Customer Reviews

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

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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.

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.

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.