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Discrete Mathematics & Theoretical Computer Science |
Maurice Margenstern - A weakly universal cellular automaton in the hyperbolic $3D$ space with three states
dmtcs:2755 - Discrete Mathematics & Theoretical Computer Science, January 1, 2010, DMTCS Proceedings vol. AL, Automata 2010 - 16th Intl. Workshop on CA and DCS - https://doi.org/10.46298/dmtcs.2755A weakly universal cellular automaton in the hyperbolic $3D$ space with three statesArticle
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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.
Source: HAL:hal-01185491v1
Volume: DMTCS Proceedings vol. AL, Automata 2010 - 16th Intl. Workshop on CA and DCS
Section: Proceedings
Published on: January 1, 2010
Imported on: January 31, 2017
Keywords: tilings,universality,cellular automata,hyperbolic geometry,$3D$ space,[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]
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