Cellular Automata: A Discrete View of the World (Wiley Series in Discrete Mathematics & Optimization) [Hardcover]

Joel L. Schiff (Author)

Book Description

ISBN-10: 047016879X | ISBN-13: 978-0470168790 | Publication Date: January 6, 2008 | Edition: 1

An accessible and multidisciplinaryintroduction to cellular automata

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

The book begins with a preliminary introduction to cellular automata, including a brief history of the topic along with coverage of sub-topics such as randomness, dimension, information, entropy, and fractals. The author then provides a complete discussion of dynamical systems and chaos due to their close connection with cellular automata and includes chapters that focus exclusively on one- and two-dimensional cellular automata. The next and most fascinating area of discussion is the application of these types of cellular automata in order to understand the complex behavior that occurs in natural phenomena. Finally, the continually evolving topic of complexity is discussed with a focus on how to properly define, identify, and marvel at its manifestations in various environments.

The author's focus on the most important principles of cellular automata, combined with his ability to present complex material in an easy-to-follow style, makes this book a very approachable and inclusive source for understanding the concepts and applications of cellular automata. The highly visual nature of the subject is accented with over 200 illustrations, including an eight-page color insert, which provide vivid representations of the cellular automata under discussion. Readers also have the opportunity to follow and understand the models depicted throughout the text and create their own cellular automata using Java applets and simple computer code, which are available via the book's FTP site. This book serves as a valuable resource for undergraduate and graduate students in the physical, biological, and social sciences and may also be of interest to any reader with a scientific or basic mathematical background.

Editorial Reviews

Review

"An interesting read and worth browsing by somebody interested in getting a general background on CA.  The examples are many and varied, and the numerous citations--both to electronic and printed media--are very helpful." (Computing Reviews, Nov 2008)

"Schiff suppresses most mathematical details, rendering his book highly accessible, informative, and entertaining, but leaving open niches for a textbook treatment with exercises or an advanced monograph with proofs." (CHOICE, October 2008)

"This book serves as a valuable resource for undergraduate and graduate students in the physical, biological, and social sciences and may also be of interest to any reader with a scientific or basic mathematical ground." (Mathematical Reviews, 2008m)

I have finished reading the preliminary MS, and I honestly think it is the best math related book I have ever read. It is easy to read, good pace, explains all and leaves nothing out. -- Dror Speiser, Tel Aviv, Israel

The preliminary manuscript was the fourth book that I have read on the subject, but also the most coherent. With all due respect to Wolfram, this really surpassed his New Kind of Science in both content and style. While he clearly deserves a place in the pantheon, in the long run, this book should stand with his in the popular academic literature. -- Marc Ratkovic -- graduate student, University of Wisconsin

From the Publisher

This book is an overview of the subject, written at the level of Scientific American. In fact, the first worldwide exposure of the subject of CA was in Scientific American, in Martin Gardner's columns on the "Game of Life". The book also includes interesting discussions on the nature of consciousness, swarm intelligence, emergence, and of course, self-organization, as these form an integral part of the CA milieu. Some of the commentary on these topics comes from overlooked historical sources as well as from the very latest scientific thinking. Additionally, explicit rules are given for each CA model so that anyone with a modicum of programming skill can delve right in and explore them further. The text should allow anyone with a basic scientific understanding, be they in biology, chemistry, physics, mathematics, computer science, economics etc., to apply the discrete modeling techniques of CA to their own scientific endeavors. Much of life on Earth, from seashell patterns to neural activity in the brain, to the formation of bacterial colonies, becomes amenable to investigation with this essentially elementary technique.

The fundamental premise of CA is that complex behavior arises out of simple rules governing local behavior, and this is a useful paradigm for the way in which much of the world works. The virtue of CA is that they are much easier to deal with than the usual partial differential equations and often allow greater insight into the underlying processes at play.

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Product Details

• Hardcover: 280 pages
• Publisher: Wiley-Interscience; 1 edition (January 6, 2008)
• Language: English
• ISBN-10: 047016879X
• ISBN-13: 978-0470168790
• Product Dimensions: 6.5 x 0.9 x 9.4 inches
• Shipping Weight: 1.4 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #409,721 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

19 of 19 people found the following review helpful:

5.0 out of 5 stars Highly Recommended, March 3, 2008

By 

Steve Silberberg (Hull, MA United States) - See all my reviews
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This review is from: Cellular Automata: A Discrete View of the World (Wiley Series in Discrete Mathematics & Optimization) (Hardcover)

Although I have been nebulously aware of the term "Cellular Automata" for about 25 years, it was not until I read the book Cellular Automata that I really understood what it entails. As a result, I have become enamored with the field and its mathematical elegance. It is unfortunate for this fascinating field of study, that it is called Cellular Automata -- a marketing disaster if you ask me.

