Cellular Automata: A Discrete View of the World

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John Wiley & Sons, Oct 18, 2011 - Mathematics - 272 pages
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An accessible and multidisciplinaryintroduction to cellularautomata

As the applicability of cellular automata broadens andtechnology advances, there is a need for a concise, yet thorough,resource that lays the foundation of key cellularautomata rules andapplications. In recent years, Stephen Wolfram's A New Kind ofScience has brought the modeling power that lies in cellularautomata to the attentionof the scientific world, and now, CellularAutomata: A Discrete View of the World presents all the depth,analysis, and applicability of the classic Wolfram text in astraightforward, introductory manner. This book offers anintroduction to cellular automata as a constructive method formodeling complex systems where patterns of self-organizationarising from simple rules are revealed in phenomena that existacross a wide array of subject areas, including mathematics,physics, economics, and the social sciences.

The book begins with a preliminary introduction to cellularautomata, including a brief history of the topic along withcoverage of sub-topics such as randomness, dimension, information,entropy, and fractals. The author then provides a completediscussion of dynamical systems and chaos due to their closeconnection with cellular automata and includes chapters that focusexclusively on one- and two-dimensional cellular automata. The nextand most fascinating area of discussion is the application of thesetypes of cellular automata in order to understand the complexbehavior that occurs in natural phenomena. Finally, the continuallyevolving topic of complexity is discussed with a focus on how toproperly define, identify, and marvel at its manifestations invarious environments.

The author's focus on the most important principles of cellularautomata, combined with his ability to present complex material inan easy-to-follow style, makes this book a very approachable andinclusive source for understanding the concepts and applications ofcellular automata. The highly visual nature of the subject isaccented with over 200 illustrations, including an eight-page colorinsert, which provide vivid representations of the cellularautomata under discussion. Readers also have the opportunity tofollow and understand the models depicted throughout the text andcreate their own cellular automata using Java applets and simplecomputer code, which are available via the book's FTP site. Thisbook serves as a valuable resource for undergraduate and graduatestudents in the physical, biological, and social sciences and mayalso be of interest to any reader with a scientific or basicmathematical background.

 

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Contents

A Discrete View of the World 1 Preliminaries
1
A Discrete View of the World 2 Dynamical Systems
25
A Discrete View of the World 3 OneDimensional Cellular Automata
39
A Discrete View of the World 4 TwoDimensional Automata
89
A Discrete View of the World 5 Applications
123
A Discrete View of the World 6 Complexity
185
A Discrete View of the World Appendix A
225
A Discrete View of the World References
233
A Discrete View of the World Index
247
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About the author (2011)

Joel L. Schiff, PhD, is Senior Lecturer in the Department of Mathematics at The University of Auckland, New Zealand. Dr. Schiff received his PhD from the University of California-Los Angelesand has published numerous articles and two books on his research specialties, which include complex function theory, potential theory, cellular automata, and the arithmetic Fourier transform.

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