Research ArticlesNo Access

COMPLEX DYNAMICS OF THE ELEMENTARY CELLULAR AUTOMATON RULE 54

JUNBIAO GUAN

School of Science, Hangzhou Dianzi University, Hangzhou, Zhejiang 310018, P. R. China

https://doi.org/10.1142/S0129183112500520Cited by:0 (Source: Crossref)

Abstract

This work deals with a discussion of complex dynamics of the elementary cellular automaton rule 54. An equation which shows some degree of self-similarity is obtained. It is shown that rule 54 exhibits Bernoulli shift and is topologically mixing on its closed invariant subsystem. Finally, many complex Bernoulli shifts are explored for the finite symbolic sequences with periodic boundary conditions.

Keywords:

PACS: 47.52.+j, 05.45.Df, 02.10.Ox

References

L. O. Chua, V. I. Sbitnev and S. Yoon, Int. J. Bifurcation Chaos 15, 1045 (2005). Link, Web of Science, Google Scholar
L. O. Chua, V. I. Sbitnev and S. Yoon, Int. J. Bifurcation Chaos 15, 3701 (2005). Link, Web of Science, Google Scholar
S. Lo and C. Hsu, Math. Comput. Model. 51, 1000 (2010). Crossref, Web of Science, Google Scholar
C. Serino, W. Klein and J. Rundle, Phys. Rev. E 81, 016105 (2010). Crossref, Web of Science, Google Scholar
C. Dürr and M. Santha, SIAM J. Comput. 31, 1076 (2002). Crossref, Google Scholar
J. A. C. Gallas and H. J. Herrmann, Int. J. Mod. Phys. C 1, 181 (1990). Link, ADS, Google Scholar
J. A. C. Gallaset al., Phys. A 180, 19 (1992). Crossref, Web of Science, Google Scholar
J. G. Freire, O. J. Brison and J. A. C. Gallas, Chaos 17, 026113 (2007). Crossref, Web of Science, Google Scholar
J. G. Freire, O. J. Brison and J. A. C. Gallas, Comput. Phys. Commun. 181, 750 (2010). Crossref, Web of Science, ADS, Google Scholar
G. Martínezet al., Int. J. Mod. Phys. C 22, 419 (2011). Link, Web of Science, ADS, Google Scholar
L. O. Chua, V. I. Sbitnev and S. Yoon, Int. J. Bifurcation Chaos 16, 1097 (2006). Link, Web of Science, Google Scholar
L. O. Chuaet al., Int. J. Bifurcation Chaos 17, 2839 (2007). Link, Web of Science, Google Scholar
D. Lind and B. Marcus , An Introduction to Symbolic Dynamics and Coding ( Cambridge University Press , 1995 ) . Crossref, Google Scholar
B. P. Kitchens , Symbolic Dynamics: One-Sided, Two-Sided and Countable State Markov Shifts ( Springer-Verlag , Berlin , 1998 ) . Crossref, Google Scholar
J. A. C. Gallas and H. J. Herrmannb, Phys. A 356, 78 (2005). Crossref, Web of Science, Google Scholar