Turing Morphogenesis

Gierer-Meinhardt reaction-diffusion — spots, stripes, labyrinths

∂ₜa = ρ(a²/h − μa) + Dₐ∇²a | ∂ₜh = ρ(a² − νh) + D_h∇²h

Da (activator diff.) Da = 0.010

Dh (inhibitor diff.) Dh = 0.200

Feed rate ρ ρ = 0.020

Speed x6

Alan Turing's 1952 paper showed two diffusing chemicals — a fast inhibitor and slow activator — can spontaneously break spatial symmetry into spots and stripes. This underpins animal coat patterns, sea shell markings, and digits on limbs.