What are cellular automata?

(Thanks to Pavel Pokorny for Contributions to this answer) A Cellular automaton (CA) is a dynamical system with discrete time (like a map, see 2.6), discrete state space and discrete geometrical space (like an ODE), see 2.7). Thus they can be represented by a state s(i,j) for spatial state i, at time j, where s is taken from some finite set. The update rule is that the new state is some function of the old states, s(i,j+1) = f(s).

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