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First steps on asynchronous lattice-gas models with an application to a swarming rule

Natural Computing volume 12, pages 551–560 (2013)Cite this article

Abstract

Lattice-gas cellular automata are often considered as a particular case of cellular automata in which additional constraints apply, such as conservation of particles or spatial exclusion. But what about their updating? How to deal with non-perfect synchrony? Novel definitions of asynchronism are proposed that respect the specific hypotheses of lattice-gas models. These definitions are then applied to a swarming rule in order to explore the robustness of the global emergent behaviour. In particular, we compare the synchronous and asynchronous case, and remark that a paradoxical phenomenon, the anti-alignment of particles, is no longer observed when a small but not infinitesimal amount of asynchronism is added.

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Notes

  1. An alternative view would consist in considering that cells may modify their neighbours channels according to their own outgoing channels.

  2. Note that our particle-oriented interpretation of the system resembles Totally Asymmetric Simple Exclusion Processes (TASEP) (Derrida 1998).

  3. For a more complete set of monitoring tools, see Bouré et al. (2013).

  4. This pattern resembles the checkerboard-like configurations observed e.g. in asynchronous binary CA with a minority rule and a von Neumann neighbourhood (Regnault et al. 2009).

  5. Note that some of the results presented here differ qualitatively from a previous report (Bouré et al. 2012a). This was mainly caused by a faulty implementation of the asynchronous interaction scheme, as well as a limited size for the initial simulations which has been shown to influence the behaviour in the synchronous case (Bouré et al. 2013). This observation underlines the difficulty to validate simulations and behaviours for a given model and justifies the use of an analytical approach presented in Sect. 4.

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Authors and Affiliations

  1. Université de Lorraine, LORIA, UMR 7503, 54506, Vandoeuvre-lès-Nancy Cedex, France

    Olivier Bouré, Nazim Fatès & Vincent Chevrier

  2. CNRS, LORIA, UMR 7503, 54506, Vandoeuvre-lès-Nancy Cedex, France

    Olivier Bouré, Nazim Fatès & Vincent Chevrier

  3. Inria, 54600, Villers-lès-Nancy, France

    Olivier Bouré, Nazim Fatès & Vincent Chevrier

Authors
  1. Olivier Bouré
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  2. Nazim Fatès
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  3. Vincent Chevrier
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Correspondence to Olivier Bouré.

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Bouré, O., Fatès, N. & Chevrier, V. First steps on asynchronous lattice-gas models with an application to a swarming rule. Nat Comput 12, 551–560 (2013). https://doi.org/10.1007/s11047-013-9389-2

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  • DOI: https://doi.org/10.1007/s11047-013-9389-2

Keywords

  • Asynchronous cellular automata
  • Lattice-gas cellular automata
  • Robustness
  • Swarming behaviour

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