Though Cellular Automata probably has a strict definition, you can think of it as how simple rules governing a cell (or a neuron or an ant or whatever) through time can give rise to complex ordered systems. People often think that there's some intelligent design behind the complexity we see in nature, but as this book demonstrates, all it takes is a few simple rules about what happens in a local neighborhood to give rise to systems that order themselves into amazing complexity.

The book is a comprehensive survey of the history and current state of Cellular Automata. I wish I had the time to follow through on the amazing panoply of interesting paths, papers, web sites and ideas presented to the reader, but this could easily require a lifetime of study (and computer time).

In spite of having no background in Cellular Automata, I found this book to be extremely accessible and clearly written with many illustrative examples. I read the book cover-to-cover and understood it all, which for a textbook is really saying something. For the layman, it helps to have a strong mathematical background as well as a keen interest in number theory, but none of this is necessary. One of the nice things about this book is that if for some reason you don't understand a topic such as say, the Sierpinski Triangle, the rest of the book is not predicated upon it, even if it is called back on occasion.

The only possible issue I had with the text is that complex theoretical concepts were on rare occasion difficult to follow. Such concepts were introduced in order to give readers a complete primer on the current state of CA research, but the reader has to trust that the results are as stated in the book, and that an army of Grad Students carried out all the dirty work. Step-by-step implementation is (and should be) beyond the scope of the text, although for math weenies like myself, it may have clarified certain concepts.

Highly recommended.

12 of 12 people found the following review helpful:

5.0 out of 5 stars Advanced enough to be a textbook, basic enough to be a primer, August 18, 2008

By 

Charles Ashbacher (Marion, Iowa United States) - See all my reviews
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This review is from: Cellular Automata: A Discrete View of the World (Wiley Series in Discrete Mathematics & Optimization) (Hardcover)

The field of cellular automata (CA) is one that appears to be finite, yet unlimited, although it is a point of major debate. Where the ultimate conclusion lands depends on the fundamental origin of complexity, in particular that of intelligence. Some very sound thinkers argue that the universe itself is a complex CA, all of the phenomena we see are fundamentally explainable by a set of simple rules whereby actions are a consequence of state changes based on those rules. The apparent complexity that we perceive is due to the enormous number of objects that are involved and the number of different interactions that take place between them.
Cellular automata became an area of mainstream study when the Game of Life was developed. The fascinating feature of the game is that a small set of such simple rules can lead to what appear to be complex individual and collective behaviors. Schiff begins with the definitions of basic cellular automata, steps through the appearance of complexity and closes with some of the major arguments in favor of the literally universal applicability of CA.
The level of mathematics is fairly low; the most complex areas are the recurrence equations that define the next state and a few partial derivatives. With some additional explanation, the material is within the grasp of the second year math major. Most of the more complex mathematics can be skipped and the reader will still be able to understand and appreciate what CA are and some of the ways they can be used to model complex activities. This is the text I would use if I were to ever teach a special topics class in CA.

11 of 11 people found the following review helpful:

5.0 out of 5 stars Outstanding overview of the field, May 13, 2008

By 

J. Cicilio (Vermont, USA) - See all my reviews
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This review is from: Cellular Automata: A Discrete View of the World (Wiley Series in Discrete Mathematics & Optimization) (Hardcover)

This book provides an excellent overview of the field of cellular automata. It brings together a broad range of concepts and ideas which have been percolating over the past 70 years. In many ways the field of cellular automata and its offshoots remind me of the principles and ideas expounded on in Thomas Kuhn's book `The Structure of Scientific Revolutions'. For this field is truly revolutionary in its ability to easily show the power of emergent properties from simple rules.

The flow of the book is easy to understand and the documentation and references are excellent. The prose is well written and the author's ability to clarify basic ideas is exceptional.

I highly recommend this book. The first chapter `Preliminaries' clearly shows the author has brought a rich scope to the presentation of the material.