Alan Turing's 1952 paper "The Chemical Basis of Morphogenesis" showed that two reacting chemicals — an activator (u) and inhibitor (v) — with different diffusion rates can spontaneously form stable spatial patterns from homogeneous noise. The Gray-Scott model shown here uses: ∂u/∂t = Du∇²u − uv² + f(1−u), ∂v/∂t = Dv∇²v + uv² − (f+k)v. The activator (bright) autocatalyzes itself but is consumed by the inhibitor. When Du >> Dv, long-range inhibition enables short-range activation — the Turing instability. Click on the canvas to add perturbations. Different (f,k) pairs produce spots, stripes, mazes, or holes.