Two chemical species · Turing instability · emergent pattern formation
The Gray-Scott model describes two chemical species U (activator substrate) and V (catalyst) reacting and diffusing on a 2D grid. Despite simple local rules, it produces stunning global patterns.
∂U/∂t = D_U ∇²U − UV² + F(1−U)
∂V/∂t = D_V ∇²V + UV² − (F+k)V
Feed rate F controls how fast U is replenished; kill rate k controls V removal. Tiny changes in (F,k) flip the system between spots, stripes, worms, and sponge-like patterns — a Turing instability landscape.