Abstract
The study of cellular automata (CA) on tilings of hyperbolic plane was initiated in [13]. Appropriate tools were developed which allow linear algorithms to implement cellular automata on the tiling of the hyperbolic plane with the regular rectangular pentagon. In this paper we tackle the problem of devising similar tools in the case of the 3D hyperbolic space. The tools are given for the rectangular dodecahedral tiling of the 3D hyperbolic space. We give an algorithm which computes all needed information from the number of a cell. The algorithm is cubic in time and quadratic in space.
Get full access to this article
View all access options for this article.