Two chemical species U,V: ∂U/∂t = Dᵤ∇²U − UV² + f(1−U), ∂V/∂t = Dᵥ∇²V + UV² − (f+k)V
0.055
0.062
0.20
Gray–Scott model: U is a substrate, V is a catalyst. They react: U+2V→3V (autocatalytic).
U is replenished at rate f; both species decay at rate (f+k)V.
Different (f,k) parameter regions yield dramatically different patterns: self-replicating spots, labyrinthine stripes, spirals, and more.
Discovered by John Gray & Scott (1984); patterns studied by Pearson (1993).