Introduction

John Horton Conway’s Game of Life (GoL) is a simple two-dimensional, two state cellular automaton (CA), remarkable for its complex behaviour.

The classic GoL is defined on a regular square lattice. The update rule depends on the state of each cell and its neighbouring eight cells with which it shares a vertex. Each cell has two states, ‘dead’ and ‘alive’. If a cell is alive at time t, then it stays alive if and only if it has two or three live neighbours (otherwise it dies of ‘loneliness’ or ‘overcrowding’). If a cell is dead at time t, then it becomes alive (is ‘born’) if and only if it has exactly three live neighbours. This rule gives a famous zoo of GoL patterns, including still lifes, oscillators, and gliders.

Here we show some results of running GoL rules on Penrose tilings. More detail can be found in [127], from which all the figures here are taken. The neighbourhood of a Penrose tile is again all the tiles with which it shares a vertex; now there can be 7–11 of these, depending on details of the tiling. We show some interesting still life patterns and oscillator patterns. For a fuller, but still preliminary, catalogue of Penrose life structures, see [127]. These patterns were discovered by a combination of systematic construction and random search.

@incollection(Stepney-ArtPL-2016,
  author = "Susan Stepney",
  title = "The Art of {Penrose} Life",
  pages = "103-109",
  crossref = "AdamatskyMartinez-2016"  
)

@book(AdamatzkyMartinez:2016:ArtCA,
  editor = "Andrew Adamatzky and Genaro Juarez Martinez",
  title = "Designing Beauty: The Art of Cellular Automata",
  booktitle = "Designing Beauty: The Art of Cellular Automata",
  publisher = "Springer",
  year = 2016
)