Turing Patterns

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Reaction-Diffusion System

This simulation implements the Gray-Scott model, where two chemicals interact and diffuse to create self-organizing patterns. Alan Turing showed in 1952 that such systems could explain morphogenesis—how organisms develop their shapes and patterns.

Parameters

Rate at which chemical A is replenished
Rate at which chemical B is removed
Diffusion rate of substrate
Diffusion rate of activator

Pattern Presets

Visualization

The Mathematics

The Gray-Scott equations describe how the concentrations of chemicals A and B change over time:

∂A/∂t = DA∇²A - AB² + f(1-A)
∂B/∂t = DB∇²B + AB² - (k+f)B

Where ∇² is the Laplacian operator (measuring diffusion), AB² represents the reaction rate, and the system exhibits pattern formation when the activator (B) diffuses slower than the inhibitor (A).