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A Universal Semi-totalistic Cellular Automaton on Kite and Dart Penrose Tilings

Abstract : In this paper we investigate certain properties of semi-totalistic cellular automata (CA) on the well known quasi-periodic kite and dart two dimensional tiling of the plane presented by Roger Penrose. We show that, despite the irregularity of the underlying grid, it is possible to devise a semi-totalistic CA capable of simulating any boolean circuit on this aperiodic tiling.
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-00839161
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Submitted on : Thursday, June 27, 2013 - 12:06:45 PM
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Katsunobu Imai, Takahiro Hatsuda, Victor Poupet, Sato Kota. A Universal Semi-totalistic Cellular Automaton on Kite and Dart Penrose Tilings. Automata & JAC, 2012, La Marana, Corsica, France. pp.267-278. ⟨lirmm-00839161⟩

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