Chaos, Fractals, and Dynamics - Computer Experiments in Mathematics

This book provides an excellent framework for understanding chaotic systems, whether for the novice or the experienced fractal scientist. The diagrams in particular helped elucidate the concepts presented. Science made simple without being dummed down - well done!

This is a nice little book whose target audience is high school students, beginning undergraduates, and science teachers. Using many examples , Devaney leads the reader through ideas of iteration and dynamical system. The latter half of the book deals with the connection between chaos and the science of fractals. The readers are encouraged to explore the various facets of chaos and fractals using simple computer programs (many sample source codes are peppered throughout the book). In addition to the book, there is a couple of companion video tapes that are also highly instructive and serve as good introduction to chaos and fractals. The first video, Chaos, Fractals and Dynamics, bears the same name as the book and brings to life many of the examples mentioned in the book in a manner that is not possible via the static book format. The visual highlight occurs when Devaney shows beautiful animations of the Julia set. If this doesn't get the students excited, I don't know what will! The second video, Transition to Chaos, describes the period-doubling approach to chaos using the now standard quadratic map. There is a nice discussion about the relationship between the period-doubling bifurcation and the Mandelbrot and Julia sets.