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).
