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

Chaotic dynamics (commonly known as chaos theory) is one of the most fascinating 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 appear to be the antithesis of chaotic systems such as weather patterns. Yet scientists are finding connections between these two areas, connections that 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. They present a series of mathematically generated, stunning computer images linking symmetry and chaos. Field and Golubitsky describe how a chaotic process can lead to symmetric patterns (for example, in a river, photographs of turbulent eddies taken over time often reveal patterns on average) and they provide clear explanations of the science behind the generation of these pictures. The images are spectacular: because of the symmetry, these full-color and black-and-white images—some chaotic and some fractal—have a surprisingly classical appearance. Through comparisons with nature—sea shells and flowers—and decorative designs—from Islamic motifs to contemporary graphic logos and ceramic tiles—the authors highlight the familiar yet unusual nature of these mysterious pictures. The book also features an appendix containing several BASIC programs that enable home computer users to experiment with similar images. This lavishly illustrated, oversized volume offers both a fascinating glimpse into 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.