Chapter 5: Two Dimensions and Beyond

Section 5: Network Systems

Cellular automata on networks

The cellular automata that we have considered so far all have cells arranged in regular arrays. But one can also set up generalizations in which the cells correspond to nodes in arbitrary networks. Given a network of the kind discussed in the main text of this section, one can assign a color to each node, and then update this color at each step according to a rule that depends on the colors of the nodes to which the connections from that node go. The behavior obtained depends greatly on the form of the network, but with networks of finite size the results are typically like those obtained for other finite size cellular automata of the kind discussed on page 259.

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