Three-component reaction-diffusion on a 2D grid. The third species (substrate) creates rich pattern variety: spirals, labyrinths, hexagons, and spots. Color = activator concentration.
Turing (1952) showed reaction-diffusion systems can spontaneously form spatial patterns if the inhibitor diffuses faster than the activator. Three-component systems allow much richer dynamics: the substrate controls pattern selection (spots vs stripes) and can enable traveling wave trains.