Cellular Automata Synthesis — User Guide

Sonifies cellular-automaton states as short additive sound generations. Active cells become sine oscillators whose frequencies are determined by cell position; the evolving CA therefore becomes an evolving spectrum.

Author: Shai Cohen Affiliation: Department of Music, Bar-Ilan University, Israel Version: 0.4.1 (2026) License: MIT License Repo: Praat AudioTools

Contents:

What this does Quick start Presets CA types Sound mapping Parameters Spatial output Visualization & QC

What this does

Cellular Automata Synthesis generates audio from three cellular-automaton families: elementary one-dimensional rules, Conway's Game of Life, and Brian's Brain. Each CA generation occupies one short time segment. Cells in the active/firing state become sine oscillators; their positions determine their frequencies. The segment is then followed by the next CA generation, so changes in cellular structure become changes in spectral population over time.

Signal path: initialize CA → evolve one generation at a time → map active cells to frequencies → sum oscillators with density compensation → apply short edge tapers → concatenate generations → optional stereo render → optional peak normalization.

The script generates sound internally; no input Sound is required. The final object is named ca_<preset-name>.

Quick start

Run Cellular_Automata_Synthesis.praat.
Choose a preset, or select Custom.
For an elementary CA, choose the rule number, boundary mode, and initial condition. For the 2D rules, the script supplies the appropriate random initial state.
Set the generation duration and frequency range.
Choose Mono, Stereo Wide, or Rotating output.
Run the script. The final Sound remains selected in the Objects window; visualization and playback are optional.

Useful distinction: Segment_duration_s is the duration assigned to one CA generation. The script uses ceiling(Duration / Segment_duration) generations and shortens the final segment when necessary, so the final Sound still matches Duration_s.

Presets

Presets replace only the fields listed below. Sample_rate_Hz, Random_seed, normalization, visualization, and playback remain as entered unless explicitly stated.

Preset	CA setup	Sound mapping	Spatial override
Rule 30 Classic	8 s; grid 32; elementary Rule 30; fixed boundary; single centre cell	100 ms/generation; 150 Hz base; 200 Hz spread	None
Rule 110 Complex	10 s; grid 40; elementary Rule 110; fixed boundary; single centre cell	80 ms/generation; 120 Hz base; 250 Hz spread	None
Rule 90 Symmetric	8 s; grid 32; elementary Rule 90; fixed boundary; single centre cell	100 ms/generation; 180 Hz base; 180 Hz spread	None
Rule 184 Traffic	8 s; grid 32; elementary Rule 184; wrap boundary; random traffic at 35% occupancy	100 ms/generation; 200 Hz base; 150 Hz spread	None
Game of Life	12 s; 18×18; B3/S23; wrap boundary; random 30% live seed	150 ms/generation; 100 Hz base; 300 Hz spread	Stereo Wide
Brian's Brain	10 s; 20×20; wrap boundary; random 22% firing + 10% refractory seed	120 ms/generation; 130 Hz base; 200 Hz spread	Rotating

CA types

Elementary CA (1D)

A row of binary cells is updated from left, centre, and right neighbours. The three bits form a number from 0 to 7; the corresponding bit of Rule_number becomes the next cell state. Rules 0–255 are accepted.

Boundary: Fixed treats cells outside the finite row as zero. Wrap connects the left and right edges.

Initial condition: single centre cell, random 35% traffic, alternating 1010, or random sparse 10%.

Game of Life (2D)

Binary B3/S23 Life: a dead cell is born with exactly three live neighbours; a live cell survives with two or three. The script begins from a random 30% live field. Only live cells are sonified.

Brian's Brain (2D)

Three states are used: dead → firing → refractory → dead. A dead cell fires when exactly two neighbours are firing. Only firing cells generate oscillators; refractory cells affect later evolution and appear in the visualization, but are not themselves sounded.

Sound mapping

One generation = one additive sound state

For every generation, the script first counts the active cells. If there are N active cells, each oscillator receives gain 0.65 / sqrt(N). This keeps changing CA density primarily audible as changing spectral population, rather than allowing dense generations to become simple gain boosts.

Position → frequency

CA	Position mapping	Result
Elementary	`u = (cell−1)/(grid−1)`	First and last cells map exactly to Base and Base+Spread.
Game of Life	`u = ((row−1)+√2(column−1)) / ((grid−1)(1+√2))`	Uses both axes and spans the requested range exactly, with a near-injective projection that reduces repeated frequencies.
Brian's Brain	Row-major cell index normalized from 0 to 1	The complete 2D grid is distributed exactly across Base…Base+Spread.

