Chapter 5: Two Dimensions and Beyond

Section 2: Cellular Automata

Networks [as basis for cellular automata]

Cellular automata can be set up so that each cell corresponds to a node in a network. (See page 936.) The only requirement is that around each node the network must have the same structure (or at least a limited number of possible structures). For nearest-neighbor rules, it suffices that each node has the same number of connections. For longer-range rules, the network must satisfy constraints of the kind discussed on page 483. (Cayley graphs of groups always have the necessary homogeneity.) If the connections at each node are not labelled, then only totalistic cellular automaton rules can be implemented. Many topological and geometrical properties of the underlying network can affect the overall behavior of a cellular automaton on it.

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From Stephen Wolfram: A New Kind of Science [citation]