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Cellular Automata in Triangular, Pentagonal and Hexagonal Tessellations

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Computational Complexity

Article Outline

Glossary

Definition of the Subject

Introduction

Two Dimensional Cellular Automata in the Triangular Grid

The Hexagonal Grid

The Pentagonal Grid

Programming Tips

Future Directions

Bibliography

Typically, cellular automata (“CA”) are defined in Cartesian space (e. g.a square grid). Here weexplore characteristics of CA in triangular and other non-cartesian grids. Methods for programming CA for these non-cartesian grids are brieflydiscussed.

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Abbreviations

Cellular automaton (CA):

a structure comprising a grid with individual cells that can have two or more states; these cells evolve in discrete time units and are governed by a rule, which usually involves neighbors of each cell.

Game of life :

a particular cellular automaton discovered by John Conway in 1968.

Neighbor:

a neighbor of cell “x” is typically a cell that is in close proximity to (frequently touching) cell “x”.

Oscillator :

a periodic shape within a specific cellular automaton rule.

Glider:

a translating oscillator that moves across the grid of a CA.

Generation:

the discrete time unit which depicts the evolution of a cellular automaton.

Rule:

determines how each individual cell within a cellular automaton evolves.

Bibliography

  1. Bays C (2005) A Note on the Game of Life in Hexagonal and PentagonalTessellations. Complex Syst 15:245–252

    MathSciNet  MATH  Google Scholar 

  2. Bays C (1994) Cellular Automata in the Triangular Tessellation. Complex Syst8:127–150

    MathSciNet  MATH  Google Scholar 

  3. Preston K Jr, Duff MJB (1984) Modern Cellular Automata. Plenum Press, NewYork

    MATH  Google Scholar 

  4. Sugimoto T, Ogawa T (2000) Tiling Problem of Convex Pentagon. Forma15:75–79

    MathSciNet  MATH  Google Scholar 

  5. Wolfram S (2002) A New Kind of Science. Wolfram Media, Champaign

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, University of South Carolina, Columbia, USA

    Carter Bays

Authors
  1. Carter Bays
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Editor information

Editors and Affiliations

  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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© 2012 Springer-Verlag

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Bays, C. (2012). Cellular Automata in Triangular, Pentagonal and Hexagonal Tessellations. In: Meyers, R. (eds) Computational Complexity. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1800-9_28

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