Turing Patterns — Image Pack

Turing patterns are the spatial structures that arise when two diffusing chemicals react at different rates. Alan Turing showed in 1952 that under the right conditions, an initially uniform mixture will spontaneously break symmetry and settle into stripes, spots, or labyrinths — purely as a consequence of diffusion rates and reaction kinetics, without any external template. The same mechanism is now believed to govern the markings on fish, the arrangement of hair follicles, and the branching of fingers in embryonic limbs. Each image in this collection is a Turing simulation run to equilibrium on a high-resolution grid. The patterns are not designed — they self-organize from random noise, the way they do on a leopard.

∂u/∂t = Du∇²u + f(u,v), ∂v/∂t = Dv∇²v + g(u,v)