{"title":"滑翔机动力学和伯努利移位规则的拓扑动力学[j]","authors":"Yi Wang, F. Chen, Yunfang Han","doi":"10.1109/IWCFTA.2010.36","DOIUrl":null,"url":null,"abstract":"In this paper, the dynamics of elementary cellular automata rule 61 is investigated in the bi-infinite symbolic sequence space. This work provides the glider properties and the interactions in rule 61, including several natural gliders, a catalog of gliders and glider collisions, which were found in Wolfram’s complex rules 110 and 54 before. In addition, It is also proved that rule 61 defines three subsystems with complicated dynamical behaviors such as topologically mixing, topologically transitive and positive topological entropy. Finally, a relation between the collisions in rule 61 and a logical operation is established.","PeriodicalId":157339,"journal":{"name":"2010 International Workshop on Chaos-Fractal Theories and Applications","volume":"17 6 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2010-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Glider Dynamics and Topological Dynamics of Bernoulli-shift Rule 61\",\"authors\":\"Yi Wang, F. Chen, Yunfang Han\",\"doi\":\"10.1109/IWCFTA.2010.36\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, the dynamics of elementary cellular automata rule 61 is investigated in the bi-infinite symbolic sequence space. This work provides the glider properties and the interactions in rule 61, including several natural gliders, a catalog of gliders and glider collisions, which were found in Wolfram’s complex rules 110 and 54 before. In addition, It is also proved that rule 61 defines three subsystems with complicated dynamical behaviors such as topologically mixing, topologically transitive and positive topological entropy. Finally, a relation between the collisions in rule 61 and a logical operation is established.\",\"PeriodicalId\":157339,\"journal\":{\"name\":\"2010 International Workshop on Chaos-Fractal Theories and Applications\",\"volume\":\"17 6 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2010-10-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2010 International Workshop on Chaos-Fractal Theories and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/IWCFTA.2010.36\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2010 International Workshop on Chaos-Fractal Theories and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/IWCFTA.2010.36","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Glider Dynamics and Topological Dynamics of Bernoulli-shift Rule 61
In this paper, the dynamics of elementary cellular automata rule 61 is investigated in the bi-infinite symbolic sequence space. This work provides the glider properties and the interactions in rule 61, including several natural gliders, a catalog of gliders and glider collisions, which were found in Wolfram’s complex rules 110 and 54 before. In addition, It is also proved that rule 61 defines three subsystems with complicated dynamical behaviors such as topologically mixing, topologically transitive and positive topological entropy. Finally, a relation between the collisions in rule 61 and a logical operation is established.
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