TuringLab

f0.0367

k0.0649

Du0.160

Dv0.080

steps0

⟨v⟩—

regimespots

step 1 / 5

Welcome to TuringLab

In 1952, Alan Turing showed that two chemicals diffusing at different rates could spontaneously produce the patterns we see in nature — leopard spots, zebra stripes, brain folds, vegetation rings in arid landscapes. You're about to play with the actual equation.

Parameters live

feed f 0.0367

kill k 0.0649

Du 0.160

Dv 0.080

brush 14

speed 14×

Phase map click to jump

f (horiz) · k (vert) · cursor = current state

Presets classic

Color colormap

The equation

∂u/∂t = Du ∇²u − u v² + f (1 − u)
∂v/∂t = Dv ∇²v + u v² − (f + k) v

u replenishes at rate f, v decays at rate f+k, and u·v² is the autocatalytic step where v consumes u to make more v. Diffusion smears each chemical out — but at different speeds.

Shortcuts

Space play/pause
R reset · C clear
←/→ shift f · ↑/↓ shift k
1–9 presets
drag add chemical V