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.
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.
1. Introduction to symmetry and chaos; 2. Planar symmetries; 3. Patterns everywhere; 4. Chaos and symmetry creation; 5. Symmetric icons; 6. Quilts; 7. Symmetric fractals; Appendix A. Picture parameters; Appendix B. Icon mappings; Appendix C. Planar lattices; Bibliography; Index.