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Chaotic Behavior of One-Dimensional Cellular Automata Rule 24
Joint Authors
Song, Lepeng
Bie, Zujie
Liu, Chao
Huang, Junjian
Han, Qi
Pei, Yangjun
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-05-15
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
Wolfram divided the 256 elementary cellular automata rules informally into four classes using dynamical concepts like periodicity, stability, and chaos.
Rule 24, which is Bernoulli στ-shift rule and is member of Wolfram’s class II, is said to be simple as periodic before.
Therefore, it is worthwhile studying dynamical behaviors of four rules, whether they possess chaotic attractors or not.
In this paper, the complex dynamical behaviors of rule 24 of one-dimensional cellular automata are investigated from the viewpoint of symbolic dynamics.
We find that rule 24 is chaotic in the sense of both Li-Yorke and Devaney on its attractor.
Furthermore, we prove that four rules of global equivalence ε52 of cellular automata are topologically conjugate.
Then, we use diagrams to explain the attractor of rule 24, where characteristic function is used to describe the fact that all points fall into Bernoulli-shift map after two iterations under rule 24.
American Psychological Association (APA)
Bie, Zujie& Han, Qi& Liu, Chao& Huang, Junjian& Song, Lepeng& Pei, Yangjun. 2014. Chaotic Behavior of One-Dimensional Cellular Automata Rule 24. Discrete Dynamics in Nature and Society،Vol. 2014, no. 2014, pp.1-8.
https://search.emarefa.net/detail/BIM-461853
Modern Language Association (MLA)
Bie, Zujie…[et al.]. Chaotic Behavior of One-Dimensional Cellular Automata Rule 24. Discrete Dynamics in Nature and Society No. 2014 (2014), pp.1-8.
https://search.emarefa.net/detail/BIM-461853
American Medical Association (AMA)
Bie, Zujie& Han, Qi& Liu, Chao& Huang, Junjian& Song, Lepeng& Pei, Yangjun. Chaotic Behavior of One-Dimensional Cellular Automata Rule 24. Discrete Dynamics in Nature and Society. 2014. Vol. 2014, no. 2014, pp.1-8.
https://search.emarefa.net/detail/BIM-461853
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-461853