Abstract
We give an exact characterization of the movement of a single kink in the elementary cellular automaton Rule 18. It is a random walk with independent increments as well as independent delay times. Its statistical parameters are computed to confirm the earlier simulation results by Grassberger.
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References
P. Grassberger, Chaos and diffusion in deterministic cellular automata,Physica D 10:52–58 (1984).
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D. A. Lind, Applications of ergodic theory and sofic systems to cellular automata,Physica D 10:36–44 (1984).
S. Wolfram, Universality and complexity in cellular automata,Physica D 10:1–35 (1984).
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Eloranta, K., Nummelin, E. The kink of cellular automaton rule 18 performs a random walk. J Stat Phys 69, 1131–1136 (1992). https://doi.org/10.1007/BF01058766
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DOI: https://doi.org/10.1007/BF01058766