A cellular automaton is a collection of "colored" cells on a grid of specified shape that evolves through a number of discrete time steps according to a set of rules based on the states of neighboring cells. The rules are then applied iteratively for as many time steps as desired.
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The theory of cellular automata is immensely rich, with simple rules and structures being capable of producing a great variety of unexpected behaviors.
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related:Cellular automaton - Wikipedia, the free encyclopedia
Cellular Automaton -- from Wolfram MathWorld
LinkNotes: John Conway's Game of Life