Title

Coxeter Groups and Asynchronous Cellular Automata

Authors

Matthew Macauley, Clemson UniversityFollow
Henning S. Mortveit, Virginia Tech

Document Type

Article

Publication Date

10-2010

Publication Title

International Conference on Cellular Automata

Publisher

Springer Link

Abstract

The dynamics group of an asynchronous cellular automaton (ACA) relates properties of its long term dynamics to the structure of Coxeter groups. The key mathematical feature connecting these diverse fields is involutions. Group-theoretic results in the latter domain may lead to insight about the dynamics in the former, and vice-versa. In this article, we highlight some central themes and common structures, and discuss novel approaches to some open and open-ended problems. We introduce the state automaton of an ACA, and show how the root automaton of a Coxeter group is essentially part of the state automaton of a related ACA.

Comments

This manuscript has been published in International Conference on Cellular Automata. Please find the published version here (note that a subscription is necessary to access this version):

https://link.springer.com/chapter/10.1007/978-3-642-15979-4_43

Recommended Citation

Please use the publisher's recommended citation. https://link.springer.com/chapter/10.1007/978-3-642-15979-4_43