Symmetry in Chaos

A Search for Pattern in Mathematics, Art and Nature, Second Edition

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Author: Michael Field,Martin Golubitsky

Publisher: SIAM

ISBN: 0898716721

Category: Mathematics

Page: 199

View: 2000

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.

Symmetry in Chaos

A Search for Pattern in Mathematics, Art and Nature

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Author: Mike Field,Michael Field

Publisher: Oxford University Press, USA

ISBN: N.A

Category: Literary Criticism

Page: 218

View: 8688

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.

The Symmetry Perspective

From Equilibrium to Chaos in Phase Space and Physical Space

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Author: Martin Golubitsky,Ian Stewart

Publisher: Birkhäuser

ISBN: 3034881673

Category: Mathematics

Page: 325

View: 4435

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

Computers and Art

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Author: Stuart Mealing

Publisher: Intellect Books

ISBN: 9781841500621

Category: Art

Page: 159

View: 8018

Computers and Art provides insightful perspectives on the use of the computer as a tool for artists. The approaches taken vary from its historical, philosophical and practical implications to the use of computer technology in art practice. The contributors include an art critic, an educator, a practising artist and a researcher. Mealing looks at the potential for future developments in the field, looking at both the artistic and the computational aspects of the field.

Die Macht der Symmetrie

Warum Schönheit Wahrheit ist

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Author: Ian Stewart

Publisher: Springer Spektrum

ISBN: 9783642364358

Category: Science

Page: 304

View: 3613

m dichten Morgennebel des 30. Mai 1832 stehen sich zwei junge franzö- sche Männer gegenüber, die Pistolen in der Hand. Sie duellieren sich wegen einer Frau. Es fällt ein Schuss, und einer der Männer liegt schwer verletzt am IBoden. Am nächsten Tag stirbt er an den Folgen seiner inneren Verletzungen. Kein Stein markiert das Grab des 20-Jährigen, und beinahe wäre eine der wi- tigsten Ideen in der Geschichte der Mathematik und der Naturwissenschaften mit ihm beerdigt worden. Der Name des Überlebenden bleibt unbekannt; der tragisch Getötete hieß Évariste Galois. In politischer Hinsicht war er ein Rebell, doch seine Leidenschaft war die Mathematik, auch wenn seine gesammelten Werke kaum sechzig Seiten umfassen. Galois hinterließ ein Erbe, das die Mathematik revolutionierte. Er e- wickelte eine Sprache zur Beschreibung von Symmetrien und ihrer Bedeutung in mathematischen Strukturen. Diese Sprache nennt man heute „Gruppentheorie“, und in allen Bereichen der reinen und angewandten Mathematik dient sie zur Charakterisierung von Mustern und Formen. Symmetrien spielen auch eine zentrale Rolle in den Gre- gebieten der Physik: der Quantenwelt im Kleinen und der Welt der Relativitä- theorie im Großen. Sie könnten sogar der Schlüssel zur lange gesuchten „Theorie von Allem“ sein, einer mathematischen Vereinigung dieser beiden Zweige der modernen Physik. Und alles begann mit einer einfachen Frage zur Lösung mat- matischer Gleichungen: Wie ?ndet man eine „unbekannte“ Zahl aus wenigen, allgemeinen mathematischen Vorgaben? Symmetrie ist keine Zahl und auch keine Form.

Nature

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Author: Sir Norman Lockyer

Publisher: N.A

ISBN: N.A

Category: Electronic journals

Page: N.A

View: 6164

Leonardo

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Author: International Society for the Arts, Sciences, and Technology

Publisher: N.A

ISBN: N.A

Category: Art, Modern

Page: N.A

View: 9552

International journal of contemporary visual artists.

The Pattern Book

Fractals, Art, and Nature

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Author: Clifford A. Pickover

Publisher: World Scientific

ISBN: 9789810214265

Category: Computers

Page: 427

View: 7770

Although the patterns are computer-generated, the book is informal and emphasis is on the fun that the true pattern lover finds in doing rather than in reading about the doing.

Choice

Publication of the Association of College and Research Libraries, a Division of the American Library Association

