Cellular Automata Transforms
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Cellular Automata Transforms
Author: Olurinde Lafe
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
Cellular Automata Transforms describes a new approach to using the dynamical system, popularly known as cellular automata (CA), as a tool for conducting transforms on data. Cellular automata have generated a great deal of interest since the early 1960s when John Conway created the `Game of Life'. This book takes a more serious look at CA by describing methods by which information building blocks, called basis functions (or bases), can be generated from the evolving states. These information blocks can then be used to construct any data. A typical dynamical system such as CA tend to involve an infinite possibilities of rules that define the inherent elements, neighborhood size, shape, number of states, and modes of association, etc. To be able to build these building blocks an elegant method had to be developed to address a large subset of these rules. A new formula, which allows for the definition a large subset of possible rules, is described in the book. The robustness of this formula allows searching of the CA rule space in order to develop applications for multimedia compression, data encryption and process modeling. Cellular Automata Transforms is divided into two parts. In Part I the fundamentals of cellular automata, including the history and traditional applications are outlined. The challenges faced in using CA to solve practical problems are described. The basic theory behind Cellular Automata Transforms (CAT) is developed in this part of the book. Techniques by which the evolving states of a cellular automaton can be converted into information building blocks are taught. The methods (including fast convolutions) by which forward and inverse transforms of any data can be achieved are also presented. Part II contains a description of applications of CAT. Chapter 4 describes digital image compression, audio compression and synthetic audio generation, three approaches for compressing video data. Chapter 5 contains both symmetric and public-key implementation of CAT encryption. Possible methods of attack are also outlined. Chapter 6 looks at process modeling by solving differential and integral equations. Examples are drawn from physics and fluid dynamics.
Cellular Automata
Author: Samira El Yacoubi
language: en
Publisher: Springer Science & Business Media
Release Date: 2006-09-19
This book constitutes the refereed proceedings of the 7th International Conference on Cellular Automata for Research and Industry, ACRI 2006. The book presents 53 revised full papers and 19 revised poster papers together with 6 invited lectures. Topical sections include CA theory and implementation, computational theory, population dynamics, physical modeling, urban, environmental and social modeling, traffic and boolean networks, multi-agents and robotics, as well as crowds and cellular automata, and more.
Cellular Automata and Groups
Author: Tullio Ceccherini-Silberstein
language: en
Publisher: Springer Science & Business Media
Release Date: 2010-08-24
Cellular automata were introduced in the first half of the last century by John von Neumann who used them as theoretical models for self-reproducing machines. The authors present a self-contained exposition of the theory of cellular automata on groups and explore its deep connections with recent developments in geometric group theory, symbolic dynamics, and other branches of mathematics and theoretical computer science. The topics treated include in particular the Garden of Eden theorem for amenable groups, and the Gromov-Weiss surjunctivity theorem as well as the solution of the Kaplansky conjecture on the stable finiteness of group rings for sofic groups. The volume is entirely self-contained, with 10 appendices and more than 300 exercises, and appeals to a large audience including specialists as well as newcomers in the field. It provides a comprehensive account of recent progress in the theory of cellular automata based on the interplay between amenability, geometric and combinatorial group theory, symbolic dynamics and the algebraic theory of group rings which are treated here for the first time in book form.