← back Cyclic Cellular Automata

Origin

Greenberg and Hastings, 1978. Fisch, Gravner, Griffeath, 1991 analyzed the phase diagram. N-species rock-paper-scissors on a grid. With 14+ colors, mesmerizing spiral galaxies self-organize from random noise.

How It Works

N colors on a wheel. Each pixel can only be eaten by the next color in the cycle. If a pixel sees enough neighbors of its successor color within its neighborhood, it advances. Greenberg-Hastings variant has only one color advance by contact, the rest auto-advance through a refractory period.

Applications

Models excitable media, cardiac arrhythmia spiral waves, chemical oscillations like the BZ reaction. Spiral form follows neighborhood shape, diamond neighborhoods make diamond spirals.

adjust colors for spiral complexity·threshold controls how many neighbors trigger advancement·toggle GH mode for Greenberg-Hastings variant
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