Symmetry in Chaos

A Search for Pattern in Mathematics, Art, and Nature

Inbunden, Engelska, 2009

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2009-04-30
Mått:152 x 229 x undefined mm
Vikt:1 065 g
Format:Inbunden
Språk:Engelska
Antal sidor:213
Upplaga:2
Förlag:Society for Industrial & Applied Mathematics,U.S.
ISBN:9780898716726

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Mer om författaren

Michael Field has been a Professor at the University of Houston since 1992. He received his PhD in mathematics from the University of Warwick in 1970. His research interests include ergodic theory, coupled cell systems, the geometric theory of dynamical systems with symmetry and the mechanisms whereby symmetry can lead to complex dynamics in low dimensional systems. Martin Golubitsky is Distinguished Professor of Mathematics and Physical Sciences at the Ohio State University, where he serves as Director of the Mathematical Biosciences Institute. He received his PhD in Mathematics from M.I.T. in 1970 and has been Professor of Mathematics at Arizona State University (1979-83) and Cullen Distinguished Professor of Mathematics at the University of Houston (1983-2008). Dr Golubitsky works in the fields of nonlinear dynamics and bifurcation theory studying the role of symmetry in the formation of patterns in physical systems and the role of network architecture in the dynamics of coupled systems. He has co-authored four graduate texts, one undergraduate text, two nontechnical trade books, and over 100 research papers.

Recensioner i media

'An impressive and beautiful exploration of an impressive and beautiful area of mathematics - the interplay between order and chaos. The images are breathtaking, the mathematics fundamental. Symmetry in Chaos is an important book, a work of art, and a joy to read.' Ian Stewart, author of Why Beauty is Truth 'A classic in the interdisciplinary field of art and mathematics, this very well written book takes the ingenious idea of combining symmetry with chaos to construct stunning images that anyone can enjoy, in particular mathematicians, who can also appreciate the underlying mathematics. Beautiful art cannot be the result of just clever computer graphics. The artist must also have a keen sense of color and that intangible artistic sensibility, which is present in Symmetry in Chaos. Anyone interested in the relationship of art and mathematics should read this book.' Nat Friedman, Director, International Society of the Arts, Mathematics and Architecture

Innehållsförteckning

Chapter 1: Introduction to Symmetry and ChaosChapter 2: Planar SymmetriesChapter 3: Patterns EverywhereChapter 4: Chaos and Symmetry CreationChapter 5: Symmetric IconsChapter 6: QuiltsChapter 7: Symmetric FractalsAppendix A: Picture ParametersAppendix B: Icon MappingsAppendix C: Planar LatticesBibliographyIndex