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SuperFractals

SuperFractals

$59.99

  • Date Published: September 2006
  • availability: Available
  • format: Hardback
  • isbn: 9780521844932

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  • 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.

    • Breathtaking graphics in four colour throughout, as to be expected in the long-awaited successor to Fractals Everywhere
    • New mathematics throughout, with key ideas explained intuitively and rigorously, making the text available to a wide range of readers
    • SuperFractals opens up many new avenues for research, suggesting novel applications in bioinformatics, image recognition, geometric modelling and content creation
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    Reviews & endorsements

    '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

    'Each new idea is preceded by an intuitive discussion, often accompanied by examples, and always by gorgeous artwork. The explanation and arguments are very clear and easy to follow, even for someone not accustomed to mathematical texts.' Journal of Statistical Physics

    '…I can recommend the book as a nice introduction to the subject of superfractals as well as to the theory of IFS's in general. It is particularly suitable for non-geometrists as well as for non-mathematicians. From my own experience, it serves well as a textbook, also for undergraduate students.' Zentralblatt MATH

    '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

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    Product details

    • Date Published: September 2006
    • format: Hardback
    • isbn: 9780521844932
    • length: 464 pages
    • dimensions: 248 x 181 x 27 mm
    • weight: 1.08kg
    • contains: 250 colour illus.
    • availability: Available
  • 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.

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    SuperFractals

    Michael Fielding Barnsley

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  • Author

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

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