Phase and segment edges

Each cell receives a deterministic phase offset derived from its cell index and a golden-ratio fractional step. The same cell therefore keeps the same phase identity across generations, while simultaneously active cells are less likely to pile up coherently.

Each generation is mostly flat in amplitude. Only the first and last up to 5 ms use a raised-cosine edge taper (also limited to 20% of a very short segment). Generations are concatenated; this is not a crossfade. A second global fade of up to 10 ms protects the final Sound endpoints.

Parameters

Parameter	Default	Behavior
Duration_s	8.0 s	Requested final Sound duration.
Sample_rate_Hz	44100	Output sample rate; minimum 2000 Hz.
Grid_size	32	Clamped to 8–64 for elementary CA; 2D rules are additionally capped at 24×24.
Rule_type	Elementary	Elementary CA, Game of Life, or Brian's Brain.
Rule_number	30	0–255; used only by Elementary CA.
Boundary_mode	Fixed	Zero outside the grid, or wrap/toroidal edges. Applies to both 1D and 2D rules.
Elementary_initial_condition	Single centre	Used only by Elementary CA.
Random_seed	0	0 uses an unpredictable initial state; a positive seed reproduces random 1D/2D initialization. Deterministic initial conditions do not depend on the seed.
Segment_duration_s	0.1 s	Nominal duration of each generation; the last generation may be shorter.
Base_frequency_Hz	150 Hz	Bottom of the frequency map.
Frequency_spread_Hz	200 Hz	Requested distance from Base to the top of the map.
Spatial_mode	Mono	Mono, Stereo Wide, or Rotating.
Normalize_output	yes	For non-silent output, scales the final absolute peak to 0.90.
Draw_visualization	yes	Draws the CA/mapping/QC figure after synthesis.
Play_result	yes	Plays the completed Sound.

Nyquist guard: the script reserves the band below 0.45 × Sample_rate_Hz. If Base+Spread would exceed that limit, the effective spread is reduced while Base is preserved. If Base itself reaches the safety limit, synthesis stops. Runs requesting more than 2000 generations are also rejected.

Spatial output

Mono

Keeps the concatenated CA synthesis as one channel.

Stereo Wide

The left channel is the mono signal. The right channel is a delayed copy. The delay is min(7 ms, 0.25 × Segment_duration_s). This produces temporal decorrelation without spectral splitting. The original source is mono, so there is no pre-existing stereo image to preserve.

Rotating

Creates complementary equal-power left/right gains at 0.15 Hz (about 6.67 seconds per cycle). The signal begins in the centre and moves smoothly across the stereo field.

Normalization

When enabled and the Sound is non-silent, Scale peak: 0.90 is applied after spatial rendering. This is target peak normalization, not an attenuate-only ceiling.

Visualization & QC

The figure combines the actual CA realization with measurements of the final Sound.

Panel	What is shown
A — Actual CA	For elementary CA: the complete evolution, downsampled to at most 200 display columns when needed. For 2D CA: true first, middle, and final snapshots. In Brian's Brain, firing and refractory states are distinguished.
B — Activity trajectory	Actual active/firing density for every rendered generation. Brian's Brain also shows refractory density as a second trajectory.
C — Model → measurement	A measured spectrogram of the final output with the realized per-generation mean frequency and min/max frequency guides overlaid. For stereo output, the channel with the higher whole-file RMS is displayed rather than folding L+R to mono.
D — Mechanism & QC	Rule summary, frequency mapping law, mean/max activity, first silent generation, realized frequency range, Nyquist adjustment status, edge-taper duration, output peak/RMS/channels, spatial mode, and seed.

Interpretation: Panel A and B are model-state views; Panel C is measured audio with model guides. The blue mean-frequency trace is therefore a control-derived descriptor of the active cells, not a pitch track estimated from the Sound.

Practical notes

CA behavior depends strongly on the finite-grid boundary condition. A pattern on a fixed finite row can die simply by reaching an edge; wrap boundaries instead make the grid topologically circular/toroidal.
Rule 184 is paired with a random-traffic seed and wrap boundaries because that combination better exposes its transport behavior than a lone centre cell on a fixed grid.
Rule 90 is an additive/XOR elementary rule and, from a single centre cell, produces the familiar Sierpiński-triangle structure. It is commonly classified as Class III rather than Class II.
Rule 110 is computationally universal, but this script uses it as a sound-generating dynamical rule; it does not construct a universal computation.