CELLULAR AUTOMATA
A Discrete Universe
by Andrew Ilachinski (Center for Naval Analyses, USA)
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.
Contents:
- Introduction: Preliminary Musings
- Formalism
- Phenomenological
Studies of Generic CA
- Dynamical Systems Theory Approach
- Analytic Approach
- Cellular Automata and Language Theory
- Probabilistic CA
- Generalized Models
- CA Models of Fluid Dynamics
- Neural Networks
- Artificial–Life
- Is Nature, Underneath It All, a CA?
Readership: Students and researchers in chaos, computer science and applied
mathematics.
"... a book that functions beautifully on many levels, offers such a definitive text ... I would highly recommend this book to students, researchers, and anything who wonders about the underlying nature of the world itself." See Full Review
Paul Halpern
Professor of Mathematics and Physics
University of the Sciences in Philadelphia |
"This is both an exceptionally beautiful and a timely book about this fascinating topic. To my knowledge, it is the only book which covers practically the whole field of cellular automata both as regards breadth and depth. What is important, the author has found the right balance between chapters and sections dealing with more mathematical and technical topics and, on the other hand, gives sufficiently many applications and discussion of models."
"The present volume is the most comprehensive single-author book on CAs to date, and provides a useful unified reference to many ideas scattered through the literature. While aimed at an audience of physicists, it should be useful and comprehensible to mathematicians and computer scientists ... there is much useful material here, and we are not aware of anything better with a comparable scope. CA enthusiasts will want copies on their shelves."
| Bulletin of the London Mathematical Society |
"This book is recommended to any person interested in the fascinating world of cellular automata; it can be a good complement for S Wolfram's book 'A New Kind of Science'."
| 840pp |
Pub. date: Jul 2001 |
