A combinatorial approach to hyperbolic geometry as a new perspective for computer science and technology

This paper is based on a new notion, being called the splitting method, see [7,8], which gives an additional way to the combinatorial approach to hyperbolic geometry, starting from considerations of computer science. In this survey, we recall several applications of this method to different situations which are mainly tessellations being based on a single polygon. Then we stress on the implementation of cellular automata. This may have interesting applications in physics, in bio-computing, in the organisation of huge data bases and in the simulation of huge nets, like the Internet.