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Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
|---|---|---|---|---|---|
Searching... | 30000010245053 | Q172.5.S95 F54 2009 f | Open Access Book | Book | Searching... |
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Summary
Summary
Mathematical symmetry and chaos come together to form striking, beautiful colour images throughout this impressive work, which addresses how the dynamics of complexity can produce familiar universal patterns.
The book, a richly illustrated blend of mathematics and art, was widely hailed in publications as diverse as the New York Review of Books, Scientific American, and Science when first published in 1992. This much-anticipated second edition features many new illustrations and addresses the progress made in the mathematics and science underlying symmetric chaos in recent years; for example, the classifications of attractor symmetries and methods for determining the symmetries of higher dimensional analogues of images in the book. In particular, the concept of patterns on average and their occurrence in the Faraday fluid dynamics experiment is described in a revised introductory chapter.
The ideas addressed in this book have been featured at various conferences on intersections between art and mathematics, including the annual Bridges conference, and in lectures to art students at the University of Houston.
Reviews 2
Booklist Review
In this stunningly visual and cogently textual tour of the structure of symmetry, patterns, and chaos, the authors examine quilts, the Rose window of Chartes, diatoms, shells, and elaborate computer graphics, including excellent examples of symmetrical fractals.
Choice Review
Barely a decade since the publication of Benoit B. Mandelbrot's The Fractal Geometry of Nature (1982), there are now books on fractals, chaos, and nonlinear processes numbering in the hundreds, some for the general reader, others targeted at special audiences ranging from mathematicians, natural scientists, and engineers, to economists, philosophers, and artists. The four volumes under review are indicative of this diversity. Moon's book is, perhaps, best suited for practicing engineers who wish to decide whether learning chaos theory will be relevant and profitable to their work. The many examples of engineering applications where chaos has been observed form the soul of the book. The noteworthy Chapter 2 offers broad heuristics for identifying chaotic phenomena in the laboratory. Actually a rewrite of the author's Chaotic Vibrations (CH, Jun'88), the book has grown to nearly twice its former size from the addition of exercises, new physical applications, and more mathematical explication. The mathematics remains vague, even though the reader must have some mathematical sophistication. As such, this book cannot be recommended for those who need to learn the details of the subject. The editing is haphazard. For example, one meets Feigenbaum's number, as though for the first time, on four occasions, the index noting only the first three. By contrast, Peitgen, Jurgens, and Saupe's book serves the mathematical neophyte who craves a deep knowledge of the mathematical foundations of chaos. This is an extremely leisurely, careful, detailed, copiously illustrated exposition. Not a popularization, it nevertheless should find the wide audience that is usually served only by diluted accounts. It is hard to think of another book like it, but then no other mathematical subject has ever so captured the public imagination. There is also much here for mathematically sophisticated readers and it is easy to find what interests one and to dig in. With its beautiful design, superb organization, and clear style, it is not premature to declare this book a classic. Some overlap notwithstanding, this volume does not supercede The Science of Fractal Images ed. by Peitgen and Saupe (CH, Mar'89) or Peitgen and P.H. Richter's The Beauty of Fractals (CH, Dec'86). Given the nearly one thousand pages, the low price is worthy of note. The raison d'etre of Field and Golubitsky's work must be the stunningly beautiful color plates of some new types of fractal images. The mathematical genesis of these images is the question that asks when the orbits of a dynamical system statistically exhibit the symmetries of the system as a whole. Remarkably, the answer may change from ^D" to ^D" as one varies a parameter-describing system; a real world example (that the authors leave underdeveloped) is wobbly train wheels that wear unevenly at slow speeds, evenly at high speeds. The abstract ideas, together with the basics of chaos theory and group theory, do receive a passable treatment, some in the text, some in technical appendixes that also give full details on the construction of the images. Unfortunately, the text is also full of uninspired generalities about symmetry and chaos and unconvincing comparisons with images from art and nature that bare superficial resemblance to these fractals. Finally, Briggs's is a popular account full of the grandiose ^D" posturing that gives chaos theory a bad name in some circles. Nevertheless, it does collate some interesting information and many fascinating and beautifully produced images. This book is not appropriate for academic libraries; this is the first book about fractals this reviewer has seen that does not contain a single equation. For coffee tables only. D. V. Feldman University of New Hampshire
Table of Contents
| 1 Introduction to symmetry and chaos |
| 2 Planar symmetries |
| 3 Patterns everywhere |
| 4 Chaos and symmetry creation |
| 5 Symmetric icons |
| 6 Quilts |
| 7 Symmetric fractals |
| Appendix A Picture parameters |
| Appendix B Icon mappings |
| Appendix C Planar lattices |
| Bibliography |
| Index |
