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
Bays C (2005) A Note on the Game of Life in Hexagonal and PentagonalTessellations. Complex Syst 15:245–252
Bays C (1994) Cellular Automata in the Triangular Tessellation. Complex Syst8:127–150
Preston K Jr, Duff MJB (1984) Modern Cellular Automata. Plenum Press, NewYork
Sugimoto T, Ogawa T (2000) Tiling Problem of Convex Pentagon. Forma15:75–79
Wolfram S (2002) A New Kind of Science. Wolfram Media, Champaign
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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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DOI: https://doi.org/10.1007/978-1-4614-1800-9_28
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-1799-6
Online ISBN: 978-1-4614-1800-9
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