SuperFractals

SuperFractals, first published in 2006, describes mathematics and algorithms for the first time in book form, with breathtaking colour pictures.

Michael Fielding Barnsley (Author)

9780521844932, Cambridge University Press

Hardback, published 7 September 2006

464 pages, 250 colour illus.
24.8 x 18.1 x 2.7 cm, 1.08 kg

'Michael Barnsley is a wonderful guide into the world of Super Fractal geometry. This book will take you on a journey of discovery that will make you look at everyday geometry in a very different way. …a must read for anyone who is interested in the way mathematics can be used to develop understanding in nature.' Mathematics TODAY

SuperFractals, first published in 2006, is the 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 explains how IFS have developed in order to address this issue. 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.

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.

Subject Areas: Image processing [UYT], Mathematical modelling [PBWH], Fractal geometry [PBMX], Calculus & mathematical analysis [PBK]