Effects of Initial Symmetry on the Global Symmetry of One-Dimensional Legal Cellular Automata
Abstract
:1. Introduction
2. Methods
The Discrete Walsh Analysis
3. Calculations
4. Results
4.1. Class
4.2. Four Types of Symmetry
4.3. The Ratio of Final Formation
Class | Horizontal Symmetry | Double Symmetry | Random |
---|---|---|---|
Periodic | 12 | 12 | 100× |
Chaotic | 43 | 44 | 100× |
Complex | 6 | 6 | 100× |
5. Discussion
5.1. Class
5.2. Four Types of Symmetry
5.3. The Ratio of Final Formation
6. Conclusions
Acknowledgements
Conflicts of Interest
References
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Tanaka, I. Effects of Initial Symmetry on the Global Symmetry of One-Dimensional Legal Cellular Automata. Symmetry 2015, 7, 1768-1779. https://doi.org/10.3390/sym7041768
Tanaka I. Effects of Initial Symmetry on the Global Symmetry of One-Dimensional Legal Cellular Automata. Symmetry. 2015; 7(4):1768-1779. https://doi.org/10.3390/sym7041768
Chicago/Turabian StyleTanaka, Ikuko. 2015. "Effects of Initial Symmetry on the Global Symmetry of One-Dimensional Legal Cellular Automata" Symmetry 7, no. 4: 1768-1779. https://doi.org/10.3390/sym7041768