This cyclic cellular automaton is a kind of automaton rule invented by David Griffeath from University of Wisconsin – Madison.
This auto-reproductive cell automaton is two-dimensional, and its cells can take four states (1, 2, 3 or 4) in the standard version.
The state of a cell at time t + 1 depends on its state at time t and the state of its 4 neighbors (Von Neumann's neighborhood).
A cell moves from a state i to a state i + 1 (mod 4) in the state cycle when the state i + 1 (mod 4) is present in at least one neighboring cell.
For 8 neighbors (Moore), Griffeath did modifications by adding a threshold (3 by default) for wich a cell changes its state:
For this version, if you simulate with 5 states, you may observe such figure:
The current cell in state i checks its state against the neighbors' states. If 3 (threshold) or more neighbors have a state between (i+1) and (i + nbStates/3), then the current cell changes to that state.
For example, if the current cell state is 2, and 3 of its neighbors are in state 3 to 6, then the current cell changes its state to 3:
For this version, if you simulate with 14 states, you may observe such figure:
