Cellular automata in hyperbolic spaces - Volume 2 : Implementation and computations eBook
The book 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 arc two distinct parallels to a given lino. A cellular automaton is a set of cells which are uniformly distributed in a space, connected locally and update their states by the same rule. The volume advances the novel results presented in volume 1 on a location of tiles in many tilings of the hyperbolic plane. These results arc appplied in further studios 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 rote in the theory of relativity. Besides specialists of these traditional fields of application, 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 in computer science. The book is unque because it skilfulliy 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.
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Computations in hyperbolic spaces Maurice Margenstern Université Paul Verlaine − Metz, LITA, EA 3097: Slides. In this paper, we give a survey on results about computations in hyperbolic spaces, mainly in the hyperbolic plane. First, we remind the setting and the very basic features of hyperbolic geometry. Next, we introduce coordinates for tilings in the hyperbolic plane. After ...