Cellular Automata in Hyperbolic Spaces Volume II: Implementation and Computations introduces the 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 that are uniformly distributed in a space, connected locally and update which their states by the same rule. This volume advances the novel results presented in Volume 1 on a location of tiles in many tilings of the hyperbolic plane. These results are applied in further studies of cellular automata in non-traditional spaces. We discuss a wide range of applications from cell phones to the theoretical problems of tilings. 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 of these traditional fields of application, many specialists in 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 in Hyperbolic Spaces Volume II: Implementation and Computations skillfully hybridizes the different disciplines of geometry and computation and is certain to be beneficial in the fields of mathematics, computer science and engineering. An outstanding treatise of concepts and implementations, the book will prove to be relevant for decades. Contains ten pages of color plates.
Maurice Margenstern is Professor and Head of the Research Department in Computer Science at the University Paul Verlaine, in Metz, France. Professor Margenstern ranks among the top world experts in the theory of computation, mathematical machines and geometry, and is a pioneer in cellular automata on hyperbolic spaces.