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Cellular Automata in Hyperbolic Spaces

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Advances in Unconventional Computing

Part of the book series: Emergence, Complexity and Computation ((ECC,volume 22))

Abstract

The chapter presents a bit more than fifteen years of research on cellular automata in hyperbolic spaces. After a short historical section, we remind the reader what is needed to know from hyperbolic geometry. Then we sum up the results which where obtained during the considered period. We focus on results about universal cellular automata, giving the main ideas which were used in the quest for universal hyperbolic cellular automata with a number of states as small as possible.

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Notes

  1. 1.

    Not on fashion problems are not necessarily uninteresting problems.

  2. 2.

    Don’t worry: nobody will ask you how you proceed for this identification. Such a question has no place in a serious, objective paper.

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Author information

Authors and Affiliations

  1. LITA, EA 3097, Université de Lorraine, UFR MIM, Campus du Saulcy, 57045, METZ Cédex 1, France

    Maurice Margenstern

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  1. Maurice Margenstern
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Correspondence to Maurice Margenstern .

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Editors and Affiliations

  1. Unconventional Computing Centre, University of the West of England Unconventional Computing Centre, Bristol, United Kingdom

    Andrew Adamatzky

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Margenstern, M. (2017). Cellular Automata in Hyperbolic Spaces. In: Adamatzky, A. (eds) Advances in Unconventional Computing. Emergence, Complexity and Computation, vol 22. Springer, Cham. https://doi.org/10.1007/978-3-319-33924-5_14

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  • DOI: https://doi.org/10.1007/978-3-319-33924-5_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-33923-8

  • Online ISBN: 978-3-319-33924-5

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