What is the Gray-Scott model?

The Gray-Scott model is a pair of coupled partial differential equations describing how two chemical species U and V diffuse and react: U is consumed when it meets V (producing V), while a feed rate replenishes U and a kill rate removes V. Depending on feed rate F and kill rate k, remarkably different spatial patterns emerge.

What are Turing patterns?

Turing patterns are stable spatial patterns that emerge spontaneously from uniform initial conditions through a mechanism called diffusion-driven instability, first described by Alan Turing in 1952. A fast-diffusing inhibitor and slower-diffusing activator interact to produce regular spots, stripes, spirals, and labyrinths -- seen in animal skin patterns, shell pigmentation, and many biological structures.

What do the F and k parameters control?

F (feed rate) controls how quickly the U chemical is replenished from an external supply. k (kill rate) controls how quickly the V chemical is removed. Different combinations of F and k produce qualitatively different patterns. Small F+k tends to produce U-skate waves; intermediate values give spots or stripes; higher values create maze and coral patterns.

Can I interact with the simulation?

Yes -- click or drag on the canvas to paint seeds of V chemical into the simulation. This lets you draw patterns, disturb existing structures, or start new reaction fronts. You can also use preset buttons to switch between classic pattern regimes, or manually adjust F and k with the sliders.

Home▸Chaos & Dynamics▸Gray-Scott Reaction-Diffusion: Turing Patterns and Morphogenesis

🧪 Gray-Scott Reaction-Diffusion: Turing Patterns and Morphogenesis

Simulate Gray-Scott reaction-diffusion and watch Turing patterns emerge: spots, stripes, coral, spirals, maze, and mitosis patterns. Explore the mathematics behind animal markings, shell patterns, and morphogenesis.

Chaos & Dynamics2DModerate60 FPS

⚙ Under the hood

This simulation demonstrates the Gray-Scott reaction-diffusion system, which produces complex patterns resembling morphogenesis – the development of form in biological organisms. It showcases how simple chemical reactions can generate intricate structures.

Gray-ScottReaction-DiffusionTuring Patterns

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install