Activator-Inhibitor Pattern Formation
Turing instability: reaction-diffusion system spontaneously forms spots, stripes, and labyrinths
Step: 0
Pattern: —
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Turing's morphogenesis (1952): Two chemicals — activator U and inhibitor V — react and diffuse. If the inhibitor diffuses faster (D_v ≫ D_u), random perturbations grow into stable spatial patterns.
Gray-Scott model: ∂U/∂t = D_u∇²U - UV² + F(1-U); ∂V/∂t = D_v∇²V + UV² - (F+k)V.
Changing F (feed) and k (kill) navigates the parameter space: spots → stripes → labyrinths → holes → homogeneous.
Color: blue=low activator, cyan/green=medium, white=high activator. Click to inject activator locally.