Dynamics Groups of Asynchronous Cellular Automata

Details Dynamics Groups of Asynchronous Cellular Automata Dynamics Groups of Asynchronous Cellular Automata

2008-08-08

arxiv.org/abs/0808.1238v2

Journal of Algebraic Combinatorics, vol. 33, no. 1 (2011) 31-55

Mathematics

Dynamical Systems

Revised per referee's comments

Scientific paper

We say that a finite asynchronous cellular automaton (or more generally, any sequential dynamical system) is pi-independent if its set of periodic points are independent of the order that the local functions are applied. In this case, the local functions permute the periodic points, and these permutations generate the dynamics group. We have previously shown that exactly 104 of the possible 256 cellular automaton rules are pi-independent. In this article, we classify the periodic states of these systems and describe their dynamics groups, which are quotients of Coxeter groups. The dynamics groups provide information about permissible dynamics as a function of update sequence and, as such, connect discrete dynamical systems, group theory, and algebraic combinatorics in a new and interesting way. We conclude with a discussion of numerous open problems and directions for future research.

Affiliated with

Also associated with

No associations

Rating

Dynamics Groups of Asynchronous 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 Dynamics Groups of Asynchronous Cellular Automata, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dynamics Groups of Asynchronous Cellular Automata will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-29863