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Chaos and fractals represent two branches of computational mathematics, and this book lives in their overlap: the fractal structure of chaotic attractors. The subject is new and experimental, and Strange Attractors provides a shortcut to the research frontier in the form of a computer-graphic laboratory for discrete dynamical systems: iterated maps (functions) from a space to itself. The complex polynomials of Julia and Fatou are very special 2D maps; Julien Sprott's book and software treat more general cases, for dimensions 1, 2, 3, and 4. The 3D case is presented in color stereograms; plastic glasses for viewing these are included in the package.
A unique feature of this book, in contrast to several similar works, is the constructive approach to the software. In fact, the diskette in the package is unnecessary, for the serious reader is guided to write the program step-by-step while studying the text. In this way, the foundations of computational mathematics may be attained, along with the software for visually (and aurally) studying the fractal structure of the chaotic attractors of maps in dimensions 2, 3, and 4, their basins and bifurcations, and thus the current research frontier of dynamical systems theory. Flows in 3D and 4D are also accommodated, by the Euler method.
The book is a bargain for the amateur explorer and seems uniquely interesting as a text for a novel course in computational math, physics, graphics, or art. It is highly evolved, as the result of a decade of experimentation, and includes a number of useful devices not found elsewhere. It is even useful for current research on chaotic attractors and their bifurcations in dimensions 2, 3, and 4. I recommend it most highly to all devotees of chaos.
--Reviewed by Ralph H. Abraham.
Ralph H. Abraham is Professor Emeritus of Computational Mathematics at the
University of California at Santa Cruz and is Director of the Visual Math
Institute. He is the author of several books on dynamics, chaos, the history
of mathematics, and a book/CD-ROM in progress called Just Plane Chaos.