Title: A Game of Life on Penrose tilings,
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.