Investigations of Game of Life cellular automata rules on Penrose Tilings: lifetime and ash statistics

Nick Owens; Susan Stepney

Investigations of Game of Life cellular automata rules on Penrose Tilings: lifetime and ash statistics

Computer Science

Research output: Contribution to conference › Paper

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.

Original language	Undefined/Unknown
Pages	1-34
Publication status	Published - 2008

Bibliographical note

Paper given at Automata 2008, Bristol, UK, June 2008

Access to Document

http://www-users.cs.york.ac.uk/~susan/bib/ss/nonstd/auto08b.htm

Cite this

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title = "Investigations of Game of Life cellular automata rules on Penrose Tilings: lifetime and ash statistics",

abstract = "Conway{\textquoteright}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.",

author = "Nick Owens and Susan Stepney",

note = "Paper given at Automata 2008, Bristol, UK, June 2008",

year = "2008",

language = "Undefined/Unknown",

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AU - Stepney, Susan

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Y1 - 2008

N2 - 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.

AB - 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.

M3 - Paper

SP - 1

EP - 34

ER -