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.
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