Chaos, Fractals and DynamicsA course designed by R. Pyke offered at the University of Toronto |
This page describes an introductory course on chaos and fractals. Topics include: What is a chaotic system? What makes a system chaotic? Fractals; drawing fractals, fractal dimension. Strange attractors. Julia sets. The Mandelbrot set. - And more. Along the way we will look at the historical development of these ideas and how they are used today in areas such as physics, biology, medicine, and economics.
An excellent textbook for this course is; Chaos and Fractals: New Frontiers of Science, by H.-O. Peitgen, H. Jurgens, and D. Saupe, Springer-Verlag, 1992 [PJS]. This book (all 1000 pages of it) is full of diagrams, supplementary mathematical material, beautiful colour pictures, and complete and detailed explanations (in ordinary language) of many topics in chaos and fractals, including not-so-elementary topics like renormalization and universality, fractal image compression, Lyaponov exponents, fractional Brownian motion, and more.
For general information about the course content see the overview of the course, and for a more detailed description of the course content see the course descriptions below for the Winter 2000 - 2002 terms.