Hyperbolic geometry is an essential part of theoretical astrophysics and
cosmology. Besides specialists of these domains, many specialists of new
domains start to show a growing interest
both to hyperbolic geometry and to cellular automata. This is especially
the case in biology and computer science.
This book gives the reader a deep and efficient introduction to an
algorithmic approach to hyperbolic geometry. It focuses the attention on
the possibilities to obtain in this frame the power of computing
everything a computer can compute, that is to say: universality.
The minimal ways to get universality are investigated in a large family
of tilings of the hyperbolic plane. In several cases the best results
are obtained.In all cases, the results are close to the theoretical best
values. This gives rise to fantastic illustrations: the results are
jewels in all meanings of the word.
Maurice MARGENSTERN is professor emeritus at the University of Lorraine,
he is a member of LITA, the research unit of computer science in the
campus of Metz of this university. Professor Margenstern is amongst top
world experts in theory of computation, mathematical machines and
geometry. He is a pioneer
in cellular automata in hyperbolic spaces.