Superfractals

by Michael Fielding Barnsley

• ISBN13: 9780521844932
• ISBN10: 0521844932
• Edition: 1st
• Format: Hardcover
• Copyright: 2006-09-11
• Publisher: Cambridge University Press

Summary

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.

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.