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Название: Cellular Automata: A Discrete View of the World (Wiley Series in Discrete Mathematics & Optimization)
Автор: Schiff J.
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.