Gray–Scott Reaction–Diffusion

DEFINITION

∂u/∂t = Dᵤ∇²u − uv² + f(1−u)
∂v/∂t = D᷅∇²v + uv² − (f+k)v

NOTES

Two chemicals: one fed in, one that consumes it autocatalytically and decays. Turing predicted in 1952 that such a system could break its own symmetry and produce stripes and spots, which is where animal coats come from. The feed and kill rates decide whether you get coral, mitosis, worms or a slow death.

PROVENANCE

Origin

Gray & Scott, Chem. Eng. Sci., 1983; Turing, Phil. Trans. R. Soc. B, 1952

Standing

Public domain — a pair of partial differential equations

Constants

f=0.037 k=0.06 gives coral; f=0.029 k=0.057 gives mitosis. The lattice sets the pattern scale, not just the detail — more cells means more, smaller features

Source

doi:10.1016/0009-2509(83)80132-8