The Fractal Geometry of Nature [Hardcover]

Benoit B. Mandelbrot (Author)

Book Description

ISBN-10: 0716711869 | ISBN-13: 978-0716711865 | Publication Date: 1982 | Edition: 1

Clouds are not spheres, mountains are not cones, and lightening does not travel in a straight line. The complexity of nature's shapes differs in kind, not merely degree, from that of the shapes of ordinary geometry, the geometry of fractal shapes.

Now that the field has expanded greatly with many active researchers, Mandelbrot presents the definitive overview of the origins of his ideas and their new applications. The Fractal Geometry of Nature is based on his highly acclaimed earlier work, but has much broader and deeper coverage and more extensive illustrations.

Editorial Reviews

Amazon.com Review

Imagine an equilateral triangle. Now, imagine smaller equilateral triangles perched in the center of each side of the original triangle--you have a Star of David. Now, place still smaller equilateral triangles in the center of each of the star's 12 sides. Repeat this process infinitely and you have a Koch snowflake, a mind-bending geometric figure with an infinitely large perimeter, yet with a finite area. This is an example of the kind of mathematical puzzles that this book addresses.

The Fractal Geometry of Nature is a mathematics text. But buried in the deltas and lambdas and integrals, even a layperson can pick out and appreciate Mandelbrot's point: that somewhere in mathematics, there is an explanation for nature. It is not a coincidence that fractal math is so good at generating images of cliffs and shorelines and capillary beds.

Review

"A rarity: a picture book of sophisticated contemporary research ideas in mathematics."--Douglas Hofstadter, author of Godel, Escher, Bach

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Product Details

• Hardcover: 460 pages
• Publisher: W. H. Freeman; 1 edition (1982)
• Language: English
• ISBN-10: 0716711869
• ISBN-13: 978-0716711865
• Product Dimensions: 9.3 x 8.2 x 1.1 inches
• Shipping Weight: 2.5 pounds (View shipping rates and policies)
• Average Customer Review: 4.1 out of 5 stars  See all reviews (22 customer reviews)
• Amazon Best Sellers Rank: #31,753 in Books (See Top 100 in Books)
  • #10 in Books > Professional & Technical > Professional Science > Physics > System Theory
  • #72 in Books > Computers & Technology > Programming > Algorithms

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Customer Reviews

Most Helpful Customer Reviews

108 of 123 people found the following review helpful:

2.0 out of 5 stars A review on the book -- not on Mandelbrot, August 25, 2002

By 

Assela Pathirana (Japan) - See all my reviews

This review is from: The Fractal Geometry of Nature (Hardcover)

Mandelbrot is the person who introduced the fractal theory to the world in its present form. Many fields of science including geophysics have gained from fractals. However, this is not the book one should read to gain knowledge on the subject.

It is not an easily readable book. 1. It is not well-organized 2. It does not cover necessary things in detail 3. Frustratingly long in some parts. Instead the books: Feder, Fractals; Turcotte, Fractals and Chaos in Geology and Geophysics can be recommended.

Fractal geometry may be interesting as a historical book, after one gains a sufficient knowledge on fractals.

41 of 45 people found the following review helpful:

5.0 out of 5 stars A seminal work, September 7, 2005

By 

Arturo Ortiz Tapia "Dr. T.A.O." (Mexico city) - See all my reviews
(REAL NAME)   

This review is from: The Fractal Geometry of Nature (Hardcover)

Very few books have so many quotes as this one. I am not sure if there is much left to be said, but I know this. For those professionals who still think that fractals are "spurious solutions coming from the discretization of differential equations", should take a closer look to this book. Not only won't harm, but also will show many interesting features about the nature of fractals and the "fractality" of nature, besides the fact that many of them come from *difference* equations, which are not necessarily related to the discretization of a differential equation. This book is based on serious work from many well-reputed mathematicians before Mandelbrot, e.g., Haussdorff, Lyapunov and some others. Although the book does talk about the mathematics behind fractals (wouldn't be so much a book of mathematics if it didn't, but also a philosophical one) and the necessity of coining some new mathematical terms, it also contains so much about history of mathematics, the path that leads towards fractals. As I said, the book is many times quoted, but (without trying to point a firing, accusing finger), there is a difference in quoting a book because it is famous, and another actually reading it, and having enlightenment for our own sake. Certainly I think is a "must-have-it" for most mathematicians, for many physicists, philosophers of science and engineers, but also it wouldn't be a bad guest in the library of any layman, provided the layman overcomes for some minutes the initial "classical" fear to mathematics. I would say this layman won't regret it at all. Mandelbrot does explain most of the concepts practically "ab initio", from the very scratch, including etymology and history as I previously said. One little thing against this book though: it doesn't have so many color plates as some other books on the subject, but it does have all the needed graphics to grasp the concepts.

76 of 92 people found the following review helpful:

3.0 out of 5 stars beauty does not equate to depth or thoroughness, February 27, 2000

By 

Bruce D. Wilner "polymathic bibliophile" (Virginia, USA) - See all my reviews
(REAL NAME)   

This review is from: The Fractal Geometry of Nature (Hardcover)

Mandelbrot's update of his classic work is certainly eye-catching. However, just like its forerunner, it fails to answer the simplest questions, including, "How do I calculate the fractal dimension of this curve?" and "How can I manage to plot the Julia set for myself?" The answers to such questions have to be gleaned by the intelligent--and mathematically sophisticated--reader for himself. (One sees this phenomenon all the time in "advanced" mathematics books. It means that either [a] the author has his head stuck in the clouds and expects the reader to use divination, or [b] he prefers to keep his readers ignorant.) For a much more practical and rewarding discussion, read "The Science of Fractal Images" edited by Peitgen and Saupe. The math is clear; the algorithms are plainly stated for the PC enthusiast with some simple programming skills; and the color plates are astounding.