Algebraic and topological aspects
in rule 110 tiles

Abdiel E. Cáceres González
Sergio V. Chapa Vergara
Harold V. McIntosh

Centro de Investigación y de Estudios Avanzados del IPN
Depto de Ingeniería Eléctrica/Sección de Computación
Av. Instituto Politécnico Nacional No. 2508
Col. San Pedro Zacatenco. 07300 México, D. F., MEXICO
Tel: (+52 55) 5061 3800 x 3758 y 3756
Fax: (+52 55) 5061 3757

Abstract:

In the 80's it was proposed, that we can handle the initial global configuration of linear cellular automata (2,1) rule 110, to made universal computation. Recently, a demonstration of that proposal was given. In this paper is given the algebraic constructions that allow us to handle the graphic patterns that arise from rule 110 evolutions, with the intention to made tiles and cover the entire euclidean discrete plane, with copies of those tiles. That implies to give another completely different approach to the named demonstration. The algebraic foundations are various operators and algebraic structures with triangles like monoids, subgroups and homomorphisms.