Classification of Two Dimensional Cellular Automata Rules for Symmetric Pattern Generation
School of Computing Science and Engineering, Vellore Institute of Technology, Chennai 600127, India
Author to whom correspondence should be addressed.
Received: 4 October 2018 / Revised: 10 December 2018 / Accepted: 14 December 2018 / Published: 19 December 2018
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
. Based on the angle
, 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.
This is an open access article distributed under the Creative Commons Attribution License
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
Share & Cite This Article
MDPI and ACS Style
Vellarayil Mohandas, N.; Jeganathan, L. Classification of Two Dimensional Cellular Automata Rules for Symmetric Pattern Generation. Symmetry 2018, 10, 772.
Vellarayil Mohandas N, Jeganathan L. Classification of Two Dimensional Cellular Automata Rules for Symmetric Pattern Generation. Symmetry. 2018; 10(12):772.
Vellarayil Mohandas, Nisha; Jeganathan, Lakshmanan. 2018. "Classification of Two Dimensional Cellular Automata Rules for Symmetric Pattern Generation." Symmetry 10, no. 12: 772.
Show more citation formats
Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.
[Return to top]
For more information on the journal statistics, click here
Multiple requests from the same IP address are counted as one view.