Mathematics – Dynamical Systems
Scientific paper
2004-07-08
Mathematics
Dynamical Systems
Scientific paper
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.
No associations
LandOfFree
Discrete Baker Transformation and Cellular Automata does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Discrete Baker Transformation and Cellular Automata, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Discrete Baker Transformation and Cellular Automata will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-222423