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Nick Owens, Susan Stepney.
Investigations of Game of Life cellular automata rules on Penrose Tilings: lifetime and ash statistics.

Automata 2008, Bristol, UK, June 2008 , pages 1-34. Luniver Press, 2008

Abstract

Conway’s Game of Life rules can be applied to Cellular Automata (CAs) running on aperiodic grids, namely Penrose tilings. Here we investigate the result of running such CAs from random initial conditions. This requires development of a Penrose tiling algorithm suitable for CA experiments, in particular, a tiling that can be lazily expanded as CA activity reaches an edge. We describe such an algorithm, our experimental setup, and demonstrate that the Penrose kite and dart tiling has significantly different statistical behaviour from the Penrose rhomb tiling.

Full paper : PDF 748K | revised journal version of the experimental results part 

@inproceedings(SS-Automata08b,
  author = "Nick Owens and Susan Stepney",
  title = "Investigations of {G}ame of {L}ife cellular automata rules on
           {P}enrose Tilings: lifetime and ash statistics",
  pages = "1-34",
  crossref = "Automata08",
)

@proceedings(Automata08,
  editors = "A. Adamatzky and R. Alonso-Sanz and A. Lawniczak
            and G. J. Martinez and K. Morita and T. Worsch",
  title = "Automata 2008, Bristol, UK, June 2008",
  booktitle = "Automata 2008, Bristol, UK, June 2008",
  publisher = "Luniver Press",
  year = 2008
)