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The terms chaos and fractals have received widespread attention in recent years. The alluring computer graphics images associated with these terms have heightened interest among scientists in these ideas. This volume contains the introductory survey lectures delivered in the American Mathematical Society Short Course, Chaos and Fractals: The Mathematics Behind the Computer Graphics, on August 6-7, 1988, given in conjunction with the AMS Centennial Meeting in Providence, Rhode Island. In his overview, Robert L. Devaney introduces such key topics as hyperbolicity, the period doubling route to chaos, chaotic dynamics, symbolic dynamics and the horseshoe, and the appearance of fractals as the chaotic set for a dynamical system. Linda Keen and Bodil Branner discuss the Mandelbrot set and Julia sets associated to the complex quadratic family z -> z2 + c. Kathleen T. Alligood, James A. Yorke, and Philip J. Holmes discuss some of these topics in higher dimensional settings, including the Smale horseshoe and strange attractors. Jenny Harrison and Michael F. Barnsley give an overview of fractal geometry and its applications. -- from dust jacket.
Introduces the mathematical topics of chaos, fractals, and dynamics using a combination of hands-on computer experimentation and precalculas mathmetics. A series of experiments produce fascinating computer graphics images of Julia sets, the Mandelbrot set, and fractals. The basic ideas of dynamics--chaos, iteration, and stability--are illustrated via computer projects.
Publisher Description
The study of nonlinear dynamical systems has exploded in the past 25 years, and Robert L. Devaney has made these advanced research developments accessible to undergraduate and graduate mathematics students as well as researchers in other disciplines with the introduction of this widely praised book. In this second edition of his best-selling text, Devaney includes new material on the orbit diagram fro maps of the interval and the Mandelbrot set, as well as striking color photos illustrating both Julia and Mandelbrot sets. This book assumes no prior acquaintance with advanced mathematical topics such as measure theory, topology, and differential geometry. Assuming only a knowledge of calculus, Devaney introduces many of the basic concepts of modern dynamical systems theory and leads the reader to the point of current research in several areas.
Introduces the mathematical topics of chaos, fractals, and dynamics using a combination of hands-on computer experimentation and precalculas mathmetics. A series of experiments produce fascinating computer graphics images of Julia sets, the Mandelbrot set, and fractals. The basic ideas of dynamics--chaos, iteration, and stability--are illustrated via computer projects.
Written by one of the most respected mathematicians in the field, this book conveys the essential mathematical ideas in dynamical systems using a combination of theory and computer experimentation. This introductory look at dynamical systems includes investigating the rates of approach to attracting and indifferent fixed points to the discovery of Feigenbaum's constant; exploring the window structure in the orbit diagram; and understanding the periods of the bulbs in the Mandelbrot set.
The dazzling world of fractals is now at the fingertips of any computer user with a wonderful new program, included with the book, which combines the features of fractal microscope, a paint prgram, and a lab bench. It's called FRACTINT, and it lets users control fractal generation, manipulation, editing, alteration and storage. The program enables users to generate any of 60 built-in fractals or type in their own fractal formulas.