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Symmetry 2018, 10(12), 772; https://doi.org/10.3390/sym10120772

Classification of Two Dimensional Cellular Automata Rules for Symmetric Pattern Generation

School of Computing Science and Engineering, Vellore Institute of Technology, Chennai 600127, India
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Received: 4 October 2018 / Revised: 10 December 2018 / Accepted: 14 December 2018 / Published: 19 December 2018
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Abstract

Cellular automata (CA) are parallel computational models that comprise of a grid of cells. CA is mainly used for modeling complex systems in various fields, where the geometric structure of the lattices is different. In the absence of a CA model to accommodate different types of lattices in CA, an angle-based CA model is proposed to accommodate various lattices. In the proposed model, the neighborhood structure in a two dimensional cellular automata (2D-CA) is viewed as a star graph. The vertices of the proposed graph are determined by a parameter, angle ( θ ) . Based on the angle ( θ ) , the neighborhood of the CA, which is treated as the vertices of the graph, varies. So this model is suitable for the representation of different types of two dimensional lattices such as square lattice, rectangular lattice, hexagonal lattice, etc. in CA. A mathematical model is formulated for representing CA rules which suit for different types of symmetric lattices. The star graph representation helps to find out the internal symmetries exists in CA rules. Classification of CA rules based on the symmetry exists in the rules, which generates symmetric patterns are discussed in this work. View Full-Text
Keywords: two dimensional cellular automata; lattice; star graph; rules; symmetry two dimensional cellular automata; lattice; star graph; rules; symmetry
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Vellarayil Mohandas, N.; Jeganathan, L. Classification of Two Dimensional Cellular Automata Rules for Symmetric Pattern Generation. Symmetry 2018, 10, 772.

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