Using transition systems to describe and predict the behaviour of structured excitable media

Abstract

I show how transition systems can be applied to the naturally concurrent behaviour of excitable media. I consider structured excitable media, in which excitations are constrained to propagate only in defined narrow channels, and cannot propagate elsewhere. I define a type of transition system that can be used to describe the complete set of behaviours exhibited by simple structures. The composition rules that result from this definition can be used to automatically deduce the behaviour of more complex structures composed from simpler structures. Several examples illustrate the method, and a software implementation is provided.

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Acknowledgements

The work was partially supported by Leverhulme Trust grant F/00577/1. Thanks to Andrew Adamatzky for useful comments on an earlier draft of this paper.

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Correspondence to William M. Stevens.

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Stevens, W.M. Using transition systems to describe and predict the behaviour of structured excitable media. Nat Comput 12, 393–410 (2013). https://doi.org/10.1007/s11047-012-9355-4

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Keywords

  • Transition systems
  • Concurrency
  • Excitable media
  • Toppling dominoes
  • Physarum polycephalum
  • Belousov–Zhabotinsky reaction