Self-Organization of Random Cellular Automata: Four Snapshots

We discuss four very simple random cellular automaton (CA) systems that self-organize over time. The first is a directed interface process which stabilizes in a coherent statistical equilibrium. The second is a model for excitable media: nucleating spiral cores lead to a locally periodic final state. The third model is a prototype for curvature-driven clustering. And the fourth illustrates the evolution of complex viable structures near phase boundaries in a parameterized family of non-linear population dynamics. For each CA we present a mix of rigorous results, conjectures, and empirical findings based on computer experimentation.

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