Chaotic Behavior of One-Dimensional Cellular Automata Rule 24
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 worthwhil...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2014/304297 |
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| author | Zujie Bie Qi Han Chao Liu Junjian Huang Lepeng Song Yangjun Pei |
| author_facet | Zujie Bie Qi Han Chao Liu Junjian Huang Lepeng Song Yangjun Pei |
| author_sort | Zujie Bie |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-dc146b2f87ab40e9982f9b3c5beec154 |
| institution | DOAJ |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-dc146b2f87ab40e9982f9b3c5beec1542025-08-20T03:23:57ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2014-01-01201410.1155/2014/304297304297Chaotic Behavior of One-Dimensional Cellular Automata Rule 24Zujie Bie0Qi Han1Chao Liu2Junjian Huang3Lepeng Song4Yangjun Pei5Internet Data Center, Chongqing University of Science and Technology, Chongqing 401331, ChinaSchool of Electrical and Information Engineering, Chongqing University of Science and Technology, Chongqing 401331, ChinaSchool of Electrical and Information Engineering, Chongqing University of Science and Technology, Chongqing 401331, ChinaDepartment of Mathematics and Information Engineering, Chongqing University of Education College, Chongqing 400065, ChinaSchool of Electrical and Information Engineering, Chongqing University of Science and Technology, Chongqing 401331, ChinaSchool of Electrical and Information Engineering, Chongqing University of Science and Technology, Chongqing 401331, ChinaWolfram 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.http://dx.doi.org/10.1155/2014/304297 |
| spellingShingle | Zujie Bie Qi Han Chao Liu Junjian Huang Lepeng Song Yangjun Pei Chaotic Behavior of One-Dimensional Cellular Automata Rule 24 Discrete Dynamics in Nature and Society |
| title | Chaotic Behavior of One-Dimensional Cellular Automata Rule 24 |
| title_full | Chaotic Behavior of One-Dimensional Cellular Automata Rule 24 |
| title_fullStr | Chaotic Behavior of One-Dimensional Cellular Automata Rule 24 |
| title_full_unstemmed | Chaotic Behavior of One-Dimensional Cellular Automata Rule 24 |
| title_short | Chaotic Behavior of One-Dimensional Cellular Automata Rule 24 |
| title_sort | chaotic behavior of one dimensional cellular automata rule 24 |
| url | http://dx.doi.org/10.1155/2014/304297 |
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