- Hardcover: 464 pages
- Publisher: Cambridge University Press; 1 edition (7 Sep 2006)
- Language English
- ISBN-10: 0521844932
- ISBN-13: 978-0521844932
- Product Dimensions: 24.8 x 18.1 x 2.7 cm
- Amazon Bestsellers Rank: 253,316 in Books (See Top 100 in Books)
- See Complete Table of Contents
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Review
'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
'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
Product 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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First Sentence
Any picture may be conceived as a mathematical object, lying on part of the euclidean plane, each point having its own colour. Read the first page
Front Cover | Copyright | Table of Contents | Excerpt | Index
Any picture may be conceived as a mathematical object, lying on part of the euclidean plane, each point having its own colour. Read the first page
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Front Cover | Copyright | Table of Contents | Excerpt | Index
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6 reviews
12 of 12 people found the following review helpful
Excellent, but takes a bit more than Calculus
10 Sep 2007
Format:Hardcover
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.
2 of 2 people found the following review helpful
Stunning visuals
3 Jun 2009
Format:Hardcover|Amazon Verified Purchase
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.
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.
6 of 9 people found the following review helpful
A Beautiful Book
31 Jan 2007
Format:Hardcover
Prof. Michael Barnsley has demonstrated once again that his approach to pattern analysis in the real-world, namely self-similar patterns, through iterated functions and random dynamical systems, works for more complex and amazingly complex and beautiful patterns, by expanding his previous theory developed in his earlier book. Besides the nice mathematics and recent theoretical developments by him and others, the many beautifully produced figures in the book are already worthy the price of the book, which I am surprised is such a bargain.
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