cell brightness multiplier that tracks a per-cell sin chain
whose phase is randomised at reset. A 1 Hz kick impulse (the
audio amplitude envelope) brightens every cell briefly so the
whole grid breathes in time with the speech rhythm.

Cell-text is sampled from a corpus of words associated with
topology / topolectures ("sheaf", "locale", "frame", "open",
"closed", "cover", "limit", "point", "net", "filter", ...). The
default cell size is 14×14 px and the default grid is 16×16, so
the rendered canvas is 240×240. Two-character cells (e.g. "≤",
"id", "~") are drawn as two 7×14 bitmaps stitched side-by-side.
"""

from __future__ import annotations

from typing import ClassVar

import numpy as np


_CORPUS: tuple[str, ...] = (
    "sheaf", "locale", "frame", "open", "closed", "cover",
    "limit", "point", "net", "filter", "basis", "ideal",
    "prime", "ring", "mod", "field", "topos", "yoneda",
    "etale", "sieve", "germ", "stalk", "space", "chart",
    "atlas", "sheaf", "gluing", "flabby", "injective",
    "kernel", "image", "rank", "trace", "spec", "scheme",
    "stack", "gerbe", "torsor", "lie", "group", "algebra",
    "module", "tensor", "hom", "ext", "tor", "der",
    "diff", "conn", "curv", "tors", "geod", "chart",
    "~", "id", "Δ", "≤", "≥", "→", "↦", "≅", "⊂", "⊃", "∧", "∨", "¬", "∀", "∃",
    "∞", "∑", "∏", "∂", "∇", "∈", "∉", "∋", "∅", "η", "π", "λ", "μ", "σ", "φ",
)


# ---------------------------------------------------------------------------
# 5x7 pixel font for ASCII printable + a few unicode glyphs
# ---------------------------------------------------------------------------

_FONT_5x7: dict[str, tuple[str, ...]] = {
    "A": ("01110", "10001", "10001", "11111", "10001", "10001", "10001"),
    "B": ("11110", "10001", "10001", "11110", "10001", "10001", "11110"),
    "C": ("01110", "10001", "10000", "10000", "10000", "10001", "01110"),
    "D": ("11110", "10001", "10001", "10001", "10001", "10001", "11110"),
    "E": ("11111", "10000", "10000", "11110", "10000", "10000", "11111"),
    "F": ("11111", "10000", "10000", "11110", "10000", "10000", "10000"),
    "G": ("01110", "10001", "10000", "10111", "10001", "10001", "01110"),
    "H": ("10001", "10001", "10001", "11111", "10001", "10001", "10001"),
    "I": ("11111", "00100", "00100", "00100", "00100", "00100", "11111"),