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∂u/∂t = Dᵤ∇²u − uv² + f(1 − u)
Reaction-Diffusion
Two chemicals reacting across a grid produce leopard spots, fingerprint whorls, and labyrinth mazes — the visual logic of every animal print.
v = curl(noise(p))
Flow Fields
Smooth Perlin noise turned into a vector field — particles trace invisible rivers across the canvas, leaving luminous trails.
birth · drift · death
Particle Genealogies
Each particle carries a lineage ID. They bloom from emitters, drift on the audio waveform, and fade into the next generation.
min |p − xᵢ|
Voronoi Cells
Scatter points, assign every pixel to its nearest neighbor — Voronoi diagrams tile the canvas into organic cells of unequal geometry.
σ=10 · ρ=28 · β=8/3
Strange Attractors
Deterministic chaos — three coupled differential equations trace the butterfly-wing curves Lorenz and Rössler made famous.
P3 · Truchet(θ)
Tessellations
Non-periodic Penrose tilings and rotating Truchet arcs pack the plane without ever repeating the same patch twice.
B3/S23 · vote(n)
Conways
Cellular automata on a grid — each cell lives, dies, or spawns based on its neighbors. Gliders, blinkers, and Gosper guns emerge unprompted.
F → F[+F]F[−F]F
Recursive Subdivisions
L-systems rewrite strings into branching trees; quadtrees and Sierpińskis recurse until they fill the plane in self-similar layers.