Discrete Baker Transformation and Cellular Automata

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 Baker transformation) acts on the n-dimensional Boolean cube Bn and the other (called index-baker transformation) acts on the cyclic group of power n. The single diagram of Baker transformation in Bn 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 [1]. 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.