Activator-Inhibitor Cellular Automata

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Starting from a random initial condition, different patterns form depending on what positive or negative contributions are received from cells at distances 2 and 3. This 2D thresholded continuous cellular automaton is a model for many systems that produce reticulated or labyrinthine patterns—notably in biological pigmentation.

Contributed by: Stephen Wolfram (March 2011)
Open content licensed under CC BY-NC-SA


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At each step, the values of all cells at a particular distance are added, and multiplied by the weight for that distance. Then the results for all distances are totalled. If the total is positive, the cell is set to value 1; otherwise it is set to value 0.



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