Cellular Automata in Hyperbolic Spaces Volume I: Theory

Cellular Automata in Hyperbolic Spaces introduces a hot topic of mathematics and computer science at the edge of hyperbolic geometry and cellular automata.

A hyperbolic space is a geometric model where, through a given point, there are two distinct parallels to a given line. A cellular automaton is a set of cells which are uniformly distributed in a space, connected locally and which update their states by the same rule.

Cellular Automata presents novel results on location of tiles in many tilings of the hyperbolic place. These results are employed to implement emerging non-classical types of cellular automata and offer insights of accessing and transferring information in hyperbolic places.

Hyperbolic geometry is an essential part of theoretical astrophysics and cosmology; therefore ideas discussed in the book will play an important role in the theory of relativity.

In addition to specialists in these traditional fields of application, many specialists of new domains are beginning to show a growing interest in both hyperbolic geometry and cellular automata. This is especially the case in biology and in computer science.

Cellular Automata is unique because it skillfully hybridizes two different domains of geometry and computation in a way beneficial for mathematics, computer science and engineering. The book is an outstanding treatise of concepts and implementations which will last for decades.