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Simple Networks on Complex Cellular Automata: From de Bruijn Diagrams to Jump-Graphs

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Evolutionary Algorithms, Swarm Dynamics and Complex Networks

Part of the book series: Emergence, Complexity and Computation ((ECC,volume 26))

Abstract

We overview networks which characterise dynamics in cellular automata. These networks are derived from one-dimensional cellular automaton rules and global states of the automaton evolution: de Bruijn diagrams, subsystem diagrams, basins of attraction, and jump-graphs. These networks are used to understand properties of spatially-extended dynamical systems: emergence of non-trivial patterns, self-organisation, reversibility and chaos. Particular attention is paid to networks determined by travelling self-localisations, or gliders.

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Notes

  1. 1.

    Repository Rule 54 http://uncomp.uwe.ac.uk/genaro/Rule54.html.

  2. 2.

    Repository Rule 110 http://uncomp.uwe.ac.uk/genaro/Rule110.html.

  3. 3.

    Complex Cellular Automata Repository http://uncomp.uwe.ac.uk/genaro/Complex_CA_repository.html.

  4. 4.

    Gliders in Rule 110 http://uncomp.uwe.ac.uk/genaro/rule110/glidersRule110.html.

  5. 5.

    Discrete Dynamics Lab http://www.ddlab.org.

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Author information

Authors and Affiliations

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

    Genaro J. Martínez & Andrew Adamatzky

  2. Escuela Superior de Cómputo, Instituto Politécnico Nacional, México City, México

    Genaro J. Martínez

  3. School of Science, Hangzhou Dianzi University, Hangzhou, China

    Bo Chen & Fangyue Chen

  4. Área Académica de Ingeniería, Universidad Autónoma del Estado de Hidalgo, Pachuca, Hidalgo, México

    Juan C. Seck-Tuoh-Mora

Authors
  1. Genaro J. Martínez
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  2. Andrew Adamatzky
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  3. Bo Chen
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  4. Fangyue Chen
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  5. Juan C. Seck-Tuoh-Mora
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Correspondence to Genaro J. Martínez .

Editor information

Editors and Affiliations

  1. Department of Computer Science, Faculty of Electrical Engineering and Computer Science VŠB-TUO, Ostrava, Poruba, Czech Republic

    Ivan Zelinka

  2. Department of Electronic Engineering, City University of Hong Kong, Kowloon, Hong Kong, China

    Guanrong Chen

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Martínez, G.J., Adamatzky, A., Chen, B., Chen, F., Seck-Tuoh-Mora, J.C. (2018). Simple Networks on Complex Cellular Automata: From de Bruijn Diagrams to Jump-Graphs. In: Zelinka, I., Chen, G. (eds) Evolutionary Algorithms, Swarm Dynamics and Complex Networks. Emergence, Complexity and Computation, vol 26. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-55663-4_12

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  • DOI: https://doi.org/10.1007/978-3-662-55663-4_12

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-55661-0

  • Online ISBN: 978-3-662-55663-4

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