The concepts of chaos and fractal have become quite popular in recent
years, even among people with little mathematical background. Among the
reasons for this surge of interest are the publication of several books and
articles intended for general audiences. These include James Gleick's Chaos:
Making a New Science and articles in Scientific American showing the great
beauty of the computer graphics images of complex dynamical systems. At
times, all the attention devoted to these topics seems to obscure the fact that
there really is some beautiful mathematics in the fields of chaotic dynamical
systems and fractal geometry. The goal of the Short Course at which these
lectures were given was to remedy this.
The course was called Chaos and Fractals: The Mathematics Behind the
Computer Graphics and was organized at the Centennial Meeting of the Amer-
ican Mathematical Society held in Providence, RI, on August 6-7, 1988. The
lectures covered a wide range of topics from dynamical systems and frac-
tal geometry. Among many other concepts, the lectures covered the period
doubling route to chaos, Smale's horseshoe and symbolic dynamics, strange
attractors and their basin boundaries, Julia sets and the Mandelbrot set, Haus-
dorff and entropy dimension, and applications in engineering and data com-
pression. This book contains expanded versions of the seven lectures deliv-
ered during the Short Course.
We would especially like to thank Jim Maxwell, Monica Foulkes, and their
staffs from the American Mathematical Society, who coordinated the Short
Course. With over 550 participants, this course was the largest in AMS
history. Despite the memorable 100° temperatures during the course, we
were very pleased with the results.
Robert L. Devaney
Linda Keen
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