Field M. Symmetry in Chaos. A Search for Pattern in Mathematics,...2009

Textbook in PDF format

Mathematical symmetry and chaos come together to form striking, beautiful color 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 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 Symmetry in Chaos 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