Network View of Binary Cellular Automata
The network view of cellular automata focuses on the effective relationships between cells rather than the states themselves. In this article, we review a network representation presented in previous papers and present network graphs derived from all independent rules of one-dimensional elementary cellular automata and totalistic five-neighbor cellular automata. Removal of the transient effects of initial configurations improves the visibility of the dynamical characteristics of each rule. Power-law distributions of lifetimes and sizes of avalanches caused by one-cell perturbations of an attractor are exhibited by the derived network of Rule 11 (or 52) of totalistic five-neighbor cellular automata.
KeywordsCellular Automaton Complex Network Scale-free
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- 1.von Neumann, J.: The theory of self-reproducing automata. In: Burks, A.W. (ed.) Essays on Cellular Automata. University of Illinois Press (1966)Google Scholar
- 7.Kayama, Y.: Complex networks derived from cellular automata. arXiv:1009.4509 (2010)Google Scholar
- 8.Kayama, Y.: Network representation of cellular automata. In: 2011 IEEE Symposium on Artificial Life (IEEE ALIFE 2011) at SSCI 2011, pp. 194–202 (2011)Google Scholar
- 9.Kayama, Y., Imamura, Y.: Network representation of the game of life. Journal of Artificial Intelligence and Soft Computing Research 1 (3), 233–240 (2011)Google Scholar
- 12.Kayama, Y.: Network representation of the game of life and self-organized criticality (extended abstract). To be appeared in the Proceedings of the 13th International Conference on the Simulation & Synthesis of Living Systems (2012)Google Scholar
- 13.Wolfram, S.: A New Kind of Science. Wolfram Media, Inc. (2002)Google Scholar
- 14.Callahan, P.: Patterns, programs, and links for conway’s game of life (1995), http://www.radicaleye.com/lifepage/ (retrieved at February 1, 2011)
- 15.Flammenkamp, A.: Achim’s game of life page (1998), http://wwwhomes.uni-bielefeld.de/achim/gol.html (retrieved at December 12, 2011)
- 16.Kayama, Y.: Network View of Conway’s Game of Life. Wolfram Demonstrations Project (2012), http://demonstrations.wolfram.com/NetworkViewOfConwaysGameOfLife/
- 19.Wasserman, S., Faust, K.: Social Network Analysis. Cambridge University Press (1994)Google Scholar
- 20.Fagiolo, G.: Clustering in complex directed networks. Phys. Rev. E 76, 026107–026114 (2007)Google Scholar