🐆 Turing Reaction-Diffusion Patterns

Turing showed that when an inhibitor diffuses faster than an activator, a near-uniform state becomes unstable. Short-wavelength disturbances grow while long ones fade, so the system settles into a periodic structure with a characteristic spacing rather than staying flat.

Chemical A acts as the activator and chemical B as the inhibitor. In the Gray-Scott equations B is autocatalytic through the AB² term, meaning it promotes its own production while consuming A, and the displayed colour maps the concentration of B.

It runs on the GPU using two ping-ponged WebGL float textures that store the A and B fields. A GLSL fragment shader updates every cell in parallel each frame, using a weighted 9-point Laplacian to approximate diffusion before applying the reaction terms.

Each preset loads a tuned pair of Feed and Kill values. Spots uses about F 0.035 and K 0.065, stripes about 0.022 and 0.051, labyrinth about 0.029 and 0.057, and giraffe about 0.039 and 0.058. Moving a slider switches you to Custom.

Yes. Clicking or dragging on the canvas paints fresh blobs of chemical B under the cursor, which then react and spread according to the current Feed and Kill settings. The Re-seed button scatters new random blobs and Reset restarts from the spots preset.

It is a faithful numerical solution of the Gray-Scott equations, which are a recognised mathematical model of Turing-type pattern formation. It is a simplified abstraction rather than a literal map of any specific biological reaction, but it captures the essential activator-inhibitor mechanism correctly.

The same reaction-diffusion mathematics is thought to underlie animal coat markings such as leopard spots and zebra stripes, the ridged surface of coral and brain tissue, and the regular spacing of fingers. In 2012 researchers confirmed Turing-like chemistry helps set digit spacing in mouse paws.