Cellular Automaton State Transition Diagrams

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Each vertex on the graph represents one of the states of a size- elementary cellular automaton, and is joined to the vertex representing the state reached after one step in the cellular automaton evolution.

Contributed by: Stephen Wolfram (March 2011)
Open content licensed under CC BY-NC-SA


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A system of limited size has a behavior that is ultimately repetitive. The maximum possible repetition period for any system is always equal to the total number of possible states of the system. Of the elementary rules, only rule 45 seems to yield periods that always stay close to the maximum of



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