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Lagniappe #8

Cellular Automaton Growth on Z2:
Theorems, Examples, and Problems

Janko Gravner and David Griffeath

We survey the phenomenology of crystal growth and asymptotic shape for two-dimensional, two-state cellular automata. In the most tractable case of Threshold Growth, a detailed rigorous theory is available. Other less orderly examples with recursively computable updates illustrate the broad range of behavior obtained from even the simplest initial seeds and update rules. Still more exotic cases seem largely beyond the scope of exact analysis, but pose fascinating problems for experimentalists. The paper concludes with a discussion of connections between deterministic shape theory and important corresponding questions for systems with random dynamics.


Threshold and Monotone Growth


Download the complete manuscript (58 pp., 1.5 M)

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