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

Michael Field , Martin Golubitsky
5.0 out of 5 stars  See all reviews (4 customer reviews)

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Book Description

August 8, 1996 0198536887 978-0198536888
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.

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Editorial Reviews


"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

Book Description

A striking full-colour book which explores how combining symmetry and chaos can lead to the construction of remarkable images. This book is an engaging look at the interplay of art and mathematics, and between symmetry and chaos. The underlying mathematics involved in the generation of the images is described. --This text refers to the Hardcover edition.

Product Details

  • Paperback: 232 pages
  • Publisher: Oxford University Press (August 8, 1996)
  • Language: English
  • ISBN-10: 0198536887
  • ISBN-13: 978-0198536888
  • Product Dimensions: 10.8 x 8.5 x 0.5 inches
  • Shipping Weight: 1.7 pounds
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (4 customer reviews)
  • Amazon Best Sellers Rank: #1,805,993 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews
4 of 5 people found the following review helpful
5.0 out of 5 stars Fresh approach! September 10, 2001
How is this book different from all the other fractal/chaos books on the market? Because of the emphasis on symmetry! Most fractal/chaos books are similar in the sense that they contain the same pictures. But even if you are fed up with Mandelbrot sets, you can safely open this book. You will love the fractal wallpapers.
The book is written by mathematicians, too, so it's factually correct, and has some real insight.
Just read it!
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1 of 1 people found the following review helpful
5.0 out of 5 stars A great array of fractal attractors. February 4, 2013
Format:Hardcover|Verified Purchase
A great array of chaotic attractors. These illustrations demonstrate that the varied forms in nature originate from mathematical building blocks that are complex and yet have continuity in that geometry. I would like to see more, accessable books on strange/chaotic attractors.
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3 of 4 people found the following review helpful
5.0 out of 5 stars Symmetry: a powerful concept July 9, 2000
This looks like another book of cool fractal pictures, but it's much more than that. The concept of symmetry is subtle and useful in the hard sciences as well as in literature and philosophy. This book provides a solid mathematical treatment of it, with excellent graphical examples. This book is great fun for math nerds, but can also entertain a more general audience that has some interest in fractals or in visualizing mathematical concepts.
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3 of 4 people found the following review helpful
5.0 out of 5 stars A visually delightful book! May 22, 1996
By A Customer
Not only is this book filled
with eye-catching colorful pictures, it also does a
wonderful job of explaining how they were generated.
They also draw many interesting parallels between
the computer-generated pictures and the structures
that occur in nature or are man-made. Check out their
Symmetric Chaos site at
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