Regular Article: Acyclic Orientations of Random Graphs
Advances in Applied Mathematics
Discrete, sequential dynamical systems
Discrete Mathematics
An Introduction to Sequential Dynamical Systems
An Introduction to Sequential Dynamical Systems
Dynamics groups of asynchronous cellular automata
Journal of Algebraic Combinatorics: An International Journal
| Hi-index | 5.23 |
In this paper we provide an overview of the possible @w-limit set structures for 104 of the 256 asynchronous elementary cellular automata over the circle graph on n vertices. We consider only fixed, sequential updates where the update sequence is given by a permutation of the vertices, that is, the class of sequential dynamical systems. The ECA rules covered are precisely the @p-invariant rules, that is, the rules for which the set of periodic points does not depend on the permutation update sequence. This paper reviews existing work on @p-invariance and cycle-equivalence, and provides and atlas of the possible limit set structures up to topological conjugation.