The rapidly growing field of complex systems is both a contributor to and a consumer of computer science. As computer architectures evolve toward networks of asynchronous, autonomous processes, complexity theory is increasingly important in designing, monitoring, and controlling them. Conversely, research in the dynamics of complex systems would be impossible without the widespread availability of powerful and relatively inexpensive computation.

Dynamics of complex systems combines a thorough introduction to the basic principles of complexity theory with exemplary applications ranging from neural networks to human civilization. One of the challenges confronting the newcomer to complexity theory is the wide range of disciplines from which it draws, including the mathematics of iterative maps, thermodynamics and statistical mechanics, computer simulation, and the theory of computation. Each of these areas is a specialty that can easily occupy an entire professional career, and the novice finds it difficult to enter the field without devouring entire textbooks in each discipline. Bar-Yam’s chapter on preliminaries, occupying more than a quarter of the entire book, provides a formal but concise introduction to these and other disciplines, enabling the reader to move quickly to the discussion of specific examples in full mathematical detail without requiring the equivalent of a graduate course in each specialty. The discussion is rigorous but tutorial. The text contains no footnotes or formal citations of work by other researchers, but an annotated list of readings at the end of the book provides selected entry points for further study.

After this introduction, the author devotes two chapters to each of four application areas. The first chapter in each set is more analytical and theoretical, while the second focuses on simulation-based studies. These chapters repeatedly refer to the concepts introduced in the preliminary chapter, reinforcing the importance and universality of those foundational disciplines.

The first application area is neural networks. Bar-Yam analyzes the dynamics of both attractor networks (such as Kohonen maps) and feedforward networks, and studies subdivided networks that combine the two architectures. He derives the well-known “seven plus-or-minus two” rule as a general consequence of the tradeoff between storing a few complete neural patterns (in a completely connected network) and storing many but uncorrelated subpatterns (in a completely subdivided network). A consideration of training mechanisms for a subdivided network leads to a novel hypothesis about the role of sleep.

The second area of application is protein folding. A protein is a one-dimensional string of amino acids, but much of its functionality derives from the three-dimensional shape assumed by this string as a result of intermolecular forces. Bar-Yam explores the question of how a protein molecule can search the space of possible configurations rapidly enough to assume the correct configuration in reasonable time.

The third area deals with two aspects of living organisms: the evolution of complexity through time, and the development of a single organism from its genome. The fourth area proposes a mathematical definition of complexity based on algorithmic information theory, then applies this measure to estimating the complexity of a wide range of systems, ultimately considering human civilization itself.

Bar-Yam is president of the New England Complex Systems Institute, which since 1997 has sponsored an annual interdisciplinary conference on complex systems. Unifying themes in complex systems is the edited proceedings of the first such conference. It includes transcripts of eight out of ten plenary talks, as well as 46 submitted papers. The domains treated by the papers include formal complexity theory, physics, biology, economy, and sociology, mirroring the breadth of subjects in Bar-Yam’s textbook. There is no integrated bibliography or index. Without the insight gained from Bar-Yam’s text, one might question what common thread brings these papers together in a single conference. With the help of that text’s masterful integration of the various threads of complexity theory, the conference papers enable the reader to appreciate the intellectual synthesis represented by complexity theory and its predictive and explanatory power. Together, these two volumes provide an accessible entry into the study of complex systems.