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SuperFractals (Englisch) Gebundenes Buch – 7. September 2006

von Michael Fielding Barnsley (Autor)

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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.

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Produktinformation

Gebundene Ausgabe: 464 Seiten
Verlag: Cambridge University Press; Auflage: 1 (7. September 2006)
Sprache: Englisch
ISBN-10: 9780521844932
ISBN-13: 978-0521844932
ASIN: 0521844932
Größe und/oder Gewicht: 17,4 x 2,7 x 24,7 cm
Durchschnittliche Kundenbewertung: Schreiben Sie die erste Bewertung
Amazon Bestseller-Rang: Nr. 1.017.658 in Fremdsprachige Bücher (Siehe Top 100 in Fremdsprachige Bücher)
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Produktbeschreibungen

Amazon.de

Book Description

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.

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Pressestimmen

'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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Amazon.com: 8 Rezensionen

judy

Excellent, enlightening book!

22. Februar 2014 - Veröffentlicht auf Amazon.com

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This book expands the Iterated Function System (IFS) to the next level with transformations that allow evolution into truly natural images. Ferns, trees, and leaves can look real. Multiple images can be merged. Numerous exercises throughout the book emphasize the important concepts. Toward the end of the book, several tables contain mistakes (e.g., Table 5.1 & 5.2 images are swapped, and the codes in Tables 5.4 & 5.5 render their images upside down. The errata file is inaccessible today, and I'm very disappointed that corrections weren't already made to this electronic book--but, overall, I still highly recommend this book to anyone who wants to expand their knowledge of fractals to the next level beyond Michael Barnsley's "Fractals Everywhere" book.

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3 Personen fanden diese Informationen hilfreich.

J. MOLDOVAN

Stunning visuals

3. Juni 2009 - Veröffentlicht auf Amazon.com

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The illustrations alone are worth the price - twice over. And the generous layout, font selection and overall readability is a delight. I also love the very practical treatment of the mathematics without descending to "popular" exposition. Warning: university level set theory, geometry and topology required.

But there is a flaw in the book. The volume is some 450 pages long but it really needs to be about three times this size to adequately cover the material presented. As it stands, those not already familiar with the topic and with adequate prerequisites will find it very heavy going. A partial solution is to get something like Falconer and a couple of maths primers as a companion.

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4 Personen fanden diese Informationen hilfreich.

Tsiaras Vassilis

A nice book about Fractals and Iterated Function Systems

18. Oktober 2012 - Veröffentlicht auf Amazon.com

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I liked this book. It isn't as revolutionary as the "Fractals Everywhere" were 20 years ago but it is still a nice account on the subject. It explains the theory and describes novel ideas on Fractal Image Processing. I found some spelling mistakes.

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what's the point?

31. Mai 2009 - Veröffentlicht auf Amazon.com

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The title implies some kind of major generalization or extension of fractals, but I didn't find any evidence of this. The author claims that there are 'many applications' for superfractals, but neglects to mention or describe even one.

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7 Personen fanden diese Informationen hilfreich.

David Matthews

Excellent, but takes a bit more than Calculus

10. September 2007 - Veröffentlicht auf Amazon.com

For someone who has had a good undergraduate analysis course (also known as "advanced calculus" some places), with a solid introduction to the topology of the real line, this book provides an excellent application to fractals, and a great extension to the real plane. Without this understanding, you can probably pick up enough from the examples to get some use out of this, but you'd have a tough time working all the exercises, or getting a full understanding of the math. I'd also suggest, for other non-programmers, that you pick up a (free) copy of the Processing programming language (Processing.org), or something similar, to try your own examples as you go. Like I said, for someone like me, a math teacher 20-some years out of college, it's a great way to review topics I haven't seen in a while, and an excellent sequel to "Fractals Everywhere." I've been waiting a while for this book; glad it's finally out.

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15 Personen fanden diese Informationen hilfreich.

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