Weisbuch introduces the reader to complex systems viewed as networks of automata. He presents, in a simple and intuitively appealing way, several tools and concepts that are central to understanding and modeling complex systems. Examples are drawn from the physics of disordered systems, the biology of the brain, and the origin and evolution of life; the similarities in the dynamic behavior of these widely differing systems are explored to highlight some basic underlying properties.
The book is organized in 12 chapters. The introductory chapter describes the scope of the book, that is, the class of systems that qualify to be considered complex and that can be usefully modeled using automata networks. The motivation for this kind of modeling is also described. Chapter 2 provides the basic definitions of an automaton, of Boolean and threshold automata, and of networks of automata. Chapter 3 considers one-dimensional cellular automata, in which automata are distributed on the nodes of a one-dimensional lattice, have only nearest neighbor interactions, and are updated in the parallel iteration mode. Various examples illustrate the three classes of behaviors--rapid convergence to attractors, short period attractors, and long periods and/or chaotic behavior. Chapter 4 considers two-dimensional cellular automata with threshold functions and window functions as the transition functions of each automaton are described as models for the growth of different types of crystals. Conway’s “Game of Life,” a simple cellular automaton that exhibits surprisingly diverse dynamical behaviors for different inputs, is briefly described. The author then informally discusses the modeling of the behavior of moving fluids using cellular automata and shows some numerical simulation results that justify the use of this approach.
In chapter 5, the author moves on to the Hopfield model--a simple model of learning and recognition in the human brain. This model consists of a network of threshold automata with the random sequential mode of iteration. The capabilities and capacity of such networks are described, and the suitability of this network as a model of a cognitive system is critically discussed. Chapter 6 looks at some variants of this model that allow the capacity of the network to be increased. Specifically, it considers the perceptron algorithm and algebraic techniques like Widrow-Hoff iteration. Weisbuch also discusses the effect of weakening some of the hypotheses on the connectivity of a Hopfield net, such as forcing the model toward short-term rather than long-term memory by suitable choices of synaptic weights. Chapter 7 extends the discussion on the limitations of the perceptron and describes how, using hidden units, layered networks can be constructed that learn synaptic weights and thresholds via a back-propagation algorithm.
The next two chapters consider probabilistic automata. From the statistical physics approach, the notion of temperature is restated, and Monte Carlo dynamics are described for systems composed of magnetic moments. Simulated annealing, a combinatorial optimization technique, is explained and illustrated via three problems in differing fields: the traveling salesman problem, the partition problem, and an image processing application.
Chapter 10 returns to a more general perspective and considers large Boolean networks with random connectivity. Generic properties of sets of these networks are explored. Scaling laws, forcing structures, and percolation are discussed. Chapter 11 applies these notions in the context of populations and evolution. It describes the emergence of collective properties of self-organizing structures. Three examples are considered: cell differentiation, the origin of life, and the evolution of species.
In the concluding chapter, the overall scope of automata networks is discussed and put into perspective. A brief bibliography lists works that the author feels are remarkably clear and that will allow the reader to delve further into a particular field.
The organization of the book is appealing. Concepts are presented in a simple and natural way, without resort to rigorous mathematical formalisms. The emphasis throughout is on clarifying concepts, not on detail. The book is a good general introduction to the field of complex systems.
The index is sparse and makes cross referencing difficult. The bibliography is also sparse, but most of the important and useful references are cited, and the reader is never left without pointers into an area. Typographical errors are few, and the legends accompanying figures are largely self-contained and clear.
The book is intended for a general audience of readers in differing fields who have an interest in complex systems. It assumes little background on the part of the reader and should be understandable to most scientists and engineers. The author discusses various topics in sufficient depth to clarify key concepts but not in so much detail as to put off the mildly interested reader. While several other books in this field have appeared in recent years, this book is notable in that it is not targeted at specialists but is designed as a comprehensive introduction for the general reader.
