Small Universal Cellular Automata in Hyperbolic Spaces

A Collection of Jewels

  • Maurice Margenstern

Part of the Emergence, Complexity and Computation book series (ECC, volume 4)

Table of contents

  1. Front Matter
    Pages 1-8
  2. Maurice Margenstern
    Pages 1-26
  3. Maurice Margenstern
    Pages 27-56
  4. Maurice Margenstern
    Pages 57-78
  5. Maurice Margenstern
    Pages 79-114
  6. Maurice Margenstern
    Pages 115-189
  7. Maurice Margenstern
    Pages 191-248
  8. Maurice Margenstern
    Pages 249-280
  9. Maurice Margenstern
    Pages 281-314
  10. Maurice Margenstern
    Pages 315-315
  11. Back Matter
    Pages 317-320

About this book


Hyperbolic geometry is an essential part of theoretical astrophysics and cosmology. Besides specialists of these domains, many specialists of new domains start to show a growing interest
both to hyperbolic geometry and to cellular automata. This is especially the case in biology and computer science.

   This book gives the reader a deep and efficient introduction to an algorithmic approach to hyperbolic geometry. It focuses the attention on the possibilities to obtain in this frame the power of computing everything a computer can compute, that is to say: universality.

   The minimal ways to get universality are invistigated in a large family of tilings of the hyperbolic plane. In several cases the best results are obtained.In all cases, the results are close to the theoretical best values. This gives rise to fantastic illustrations: the results are jewels in all meanings of the word.


   Maurice MARGENSTERN is professor emeritus at the University of Lorraine, he is a member of LITA, the research unit of computer science in the campus of Metz of this university. Professor Margenstern is amongst top world experts in theory of computation, mathematical machines and geometry. He is a pioneer
in cellular automata in hyperbolic spaces.


Cellular Automata Hyperbolic Geometry Indecidability Tessellations Tilings Universality Theorems

Authors and affiliations

  • Maurice Margenstern
    • 1
  1. 1.LITAUniversité de LorraineMETZ Cédex 1France

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2013
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Engineering
  • Print ISBN 978-3-642-36662-8
  • Online ISBN 978-3-642-36663-5
  • Series Print ISSN 2194-7287
  • Series Online ISSN 2194-7295
  • Buy this book on publisher's site
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