Starting with an analysis of the forms of symmetry, the authors show how a few key principles can help us understand everything from cat's movements, corn circles, and snow crystals to subatomic particles and the overall structure of the cosmos. 127 figures. of full-color illustrations.

Fearful Symmetry: Is God a Geometer?

Politics & Social Sciences

STEWART, Ian

Golubitsky, Martin

Philosophy

Penguin??Books

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.

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

FIELD, MICHAEL

Computers & Technology

Oxford University Press

This book has been written in a frankly partisian spirit-we believe that singularity theory offers an extremely useful approach to bifurcation prob lems and we hope to convert the reader to this view. In this preface we will discuss what we feel are the strengths of the singularity theory approach. This discussion then Ieads naturally into a discussion of the contents of the book and the prerequisites for reading it. Let us emphasize that our principal contribution in this area has been to apply pre-existing techniques from singularity theory, especially unfolding theory and classification theory, to bifurcation problems. Many ofthe ideas in this part of singularity theory were originally proposed by Rene Thom; the subject was then developed rigorously by John Matherand extended by V. I. Arnold. In applying this material to bifurcation problems, we were greatly encouraged by how weil the mathematical ideas of singularity theory meshed with the questions addressed by bifurcation theory. Concerning our title, Singularities and Groups in Bifurcation Theory, it should be mentioned that the present text is the first volume in a two-volume sequence. In this volume our emphasis is on singularity theory, with group theory playing a subordinate role. In Volume II the emphasis will be more balanced. Having made these remarks, Iet us set the context for the discussion of the strengths of the singularity theory approach to bifurcation. As we use the term, bifurcation theory is the study of equations with multiple solutions.

Singularities and Groups in Bifurcation Theory: Volume I (Applied Mathematical Sciences, 51)

Science & Math

Schaeffer, David G.

Mathematics

Springer

Bifurcation theory studies how the structure of solutions to equations changes as parameters are varied. The nature of these changes depends both on the number of parameters and on the symmetries of the equations. Volume I discusses how singularity-theoretic techniques aid the understanding of transitions in multiparameter systems. This volume focuses on bifurcation problems with symmetry and shows how group-theoretic techniques aid the understanding of transitions in symmetric systems. Four broad topics are covered: group theory and steady-state bifurcation, equicariant singularity theory, Hopf bifurcation with symmetry, and mode interactions. The opening chapter provides an introduction to these subjects and motivates the study of systems with symmetry. Detailed case studies illustrate how group-theoretic methods can be used to analyze specific problems arising in applications.

Singularities and Groups in Bifurcation Theory: Volume II (Applied Mathematical Sciences, 69)

This fascinating study explores a fundamental paradox behind the patterns of the natural world, in which symmetrical causes lead to asymmetrical effects. Lesser and greater patterns—the structure of subatomic particles, a tiger's stripes, the shapes of clouds, and the vibrations of the stars—are produced by broken symmetry. This accessible exploration of the physical and biological world employs the mathematical concepts of symmetry to consider the deepest questions of modern physics. An active popularizer of mathematics, Ian Stewart is a university professor and former columnist for Scientific American's "Mathematical Games" column. 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. Both authors share an interest in the application of new mathematical ideas to scientific problems. More than 120 figures illustrate their illuminating survey of the interaction of symmetry with dynamics and the mathematical unity of nature's patterns.

Fearful Symmetry: Is God a Geometer? (Dover Books on Mathematics)

Biological Sciences

Dover Publications

These world-renowned authors integrate linear algebra and ordinary differential equations in this unique book, interweaving instructions on how to use MATLAB with examples and theory. They use computers in two ways: in linear algebra, computers reduce the drudgery of calculations to help students focus on concepts and methods; in differential equations, computers display phase portraits graphically for students to focus on the qualitative information embodied in solutions, rather than just to learn to develop formulas for solutions.

Linear Algebra and Differential Equations Using MATLAB

Dellnitz, Michael

Computer Science

Cengage Learning'

Contains supplemental exercises and practice tests for students.

Student Solutions Manual for Golubitsky/Dellnitz's Linear Algebra and Differential Equations Using MATLAB

Brooks/Cole

This sequel to the bestselling Does God Play Dice? will open your eyes to the broken symmetries that lie all around you, from the shapes of clouds to the drops of dew on a spider's web, from centipedes to corn circles. It will take you to the farthest reaches of the universe and bring you face-to-face with some of the deepest questions of modern physics.

Physics

Blackwell Pub.

Symmetry suggests order and regularity whilst chaos suggests disorder and randomness. Symmetry in Chaos is an exploration of how combining the seemingly contradictory symmetry and chaos can lead to the construction of striking and beautiful 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 second edition has been updated to include the Faraday experiment, a classical experiment from fluid dynamics which illustrates that increasing the vibration amplitude of a container of liquid causes the liquid to form surface waves, instead of moving as a solid body. This second edition also includes updated methods for numerically determining the symmetry of higher dimensional analogues of the images. As well as this, it contains new and improved quality images.

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

Society for Industrial and Applied Mathematics

See the best price to sell, buy, or rent books by Golubitsky, Martin. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Golubitsky, Martin

See the best price to sell, buy, or rent books by Golubitsky, Martin. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Fearful Symmetry: Is God a Geometer?

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

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

Singularities and Groups in Bifurcation Theory: Volume I (Applied Mathematical Sciences, 51)

Singularities and Groups in Bifurcation Theory: Volume II (Applied Mathematical Sciences, 69)

Fearful Symmetry: Is God a Geometer? (Dover Books on Mathematics)

Linear Algebra and Differential Equations Using MATLAB

Student Solutions Manual for Golubitsky/Dellnitz's Linear Algebra and Differential Equations Using MATLAB

Fearful Symmetry: Is God a Geometer?

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