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For Students · Reaction-Diffusion

Reaction-Diffusion for a traffic jam

Built for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition. Simulate a traffic jam live below — adjust the inputs and watch it respond, right in your browser.

Reaction-Diffusion (Gray-Scott)Live

Turing patterns from chemistry

Controls

Presets

Feed rate F

Kill rate k

Speed1×

Two chemicals diffuse and react by the Gray-Scott equations. Different feed and kill rates spontaneously form spots, stripes, and mazes — the mechanism Alan Turing proposed for animal coat patterns.

▶ Run in Python

Data Inspector

Feed F0.0545

Kill k0.0620

Steps0

Governing equation

\frac{\partial u}{\partial t} = D_{u} \nabla^{2} u - u v^{2} + F (1 - u), \frac{\partial v}{\partial t} = D_{v} \nabla^{2} v + u v^{2} - (F + k) v (F = 0.0545, k = 0.0620)

Reading this result: High feed (F=0.0545): abundant substrate lets spots grow and merge into branching maze and coral networks.

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Frequently asked questions

Is this good for students?: Yes — this version of "Reaction-Diffusion for a traffic jam" is framed for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.