Michael Fielding Barnsley

SuperFractals (eBook, ePUB)

• Format: ePub

Produktbeschreibung

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.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 7. September 2006
• Englisch
• ISBN-13: 9781139861489
• Artikelnr.: 53005153

Autorenporträt

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

Inhaltsangabe

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.

Rezensionen

'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.' J. R. Mureika, Nature