Gierer-Meinhardt Activator-Inhibitor

Turing pattern formation: fast-diffusing inhibitor and slow-diffusing activator spontaneously break symmetry from a homogeneous state. Spots, stripes, and labyrinths emerge depending on parameters.

Controls

Step: 0
Max activator: —
Pattern type: —
∂a/∂t = D_a∇²a + a²/h − b·a + ρ
∂h/∂t = D_h∇²h + a² − c·h

Turing condition:
D_h/D_a >> 1 (inhibitor spreads faster)

Spots: small a, large D ratio
Stripes: near transition

Turing 1952: proposed as
mechanism for animal markings