Simulating natural systems: automata, flow fields, and growth

Nature simulations are the visual backbone of an audiovisual live set: an automaton pulsing on the beat, a flow field carrying particles through a breakdown, a dendritic growth blooming over a build. This module turns three families of natural-system algorithms into self-contained sketches you can drop into a projection rig and mutate live — where every sketch must keep running while you edit it, so clean state handling matters as much as the rule itself.

The arc starts with the most constrained system: grid automata. Begin from the local-neighbour-rule model and its non-negotiable two-phase update (compute all next states, then apply), instantiate it as Conway’s two survival/birth rules, then loosen it twice — Langton’s Ant swaps the synchronous grid for a single agent writing its memory into the environment, and the continuous-value averaging CA trades discrete states for fluid wave propagation. Next you leave the grid’s lockstep for continuous space: 2D noise traversal (nested loops, per-axis seeds, the typewriter-style row reset) generates smooth fields, noise-driven grid displacement clusters shapes organically, and mapping noise to angles yields the flow field that steers your particles. Finally, growth: DLA’s snap-to-nearest-neighbour accretion and collision-frozen circle packing each build structure no one designed.

The nine required atoms gate the capstone directly — each of its three sketches fails without its rule set, and the noise-traversal mechanics recur in all field work, which is why the two-phase CA update and 2D noise loop are drilled to automaticity. Supporting atoms deepen rather than gate: the random-walk lineage behind DLA, emergence as the unifying idea, organic geometry as the aesthetic frame, plus pointers toward the Nature of Code track and camera-input extensions.

Runnable examples

Generated from the context/ instrument corpus by concept (redistributable idioms only). Do not edit — regenerate with gen-module-examples.mjs.

modulation-warp

osc(4).modulate(src(o0), 0.6).out(o0)

_{hydra-0022 · CC0-1.0}

s0.initP5(); src(s0).modulate(noize(), 0.3).out()

_{p5live-0038 · CC0-1.0}

feedback-trail

osc(4).modulate(src(o0), 0.6).out(o0)

_{hydra-0022 · CC0-1.0}

function draw(){ fill(0, 20); rect(0, 0, width, height); circle(mouseX, mouseY, 40) }

_{p5live-0003 · CC0-1.0}

noise-field

noise(4, 0.1).out()

_{hydra-0002 · CC0-1.0}

float h21(vec2 p){return fract(sin(dot(p,vec2(12.9898,78.233)))*43758.5453);}

_{glsl-0013 · public-domain}

flow-field

let ang = noise(x*0.01, y*0.01) * TWO_PI

_{p5live-0008 · CC0-1.0}

blur-soften

filter(BLUR, 4)

_{p5live-0073 · CC0-1.0}

noise-drift

let x = noise(frameCount*0.002)*width, y = noise(frameCount*0.003)*height

_{p5live-0007 · CC0-1.0}