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  1. Home > Articles & Issues >
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  3. A weakly universal c ...
Conference paper

A weakly universal cellular automaton in the hyperbolic $3D$ space with three states

Maurice Margenstern (1)
(1) Laboratoire d'Informatique Théorique et Appliquée
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Imported on
January 31, 2017
Published on
December 31, 2009
Last modified on
March 31, 2025
Volume
DMTCS Proceedings vol. AL, Automata 2010 - 16th Intl. Workshop on CA and DCS
Proceedings
DOI
10.46298/dmtcs.2755
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https://about.hal.science/hal-authorisation-v1
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A weakly universal cellular automaton in the hyperbolic $3D$ space with three states

Maurice Margenstern (1)
(1) Laboratoire d'Informatique Théorique et Appliquée
Abstract
In this paper, we significantly improve a previous result by the same author showing the existence of a weakly universal cellular automaton with five states living in the hyperbolic $3D$-space. Here, we get such a cellular automaton with three states only.
Keywords
  • [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
  • [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS]
  • [NLIN.NLIN-CG]Nonlinear Sciences [physics]/Cellular Automata and Lattice Gases [nlin.CG]
  • [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
  • universality
  • cellular automata
  • hyperbolic geometry
  • $3D$ space
  • tilings
Cited by

Source: OpenCitations

  • Cellular Automata in Hyperbolic Spaces

    Encyclopedia of Complexity and Systems Science

    Authors : Maurice Margenstern

    Journal reference : Volume , 2015, pp. 1-17

    DOI : 10.1007/978-3-642-27737-5_53-5
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