Cellular Automata in Hyperbolic Spaces, Volume I: Theory

Cellular Automata in Hyperbolic Spaces, Volume I: Theory introduces a hot topic in 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 in Hyperbolic Spaces, Volume I: Theory 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 into accessing and transferring information in hyperbolic spaces. 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 in new domains are beginning to show a growing interest in hyperbolic geometry and cellular automata. This is especially the case in biology and computer science. Cellular Automata in Hyperbolic Spaces, Volume I, Theory is a unique work which skillfully hybridizes two different domains of geometry and computation in a way beneficial for mathematics, computer science and engineering. Interest in the concepts, and their possible implementations, contained in this outstanding treatise is sure to last for decades.