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Author: N.A

Publisher: N.A

ISBN: N.A

Category: Academic libraries

Page: N.A

View: 2801

The Pattern Book: Fractals, Art, and Nature

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Author: Clifford A Pickover

Publisher: World Scientific

ISBN: 9814504033

Category: Mathematics

Page: 464

View: 3482

This book will allow you to travel through time and space. To facilitate your journey, the editor has scoured the four corners of the earth in a quest for unusual people and their fascinating patterns. From Mozambique, to Asia, to many European countries, the contributors to The Pattern Book include world-famous cancer researchers, little-known artists and eclectirc computer programmers. Some of the patterns are ultramodern, while others are centuries old. Many of the patterns are drawn from the universe of mathematics. Computer recipes are scattered throughout. Although the emphasis is on computer-generated patterns, the book is informal and the intended audience spans several fields. The emphasis is on the fun that the true pattern lover finds in doing, rather than in reading about the doing! The book is organized into three main parts: Representing Nature (for those patterns which describe or show real physical phenomena, e.g., visualizations of protein motion, sea lilies, etc.), Mathematics and Symmetry (for those patterns which describe or show mathematical behavior, e.g. fractals), and Human Art (for those patterns which are artistic works of humans and made without the aid of a computer, e.g. Moslem tiling patterns.) Contents:Representing NatureMathematics and SymmetryHuman Art Readership: Computer graphic scientists, computer scientists, artists and mathematicians. keywords:Fractals;Pattern;Computer Graphics;Computer Art;Scientific Visualization;Mathematics;Mandelbrot Set;Tilings;Symmetry;Beauty;Aesthetics;Nature “Fractals can be found everywhere, and Clifford Pickover has done a good job in selecting some of the best. The range of the collection is considerable, from ‘Wood Pattern’ to ‘Trajectories of A Neural Network Quantizer in Rhythm Space’. And all posses a simplistic beauty that justifies the presence of art in the title. Such creations, possessing enormous complexity from very simple origins, truly force us to stretch our imaginations. All of the generation processes are very easy to understand, and some modifications for additional exploration are obvious … One more in the collection of works devoted to fractals, this book ranks among the easiest to understand. A natural first book for those interested in fractals as objects of mathematical study or art.” Charles Ashbacher Journal of Recreational Mathematics “Artists, scientists, and computer enthusiasts will be delighted by this inspiring collection of visually striking patterns with accompanying explanations and references.” Julien C Sprott Strange Attractors: Creating Patterns in Chaos “The Pattern Book: Fractals, Art, & Nature — fascinating! A feast for both the eyes and mind! … This book helps us gain insights on how patterns are created and their scientific connections, while letting us enjoy the impact of their visual beauty. A must for those interested in science, nature, or art.” div style="text-align: right;">Theoni Pappas The Joy of Mathematics and The Magic of Mathematics “Particularly noteworthy are the many contributions by Dr. I D Entwistle, whose name is well known to readers of Fractal Report. The images submitted by him show outstanding originality and artistry; of their class they are unique. Other contributors worthy of special mention here include Earl F Glynn and Mieczyszlaw Szyszkowicz for their striking and original images … This beautifully illustrated and informative book can be highly recommended.” C J Freeman Fractal Report “Interesting introduction to the world of patterns.” The American Mathematical Monthly “The patterns, many in black and white, some in color, are generally intricate and beautiful. Pseudocode and code are provided for many of the patterns. The book stimulates experiment. An excellent resource for entry into the world of patterns. Recommended for artists, scientists, and computer enthusiasts, undergraduates through professionals.” G J G Junevicus Choice “The Pattern Book is a visual smorgasbord … My first prize goes to the microphotograph of leaf structure showing its dendritic and fractal character.” The Chemical Intelligencer

Fearful Symmetry

Is God a Geometer?

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Author: Ian Stewart,Martin Golubitsky

Publisher: Courier Corporation

ISBN: 0486477584

Category: Science

Page: 287

View: 3208

"From the shapes of clouds to dewdrops on a spider's web, this accessible book employs the mathematical concepts of symmetry to portray fascinating facets of the physical and biological world. More than 120 figures illustrate the interaction of symmetry with dynamics and the mathematical unity of nature's patterns"--

Fractals

The Patterns of Chaos : a New Aesthetic of Art, Science, and Nature

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Author: John Briggs

Publisher: Simon and Schuster

ISBN: 0671742175

Category: Science

Page: 192

View: 7755

Describes how fractals were discovered, explains their unique properties, and discusses the mathematical foundation of fractals

Patterns in Nature

Why the Natural World Looks the Way It Does

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Author: Philip Ball

Publisher: University of Chicago Press

ISBN: 022633242X

Category: Nature

Page: 288

View: 5372

While the natural world is often described as organic, it is in fact structured to the very molecule, replete with patterned order that can be decoded with basic mathematical algorithms and principles. In a nautilus shell one can see logarithmic spirals, and the Golden Ratio can be seen in the seed head of the sunflower plant. These patterns and shapes have inspired artists, writers, designers, and musicians for thousands of years. "Patterns in Nature: Why the Natural World Looks the Way It Does" illuminates the amazing diversity of pattern in the natural world and takes readers on a visual tour of some of the world s most incredible natural wonders. Featuring awe-inspiring galleries of nature s most ingenious designs, "Patterns in Nature" is a synergy of art and science that will fascinate artists, nature lovers, and mathematicians alike."

Computers, Pattern, Chaos and Beauty

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Author: Clifford A. Pickover

Publisher: Courier Corporation

ISBN: 0486151611

Category: Science

Page: 416

View: 3236

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.