SuperFractals

by Michael Fielding Barnsley

Overview

SuperFractals is the long-awaited successor to Fractals Everywhere, in which the power and beauty of Iterated Function Systems were introduced and applied to producing startling and original images that reflect complex structures found for example in nature. This provoked the question of whether there is a deeper connection between topology, geometry, IFS and codes on the one hand and biology, DNA and protein development on the other. Now, 20 years later, Barnsley brings the story up to date by explaining how IFS have developed in order to address this issue. New ideas such as fractal tops and superIFS are introduced, and the classical deterministic approach is combined with probabilistic ideas to produce new mathematics and algorithms that open a whole theory that could have applications in computer graphics, bioinformatics, economics, signal processing and beyond. For the first time these ideas are explained in book form, and illustrated with breathtaking pictures.

Product Details

ISBN-13:	9780521844932
Publisher:	Cambridge University Press
Publication date:	09/07/2006
Edition description:	First Edition
Pages:	464
Product dimensions:	7.13(w) x 9.76(h) x 1.06(d)

About the Author

Michael Barnsley is a Professor at the Mathematical Sciences Institute, Australian National University.

Table of Contents

Part I. Geometries and Transformations: 1. Codes, metrics and topologies; 2. Transformations of points, sets, pictures and measures; 3. Semigroups on sets, measures and pictures; Part II. Iterated Function Systems: 4. IFS acting on measures; 5. More on IFS; Part III. Applications to Graphics: 6. Digital content production; 7. Image compression; 8. Super IFS.

Editorial Reviews

"Overall, SuperFractals would be a superb addition to the bookshelves of any scientists who use fractal analysis techniques in their research, be they physicist, biologist or economist. The author concludes by promising that the introduction of superfractals will revolutionize the way mathematics, physics, biology and art are combined, to produce a unified description of the complex world in which we live. After reading this book I have no doubt he is correct."
Nature

"The book is well structured and an enjoyable read...The book contains some interesting, very deep and even enthralling mathematics. The author's ability to clearly describe complicated phenomena paired with a pleasant writing style make this book a must read for all people interested in the mathematics of fractals...There are many wonderful, colorful pictures that spark one's imagination. Examples spread liberally throughout the book together with relevant exercises help illuminate this new look at 'patterns in nature'."
Kai Brunkalla, MAA Reviews, MathDL

"Exuberant, light-hearted, chatty, idiosyncratic, and lavishly illustrated by many beautiful and breathtaking pictures."
Lars Olsen, Mathematical Reviews

From the Publisher