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Symmetry in Chaos

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.

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Crystal and Dragon

We live in a universe of apparent dualities: light and darkness, reason and romance, order and chaos. Exploring the interplay of form and energy, David Wade takes the reader on a journey through the world of successive ages--from Plato's conception of the ideal form and the ancient Chinese philosophy of change to the modern scientific view of structure and indeterminacy as embodied in the laws of physics. The author shows us how perceptions about the nature of the universe are reflected in the art of of a given period. He details the form and fluidity of prehistoric art, the crystalline order of Islamic patterns, and the subtlety and vitality of Chinese landscapes and calligraphy.

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Symmetry in Chaos

Symmetry suggests order and regularity whilst chaos suggests disorder and randomness. 'Symmetry in Chaos' is an exploration of how combining seemingly contradictory principles can lead to the construction of striking and beautiful images. This book is an engaging look at the interplay of art and mathematics.

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Symmetry in Chaos

In fifty-four colour plates, Symmetry in Chaos illustrates the many varied and beautiful pictures that may be produced when the seemingly contradictory ideas of symmetry and chaos are combined. The mathematical ideas behind these pictures are presented in an elementary fashion, and computer programs are provided in appendices. These programs allow the reader to generate on a home computer black and white versions of the many and varied patterns shown throughout this book. The authorshad two reasons for writing this book: to present the surprisingly beautiful and intricate pictures that are produced by combining symmetry and chaos, and to present in as elementary a way as possible the mathematical ideas that lead to these pictures.

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The Symmetry Perspective

The framework of ‘symmetry’ provides an important route between the abstract theory and experimental observations. The book applies symmetry methods to dynamical systems, focusing on bifurcation and chaos theory. Its exposition is organized around a wide variety of relevant applications. From the reviews: "[The] rich collection of examples makes the book...extremely useful for motivation and for spreading the ideas to a large Community."--MATHEMATICAL REVIEWS

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Chaos et l harmonie

For 300 years, Trinh Xuan Thuan writes, since the time of Isaac Newton, scientists saw reality as a giant clock--a sterile mechanism in which one part acts on another in a deterministic fashion. But the discoveries of the last few decades have changed all that, conjuring up instead a universe brimming with unpredictability, creativity, and chance. Writing with exceptional grace and clarity, Thuan vividly describes these important scientific discoveries, intriguing new theories about chaos, gravity, strange attractors, fractals, symmetry, superstrings, and the strangeness of atoms. Equally important, he reveals how these discoveries have shaped our view of the universe--for instance, how quantum mechanics brought indeterminism to the subatomic universe. Thuan deftly describes quantum mechanics, discusses its relationship to the theories of relativity (which deal inability to accept it. Indeed, throughout Chaos and Harmony, he makes clear as never before the mind-bending ideas of modern physics, such as the effect of gravity on time (it slows it down), the impossibility of crossing the speed-of-light barrier (it would actually reverse time), the role of fractals as "the language of nature," and the unreasonable effectiveness of mathematics in understanding the universe. From the subatomic world to the vast realm of quasars and galaxies, from the nature of mathematics to the fractal characteristics of the human circulatory system, Trinh Xuan Thuan takes us on a breathtaking tour of the universe. With striking examples and clear, plain language, he shows how science has actually restored mystery to the world around us--a world of symmetry and chaos, contingency and creativity.

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The symmetry of chaos

There is a tremendous fascination with chaos and fractals, about which picture books can be found on coffee tables everywhere. Chaos and fractals represent hands-on mathematics that is alive and changing. One can turn on a personal computer and create stunning mathematical images that no one has ever seen before. Chaos and fractals are part of dynamics, a larger subject that deals with change, with systems that evolve with time. Whether the system in question settles down to equilibrium, keeps repeating in cycles, or does something more complicated, it is dynamics that scientists and mathematicians use to analyze a system's behavior. Chaos is the term used to describe the apparently complex behavior of what we consider to be simple, well-behaved systems. Chaotic behavior, when looked at casually, looks erratic and almost random. The type of behavior that in the last 20 years has come to be called chaotic arises in very simple systems. In fact, these systems are essentially deterministic; that is, precise knowledge of the conditions of a system allow future behavior of the system to be predicted. The problem of chaos is to reconcile these apparently conflicting notions: randomness and predictability. Why have scientists, engineers, and mathematicians become intrigued by chaos? The answer to that question has two parts: (1) the study of chaos has provided new conceptual tools enabling scientists to categorize and understand complex behavior and (2) chaotic behavior seems to be universal - from electrical circuits to nerve cells. Chaos is about predictability in even the most unstable systems, and symmetry is a pattern of predictability - a conceptual tool to help understand complex behavior. The Symmetry of Chaos treats this interplay between chaos and symmetry. This graduate textbook in physics, applied mathematics, engineering, fluid dynamics, and chemistry is full of exciting new material, illustrated by hundreds of figures. Nonlinear dynamics and chaos are relatively young fields, and in addition to serving textbook markets, there is a strong interest among researchers in new results in the field. The authors are the foremost experts in this field, and this book should give a definitive account of this branch of dynamical systems theory.

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Computers Pattern Chaos and Beauty

Fractals and chaos theory lead to startling graphics in this book by a renowned scientist, inventor, and artist, who coordinates information from disparate fields. Over 275 illustrations, 29 in color.

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Normal Forms and Homoclinic Chaos

This volume presents new research on normal forms, symmetry, homoclinic cycles, and chaos, from the Workshop on Normal Forms and Homoclinic Chaos held during The Fields Institute Program Year on Dynamical Systems and Bifurcation Theory in November 1992, in Waterloo, Canada. The workshop bridged the local and global analysis of dynamical systems with emphasis on normal forms and the recently discovered homoclinic cycles which may arise in normal forms. Specific topics covered in this volume include normal forms for dissipative, conservative, and reversible vector fields, and for symplectic maps; the effects of symmetry on normal forms; the persistence of homoclinic cycles; symmetry-breaking, both spontaneous and induced; mode interactions; resonances; intermittency; numerical computation of orbits in phase space; applications to flow-induced vibrations and to mechanical and structural systems; general methods for calculation of normal forms; and chaotic dynamics arising from normal forms. Of the 32 presentations given at this workshop, 14 of them are represented by papers in this volume.