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El. knyga: SuperFractals

3.60/5 (10 ratings by Goodreads)
(Australian National University, Canberra)
  • Formatas: EPUB+DRM
  • Išleidimo metai: 07-Sep-2006
  • Leidėjas: Cambridge University Press
  • Kalba: eng
  • ISBN-13: 9781139861489
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SuperFractalsDidesnis paveikslėlis
  • Formatas: EPUB+DRM
  • Išleidimo metai: 07-Sep-2006
  • Leidėjas: Cambridge University Press
  • Kalba: eng
  • ISBN-13: 9781139861489
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SuperFractals describes new mathematics and algorithms for the first time in book form, with breathtaking colour pictures.

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.

Recenzijos

'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

Daugiau informacijos

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


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