Gray-Scott Reaction-Diffusion
∂u/∂t = D_u∇²u − uv² + F(1−u) · ∂v/∂t = D_v∇²v + uv² − (F+k)v
The Gray-Scott model simulates two chemical species U (activator) and V (inhibitor) with the autocatalytic reaction U + 2V → 3V and replenishment/decay.
Despite its simplicity, the (F, k) parameter space produces an extraordinary variety of self-organizing patterns — spots, stripes, labyrinths, spirals, and traveling waves —
all arising from the interplay of local activation and long-range inhibition (Turing 1952 mechanism).
The patterns form when the diffusion ratio D_u/D_v > 1: the activator diffuses slower than the inhibitor, creating local instabilities.
Select presets or sweep F and k manually to explore the rich phase diagram.