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The growth of configurations

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Abstract

The transition ruleF of a cellular automaton may sometimes be regarded as a “rule of growth” of a crystal from a “seed”ω. A study is made of the iteratesω,Fω,F 2 ω⋯.For certain one-dimensional growth rules, the limiting “shapes” of the crystals are computed, and an asymptotic formula for the size of the crystal as a function of time is obtained.

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References

  1. A. W. Burks, ed.:Essays on Cellular Automata. Urbana: University of Illinois Press (1970).

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  2. E. F. Codd:Cellular Automata. New York: Academic Press (1968).

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  3. S. J. Willson: On the ergodic theory of cellular automata.Mathematical Systems Theory,9, (1975) 132–141.

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  4. S. J. Willson:Limiting shapes for configurations. To appear inJournal of Computer and System Sciences.

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Authors and Affiliations

  1. Department of Mathematics, Iowa State University, 50011, Ames, Iowa, USA

    Stephen J. Willson

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  1. Stephen J. Willson
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Willson, S.J. The growth of configurations. Math. Systems Theory 10, 387–400 (1976). https://doi.org/10.1007/BF01683286

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  • DOI: https://doi.org/10.1007/BF01683286

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