Science Narratives

Cyclic Cellular Automata

Four phases of spiral wave emergence from excitable media — Archimedean spirals, defect-mediated turbulence, and the boundary between order and chaos.

Cellular automata are grids of simple cells that update in parallel according to local rules. The cyclic variant, studied by David Griffeath and others, models excitable media: each cell cycles through a finite number of states, and when a cell in a high state touches a cell in a low state, it triggers a wave. The result is spontaneous spiral formation—target patterns and rotating spirals that persist indefinitely. This piece captures four phases of that evolution. The spirals you see are not programmed directly; they emerge from the collision of thousands of identical local updates. Each phase isolates a different snapshot in time, letting the plotter trace the wavefronts as they propagate, collide, and annihilate. The layered output reveals the geometry of excitable dynamics.

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