Classical Homogeneous Structures Cellular Automata

Book on cellular automata (CA) considers such questions as nonconstructible configurations, extremal possibilities of CA, complexity of finite configurations and global transition functions, modeling in CA, decomposition of global transition functions, appendices of CA, etc.

In the monograph we present certain results of the work we have done in mathematical theory of the classical homogeneous structures (HS; English synonym "Cellular Automata (CA)") during 1968 - 2008. At present, the HS theory forms an original part of the modern mathematical cybernetics.

Book Description The book represents a library of well-designed software, which well supplements the already available Maple software with the orientation towards the widest circle of the Maple users, greatly enhancing its usability and effectiveness. The current library version contains tools (more than 570 procedures and program modules) that are oriented onto wide enough spheres of computing and information processing. The library is structurally similar to the main Maple library and is supplied with the advanced Help system about the tools located in it. In addition, the library is logically connected with the main Maple library, providing access to the tools contained in it similarly to the package tools. The library will be of special interest above all to those who use Maple of releases 6 - 9.5 not only as a highly intellectual calculator but also as environment for programming of different problems in own professional activities. The represented source codes of the library tools, using both the effective and the non-standard technique, can serve as an useful enough practical programming guide on the Maple language. Author Biography Professor Aladjev V. was born on June 14, 1942 in the town Grodno (Byelorussia). Now, he is the First vice-president of the International Academy of Noosphere and the president of Tallinn Research Group, whose scientific results have received international recognition, first, in the field of mathematical theory of Cellular Automata (CA). He is member of a series of Russian and International Academies. Aladjev V. is the author of more than 300 scientific publications, including 60 books, published in many countries. He participates as a member of the organizing committee and/or a guest lecturer in many international scientific forums in mathematics and cybernetics. Category: NonFiction/Science/Mathematics/Mathematical & Statistical Software/Algebra

Cellular automata are a class of spatially and temporally discrete mathematical systems characterized by local interaction and synchronous dynamical evolution. Introduced by the mathematician John von Neumann in the 1950s as simple models of biological self-reproduction, they are prototypical models for complex systems and processes consisting of a large number of simple, homogeneous, locally interacting components. Cellular automata have been the focus of great attention over the years because of their ability to generate a rich spectrum of very complex patterns of behavior out of sets of relatively simple underlying rules. Moreover, they appear to capture many essential features of complex self-organizing cooperative behavior observed in real systems. This book provides a summary of the basic properties of cellular automata, and explores in depth many important cellular-automata-related research areas, including artificial life, chaos, emergence, fractals, nonlinear dynamics, and self-organization. It also presents a broad review of the speculative proposition that cellular automata may eventually prove to be theoretical harbingers of a fundamentally new information-based, discrete physics. Designed to be accessible at the junior/senior undergraduate level and above, the book will be of interest to all students, researchers, and professionals wanting to learn about order, chaos, and the emergence of complexity. It contains an extensive bibliography and provides a listing of cellular automata resources available on the World Wide Web.

Computing in Nonlinear Media and Automata Collectives presents an account of new ways to design massively parallel computing devices in advanced mathematical models, such as cellular automata and lattice swarms, from unconventional materials, including chemical solutions, bio-polymers, and excitable media.