Morphogenesis — 3-Component Reaction-Diffusion

Turing's morphogenesis: short-range activation + long-range inhibition spontaneously generates patterns. A 3-component system (activator A, inhibitor B, substrate S) produces spots, stripes, and labyrinthine patterns.

Feed Rate f 0.035

Kill Rate k 0.060

Diffusion A (×10⁻⁴) 2.0

Diffusion B (×10⁻⁴) 8.0

Preset

Gray-Scott model:
∂A/∂t = Dₐ∇²A − AB² + f(1−A)
∂B/∂t = D_b∇²B + AB² − (f+k)B

Turing instability: A homogeneous steady state is stable to uniform perturbations but unstable to spatially varying ones — producing self-organized spatial patterns. Wavelength set by √(D/reaction rate).