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Gray-Scott · 200×200 grid · toroidal

∂a/∂t = D_a∇²a − ab² + F(1−a)

F = 0.0250 · k = 0.0600 · D_a = 0.16 · D_b = 0.08 · 8 steps/frame

Turing Patterns

Where leopard spots come from

In 1952 Alan Turing showed that two interacting 'chemicals' diffusing at different rates can spontaneously break symmetry and form stable patterns — spots, stripes, branching networks. The same equations explain leopard fur, zebra stripes, angelfish skin and parts of embryonic development. A small reaction-diffusion system, an astonishing reach.

Pattern preset

F · feed rate

0.0250

k · kill rate

0.0600

D_a · substrate (inhibitor) diffusion

0.160

D_b · activator diffusion

0.080

Initial seed

Speed · sim steps / frame

8 steps

Colour map

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Foldscape · An atlas of mathematical curiosities

Curated by Simon Franzen · zauberware

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