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cyclic cellular automaton : ウィキペディア英語版
cyclic cellular automaton

The cyclic cellular automaton is a cellular automaton rule developed by David Griffeath and studied by several other cellular automaton researchers. In this system, each cell remains unchanged until some neighboring cell has a modular value exactly one unit larger than that of the cell itself, at which point it copies its neighbor's value. One-dimensional cyclic cellular automata can be interpreted as systems of interacting particles, while cyclic cellular automata in higher dimensions exhibit complex spiraling behavior.
== Rules ==

As with any cellular automaton, the cyclic cellular automaton consists of a regular grid of cells in one or more dimensions. The cells can take on any of n states, ranging from 0 to n-1. The first generation starts out with random states in each of the cells. In each subsequent generation, if a cell has a neighboring cell whose value is the successor of the cell's value, the cell is "consumed" and takes on the succeeding value. (Note that 0 is the successor of n-1; see also modular arithmetic.) More general forms of this type of rule also include a ''threshold'' parameter, and only allow a cell to be consumed when the number of neighbors with the successor value exceeds this threshold.

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