SuperFractals [Hardcover]

Michael Fielding Barnsley (Author)

Book Description

ISBN-10: 0521844932 | ISBN-13: 978-0521844932 | Publication Date: September 11, 2006 | Edition: 1

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.

Editorial Reviews

Amazon.com Review

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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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."
Nature

"The book is well structured and an enjoyable read...The book contains some interesting, very deep and even enthralling mathematics. The author's ability to clearly describe complicated phenomena paired with a pleasant writing style make this book a must read for all people interested in the mathematics of fractals...There are many wonderful, colorful pictures that spark one's imagination. Examples spread liberally throughout the book together with relevant exercises help illuminate this new look at 'patterns in nature'."
Kai Brunkalla, MAA Reviews, MathDL

"Exuberant, light-hearted, chatty, idiosyncratic, and lavishly illustrated by many beautiful and breathtaking pictures."
Lars Olsen, Mathematical Reviews

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Product Details

• Hardcover: 464 pages
• Publisher: Cambridge University Press; 1 edition (September 11, 2006)
• Language: English
• ISBN-10: 0521844932
• ISBN-13: 978-0521844932
• Product Dimensions: 9.8 x 7.1 x 1 inches
• Shipping Weight: 2.6 pounds (View shipping rates and policies)
• Average Customer Review: 3.7 out of 5 stars  See all reviews (6 customer reviews)
• Amazon Best Sellers Rank: #567,832 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

12 of 12 people found the following review helpful:

5.0 out of 5 stars Excellent, but takes a bit more than Calculus, September 10, 2007

By 

David Matthews (Minnesota, USA) - See all my reviews
(REAL NAME)   

This review is from: SuperFractals (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:

4.0 out of 5 stars Stunning visuals, June 3, 2009

By 

J. MOLDOVAN - See all my reviews
(REAL NAME)   

Amazon Verified Purchase

This review is from: SuperFractals (Hardcover)

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.

6 of 9 people found the following review helpful:

4.0 out of 5 stars A Beautiful Book, January 31, 2007

By 

Random Thoughts (Maryland) - See all my reviews

This review is from: SuperFractals (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.