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Automata and Complexity pp 43–55Cite as

Periods in the Q2R, X2R and Kawasaki-Q2R Cellular Automata

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Part of the Emergence, Complexity and Computation book series (ECC,volume 42)

Abstract

We study global and local periods of the cellular automaton Q2R, the equivalent model on a triangular grid (X2R) and a Kawasaki-Q2R update. The first two show similar results in both the global and local periods. We find a critical energy \(E_{cp}=-0.8700 \pm 0.0006\) for Q2R and \(E_{cp} = -0.88408 \pm 0.0004\) for X2R. In the Kawasaki-Q2R automaton dynamics finite global periods are present exclusively at very low energies and no critical energy is found. However, in all three cellular automata there is an evident formation of clusters of finite cycles. Ergodicity is violated.

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Author information

Authors and Affiliations

  1. Institute for Theoretical Physics, ETH Zurich, 8093, Zurich, Switzerland

    Lidia Stocker

  2. PMMH, ESPCI, 75005, Paris, France

    Hans J. Herrmann

Authors
  1. Lidia Stocker
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  2. Hans J. Herrmann
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Corresponding author

Correspondence to Hans J. Herrmann .

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Editors and Affiliations

  1. Unconventional Computing Centre, University of the West of England, Bristol, UK

    Prof. Andrew Adamatzky

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Stocker, L., Herrmann, H.J. (2022). Periods in the Q2R, X2R and Kawasaki-Q2R Cellular Automata. In: Adamatzky, A. (eds) Automata and Complexity. Emergence, Complexity and Computation, vol 42. Springer, Cham. https://doi.org/10.1007/978-3-030-92551-2_4

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  • DOI: https://doi.org/10.1007/978-3-030-92551-2_4

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-030-92551-2

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