Discrete Baker Transformation and Cellular Automata
| dc.creator | Bulitko, Valeriy K. | |
| dc.date | 2004-07-08 | |
| dc.date.accessioned | 2026-07-07T05:10:03Z | |
| dc.date.available | 2026-07-07T05:10:03Z | |
| dc.description | In 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.identifier | https://arxiv.org/abs/math/0407116 | |
| dc.identifier | http://arxiv.org/abs/math/0407116 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71809 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Combinatorics | |
| dc.subject | 68q80; 37b15, 03d05 | |
| dc.title | Discrete Baker Transformation and Cellular Automata | |
| dc.type | text |