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arXiv · 1708.09301

A Game of Life on Penrose tilings

Duane A. Bailey·Kathryn A. Lindsey
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Abstract

We define rules for cellular automata played on quasiperiodic tilings of the plane arising from the multigrid method in such a way that these cellular automata are isomorphic to Conway's Game of Life. Although these tilings are nonperiodic, determining the next state of each tile is a local computation, requiring only knowledge of the local structure of the tiling and the states of finitely many nearby tiles. As an example, we show a version of a "glider" moving through a region of a Penrose tiling. This constitutes a potential theoretical framework for a method of executing computations in non-periodically structured substrates such as quasicrystals.

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Duane A. Bailey, Kathryn A. Lindsey. 2017-08-29. A Game of Life on Penrose tilings. https://arxiv.org/abs/1708.09301

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