Tessellation Automata in Hyperbolic Spaces (I)

This paper surveys the theory of tessellation automata in hyperbolic spaces. There has been many illuminating papers on tessellation automata. But all of them limited themselves in Euclidean tessellations. Some fundamental theorems (in [1]) on period-preservability are extended to Hyperbolic Spaces. In this paper a typical example is given in a way to shed light on the general theory