Reaction-Diffusion (Gray-Scott)

The mechanism Alan Turing proposed for the spots on a leopard and the stripes on a zebra — two chemicals, diffusing and reacting, that spontaneously break symmetry into living patterns.

Reaction-Diffusion (Gray-Scott)Live

Turing patterns from chemistry

Controls

Presets

Feed rate F

Kill rate k

Speed1×

Two chemicals diffuse and react by the Gray-Scott equations. Different feed and kill rates spontaneously form spots, stripes, and mazes — the mechanism Alan Turing proposed for animal coat patterns.

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Data Inspector

Feed F0.0545

Kill k0.0620

Steps0

Governing equation

\frac{\partial u}{\partial t} = D_{u} \nabla^{2} u - u v^{2} + F (1 - u), \frac{\partial v}{\partial t} = D_{v} \nabla^{2} v + u v^{2} - (F + k) v (F = 0.0545, k = 0.0620)

Reading this result: High feed (F=0.0545): abundant substrate lets spots grow and merge into branching maze and coral networks.

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How it works

The Gray-Scott model couples two reacting chemicals that diffuse at different rates. Tiny changes to the feed and kill rates flip the system between spots, stripes, mazes, and self-replicating blobs. This runs the full nonlinear PDE on a grid in your browser.

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