A new weakly universal cellular automaton in the 3D hyperbolic space with two states

Authors:
Maurice Margenstern
Affiliations:
Université Paul Verlaine-Metz, LITA, UFR, MIM and CNRS, LORIA, METZ Cédex 1, France
Venue:
RP'11 Proceedings of the 5th international conference on Reachability problems
Year:
2011

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Abstract

In this paper, we show a construction of a weakly universal cellular automaton in the 3D hyperbolic space with two states. Moreover, based on a new implementation of a railway circuit in the dodecagrid, the construction is a truly 3D-one. This result under the hypothesis of weak universality and in this space cannot be improved.