Symmetry in Chaos: A Search for Pattern in Mathematics, Art and Nature 2nd Edition by Michael Field (PDF)

Description

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.

User’s Reviews

Editorial Reviews: Review ‘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 Book Description A striking, full-colour book which explains how combining symmetry and chaos can lead to the construction of remarkable images. 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. About the Author 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. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Was in great condition. Love it!

⭐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.

⭐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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