Turing Reaction-Diffusion

A live Gray-Scott simulation grows spots and stripes on an undulating surface, driven by two reacting chemicals.

The Gray-Scott model is a pair of coupled PDEs describing two chemicals, U and V, that diffuse across a grid and react as U is consumed to produce V (uvv term) while both are replenished/removed by feed and kill rates. Alan Turing showed in 1952 that such reaction-diffusion systems can spontaneously break symmetry to form the spots and stripes seen in animal coats. Here the PDEs are integrated explicitly on a toroidal grid using a weighted 3x3 Laplacian stencil, several sub-steps run per rendered frame, and the resulting V concentration field is written into an HTML canvas each frame and streamed to the GPU as a live-updating texture mapped onto a displaced plane.

Grid resolution: 128 x 128 cells
Diffusion rates: Du 0.16 / Dv 0.08
Feed rate: 0.037   Kill rate: 0.06
Sub-steps per frame: 8
Boundary: toroidal (wrap-around)

Simulation Settings