Discrete Baker Transformation and Cellular Automata

dc.creatorBulitko, Valeriy K.
dc.date2004-07-08
dc.date.accessioned2026-07-07T05:10:03Z
dc.date.available2026-07-07T05:10:03Z
dc.descriptionIn this paper we propose a rule-independent description of applications of cellular automata rules for one-dimensional additive cellular automata on cylinders of finite sizes. This description is shown to be a useful tool for for answering questions about automata's state transition diagrams (STD). The approach is based on two transformations: one (called {\sl Baker transformation}) acts on the $n$-dimensional Boolean cube $\frak B^n$ and the other (called {\sl index-baker transformation}) acts on the cyclic group of power $n$. The single diagram of Baker transformation in $\frak B^n$ contains an important information about all automata on the cylinder of size $n$. Some of the results yielded by this approach can be viewed as a generalization and extension of certain results by O. Martin, A. Odlyzko, S. Wolfram. Additionally, our approach leads to a convenient language for formulating properties, such as possession of cycles with certain lengths and given diagram heights, of automaton rules.
dc.identifierhttps://arxiv.org/abs/math/0407116
dc.identifierhttp://arxiv.org/abs/math/0407116
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/71809
dc.subjectDynamical Systems
dc.subjectCombinatorics
dc.subject68q80; 37b15, 03d05
dc.titleDiscrete Baker Transformation and Cellular Automata
dc.typetext

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