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A survey of cellular automata: types, dynamics, non-uniformity and applications

Abstract

Cellular automata (CAs) are dynamical systems which exhibit complex global behavior from simple local interaction and computation. Since the inception of cellular automaton (CA) by von Neumann in 1950s, it has attracted the attention of several researchers over various backgrounds and fields for modeling different physical, natural as well as real-life phenomena. Classically, CAs are uniform. However, non-uniformity has also been introduced in update pattern, lattice structure, neighborhood dependency and local rule. In this survey, we tour to the various types of CAs introduced till date, the different characterization tools, the global behavior of CAs, like universality, reversibility, dynamics etc. Special attention is given to non-uniformity in CAs and especially to non-uniform elementary CAs, which have been very useful in solving several real-life problems.

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Notes

  1. Some authors call the non-uniform CAs with linear/additive and complemented rules as additive CAs. The reason may be that, these CAs can be characterized using the tools of linear CAs. However, strictly speaking, these CAs are not additive, in general.

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Acknowledgements

The authors gratefully acknowledge the anonymous reviewers for their comments and suggestions, which have helped to improve the quality and readability of the paper.

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Correspondence to Kamalika Bhattacharjee.

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This research is partially supported by Innovation in Science Pursuit for Inspired Research (INSPIRE) under Dept. of Science and Technology, Govt. of India.

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Bhattacharjee, K., Naskar, N., Roy, S. et al. A survey of cellular automata: types, dynamics, non-uniformity and applications. Nat Comput 19, 433–461 (2020). https://doi.org/10.1007/s11047-018-9696-8

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  • DOI: https://doi.org/10.1007/s11047-018-9696-8

Keywords

  • Cellular automata (CAs)
  • Types
  • Characterization tools
  • Dynamics
  • Non-uniformity
  • Technology

Mathematics Subject Classification

  • 68Q80
  • 37B15