A contribution of computer science to the combinatorial approach to hyperbolic geometry

It is still to soon to propose the guidelines of a combinatorial approach to hyperbolic geometry, starting from considerations of computer science. However, such an approach does exist and our goal is to give a few striking examples of that claim. We are convinced that the point of view of computer science is a possible approach which should be considered as a possibly creating one also in the field of pure mathematics. The key point is the word simulation which is a real sesame to which informatics gave reality and which, in most cases, can act as a good genius.