A 6-state 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 and any Turing machine on this aperiodic tiling.
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