Table of contents

  1. Front Matter
    Pages i-xxv
  2. Maurice Margenstern
    Pages 11-27
  3. Andrew Ilachinski
    Pages 29-71
  4. Nazim Fatès
    Pages 73-92
  5. Karoline Wiesner
    Pages 93-104
  6. Kenichi Morita
    Pages 105-128
  7. Burton Voorhees
    Pages 129-151
  8. Ramón Alonso-Sanz
    Pages 153-183
  9. Klaus Sutner
    Pages 185-200
  10. Tullio Ceccherini-Silberstein, Michel Coornaert
    Pages 221-238
  11. Gianluca Tempesti, Daniel Mange, André Stauffer
    Pages 239-259
  12. Carter Bays
    Pages 261-273
  13. Janko Gravner
    Pages 291-308
  14. James E. Hanson
    Pages 309-321
  15. Enrico Formenti, Petr Kůrka
    Pages 323-335
  16. Julien Cervelle, Alberto Dennunzio, Enrico Formenti
    Pages 357-371
  17. Marcus Pivato
    Pages 373-418
  18. Petr Kůrka
    Pages 419-444
  19. Franco Bagnoli, Samira El Yacoubi, Raúl Rechtman
    Pages 445-458
  20. Julien Cervelle, Enrico Formenti
    Pages 459-477
  21. Juan C. Seck-Tuoh-Mora, Genaro J. Martínez
    Pages 479-492
  22. Martin Kutrib
    Pages 513-542
  23. Martin Cenek, Melanie Mitchell
    Pages 543-554
  24. Georgios Ch. Sirakoulis
    Pages 555-582
  25. Jérôme Durand-Lose
    Pages 641-656
  26. Bastien Chopard
    Pages 657-689
  27. Nino Boccara
    Pages 705-718
  28. Andrew Adamatzky
    Pages 733-747
  29. Back Matter
    Pages 749-760

About this book


This volume of the Encyclopedia of Complexity and Systems Science, Second Edition, provides an authoritative introduction and overview of the latest research in cellular automata (CA) models of physical systems, emergent phenomena, computational universality, chaos, growth phenomena, phase transitions, self-organised criticality, reaction-diffusion systems, self-replications, parallel computation, and more. Fundamental topics of algorithmic complexity, algebraic groups, language theory, evolving CA, ergodic theory, synchronisation, tiling problems and undecidability and topological dynamics of CA are addressed. Cellular automata are regular uniform networks of locally-connected finite-state machines, and represent discrete systems with non-trivial behavior, including waves, patterns and travelling localisations. CA are ubiquitous: they are mathematical models of computation and computer models of natural systems. Classes of CA presented in this book include additive CA, automata in hyperbolic spaces and non-compact spaces, CA in triangular, pentagonal and hexagonal tessellations, automata with memory, quantum and reversible automata, structurally-dynamic CA, and asynchronous automata. Topics added to the second edition include: asynchronous cellular automata, stochastic cellular automata as models of reaction-diffusion processes, cellular automata hardware implementation, cellular automata basins of attraction, orbits of Bernoulli measures in cellular automata, and graphs related to reversibility and complexity in cellular. This state-of-the-art reference is unique in bringing together unequalled expertise of interdisciplinary studies at the edge of mathematics, computer science, and physics.


mathematical machines parallel computing complex systems modeling physical systems Firing Squad Synchronization Problem Self-Organized Criticality dynamics of evolution phase transitions

Editors and affiliations

  • Andrew Adamatzky
    • 1
  1. 1.Unconventional Computing CentreUniversity of the West of EnglandBristolUK

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