Symmetry in Chaos: A Search for Pattern in Mathematics, Art, and Nature

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Chaotic dynamics (known popularly as chaos theory or, more simply, chaos) is among the most fascinating new fields in modern science, revolutionizing our understanding of order and pattern in nature. Symmetry, a traditional and highly developed area of mathematics, would seem to lie at the opposite end of the spectrum. From the branching of trees to the rose windows of great cathedrals, symmetric patterns seem the antithesis of such chaotic systems as weather patterns. And yet, scientists are now finding ...
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Overview


Chaotic dynamics (known popularly as chaos theory or, more simply, chaos) is among the most fascinating new fields in modern science, revolutionizing our understanding of order and pattern in nature. Symmetry, a traditional and highly developed area of mathematics, would seem to lie at the opposite end of the spectrum. From the branching of trees to the rose windows of great cathedrals, symmetric patterns seem the antithesis of such chaotic systems as weather patterns. And yet, scientists are now finding connections between these two areas, connections which could have profound consequences for our understanding of the physical world. In Symmetry in Chaos, mathematicians Michael Field and Martin Golubitsky offer an engaging look at where these two fields meet. In the process, they have generated mathematically a series of stunning computer images linking symmetry and chaos.
Field and Golubitsky describe how a chaotic process eventually can lead to symmetric patterns (in a river, for instance, photographs of the turbulent movement of eddies, taken over time, often reveal patterns on average) and they provide clear explanations of the science that lies behind the generation of these pictures. And the images they generate are spectacular. Because of the symmetry, these full-color and black-and-white images--some chaotic and some fractal--have a surprisingly classical appearance. Indeed, through comparisons with pictures from nature, such as sea shells and flowers, and decorative designs ranging from Islamic motifs to contemporary graphic logos to ceramic tiles, the authors highlight the familiar yet unusual nature of these mysterious pictures. Finally, the book features an appendix containing several BASIC programs, which will enable home computer owners to experiment with similar images.
This lavishly illustrated, oversized volume offers both a fascinating glimpse of the frontier of modern science and a stunning collection of remarkable images. Symmetry in Chaos will intrigue science buffs as well as anyone interested in decorative art and pattern design.

Chaotic dynamics (known popularly as chaos) is among the most fascinating new fields in modern science, revolutionizing our understanding of order and pattern in nature. Mathematicians Field and Golubitsky present a series of stunning computer images linking symmetry and chaos in this fascinating glimpse of the frontier of modern science. 54 computer-generated color illustrations; 25 color halftones; 24 line drawings.

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Editorial Reviews

From the Publisher

"Field and Golubitsky are very good in explaining how equations and natural forces can produce stunning chaotic patterns."--The New York Review of Books

"A spectacular picture book with background mathematical information for the reader who wants to explore the theory behind it all."--The Times Higher Education Supplement

"Full of beautiful pictures. If Socrates had been able to interrogate Dr. Field and Dr. Golubitsky, his search for wisdom might have ended right there....Takes the reader with no previous knowledge through an impressive array of topics."--American Journal of Physics

Booknews
Large, brilliantly colored computer images demonstrate how a chaotic process can lead to a symmetric pattern, and what that can teach us about the relation between chaotic and symmetrical patterns in nature. The listed computer programs allow readers with a high-school level of mathematics to reproduce many of the designs on home computers in QBasic or Microsoft environments. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780198536888
  • Publisher: Oxford University Press, USA
  • Publication date: 8/8/1996
  • Edition number: 1
  • Pages: 232
  • Product dimensions: 8.63 (w) x 10.88 (h) x 0.54 (d)

Meet the Author

About the Authors:
Michael Field is Reader in Pure Mathematics at the University of Sydney. He has published several books and papers in advanced mathematics. In 1990, he was Visiting Scientist at the Mathematical Sciences Institute, Cornell University.
Martin Golubitsky is Cullen Professor of Mathematics at the University of Houston. He is co-author with Ian Stewart of Fearful Symmetry: Is God a Geometer.

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Table of Contents

1 Introduction to Symmetry and Chaos 1
2 Planar Symmetries 42
3 Patterns Everywhere 62
4 Chaos and Symmetry Creation 98
5 Symmetric Icons 116
6 Quilts 145
7 Symmetric Fractals 157
Appendix A Picture Parameters 193
Appendix B Basic Programs 197
Appendix C Icon Mappings 204
Appendix D Planar Lattices 207
Bibliography 216
Index 217
Figure Acknowledgements 218
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