A Universal Semi-totalistic Cellular Automaton on Kite and Dart Penrose Tilings
Katsunobu Imai (Graduate School of Engineering, Hiroshima University,, Japan), Takahiro Hatsuda (Graduate School of Engineering, Hiroshima, University, Japan), Victor Poupet (Laboratoire d'Informatique Fondamentale de, Marseille, Aix-Marseille University, France)
TL;DR
This paper demonstrates that semi-totalistic cellular automata can simulate any boolean circuit on Penrose kite and dart tilings, despite their aperiodic and irregular structure.
Contribution
It introduces a universal semi-totalistic cellular automaton on Penrose tilings, showing computational universality on aperiodic grids.
Findings
CA can simulate boolean circuits on Penrose tilings
Despite irregularity, universal computation is possible
The automaton operates effectively on aperiodic 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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