Cyclic Cellular Automaton

DEFINITION

k states in a ring
s → s+1 (mod k) when ≥ θ von Neumann
neighbours already hold s+1

NOTES

Rock-paper-scissors on a grid: every state is eaten by its successor, and the ring closes so nobody wins. From random debris the grid organises itself — droplets first, then spirals, which are the only structures that can feed forever — until every cell is turning in perfect lockstep. The plate detects that endgame and reseeds. The state ring maps straight onto the colour ramp, which is also a ring, so the wrap is seamless by construction.

PROVENANCE

Origin

D. Griffeath, University of Wisconsin, late 1980s; A. K. Dewdney, "Computer Recreations", Scientific American, August 1989

Standing

Public domain — a transition rule

Constants

Around 14 states the spirals win; far fewer and the debris never organises