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Superfractals

von Barnsley, Michael   (Autor)

SuperFractals is about a new kind of geometry and this book explains clearly and accessibly how it is born from a union of randomness, geometry and computation. Mathematical ideas are explained and illustrated through a profusion of full-colour images. Potential applications are explored: for example, SuperFractals enable a vast improvement in terms of texture and variety than conventional computer graphics methods currently used in games and films; they may lead to insights in economics, science, medical imaging and biology; they will have application for image and signal compression. SuperFractals, first published in 2006, describes mathematics and algorithms for the first time in book form, with breathtaking colour pictures.

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Produktbeschreibung

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. 

Inhaltsverzeichnis

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.
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. 

Autoreninfo

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

Mehr vom Verlag:

Cambridge University Press

Mehr vom Autor:

Barnsley, Michael

Produktdetails

Medium: Buch
Format: Gebunden
Seiten: 464
Sprache: Englisch
Erschienen: Mai 2013
Auflage: 2. Aufl
Maße: 250 x 175 mm
Gewicht: 974 g
ISBN-10: 0521844932
ISBN-13: 9780521844932

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P_ABB: 250 colour figures
KNOABBVERMERK: 2006. 464 S. 250 colour illus. 248 mm
Einband: Gebunden
Auflage: 2. Aufl
Sprache: Englisch
Beilage(n): HC gerader Rücken kaschiert

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