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The Fractal Geometry of Nature [Hardcover]

Benoit B. Mandelbrot
4.3 out of 5 stars  See all reviews (33 customer reviews)

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Book Description

1982 0716711869 978-0716711865 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.

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Editorial Reviews 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.


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

Product Details

  • Hardcover: 468 pages
  • Publisher: W. H. Freeman and Company; 1 edition (1982)
  • Language: German
  • ISBN-10: 0716711869
  • ISBN-13: 978-0716711865
  • Product Dimensions: 9.3 x 8.2 x 1.1 inches
  • Shipping Weight: 2.3 pounds (View shipping rates and policies)
  • Average Customer Review: 4.3 out of 5 stars  See all reviews (33 customer reviews)
  • Amazon Best Sellers Rank: #55,909 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews
60 of 65 people found the following review helpful
5.0 out of 5 stars A seminal work September 7, 2005
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.
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137 of 157 people found the following review helpful
2.0 out of 5 stars A review on the book -- not on Mandelbrot August 25, 2002
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.
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88 of 112 people found the following review helpful
3.0 out of 5 stars beauty does not equate to depth or thoroughness February 27, 2000
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.
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22 of 27 people found the following review helpful
By A Customer
This tome is the immortal classic that introduces fractals to the layman and scholar alike. The mechanics and beauty of fractals are presented in a very readable manner that is sure to pique the interest of anyone seeking a deterministic, yet almost supernaturally pervasive paradigm of the structure of the universe. This book fundamentally affected my personal outlook on nature irrecovably. I would advise leaving it on the coffee table for your children to examine.
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18 of 22 people found the following review helpful
3.0 out of 5 stars A dated but still fascinating book August 26, 2002
This was the book that first caught my attention. It was the cover diagram: a figure the like of which I had never seen. One thing led to another until I finally wrote my own application of fractals, Fractals in Music.
Mandelbrot is an odd character, but a superb thinker. His book does not offer a lot of science, but rather a compelling view of how this fascinating and growing topic developed. I recommend it highly.
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11 of 13 people found the following review helpful
5.0 out of 5 stars This book started it all June 14, 1998
By A Customer
This book is by far the very root by which chaos and the interrelations with that of nature came into existance. Mandelbrot describes chaos and dynamical systems as applied in the real world, and how fractals do appear in nature. Mandelbrot gets an A+.
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7 of 8 people found the following review helpful
3.0 out of 5 stars It's OK but.... June 4, 2008
Benoît Mandelbrot is unquestionably a great savant but he should have taken some lessons on how to write books.

There is an intense feeling of disappointment after reading this book and it is hard to pinpoint why. It's all there: nature in a wondrous new light. An original work which almost singlehandedly (well... almost) spawned a new field, a field which is not only beautiful but immensely useful as well. The discourse is not too complicated and it is not simplistic pap-science either. Yet there is something missing, a passion or what some might call 'heart'.

When I pick up a book about fractals, even when it is a highly technical work like formal fractal geometry, there is always a certain sense of excitement, of dabbling with a new and beautiful toy. You won't get that feeling with this book.

I still recommend it, in fact I think that it is a must-have if you are serious about this topic, but don't expect too much excitement.
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Most Recent Customer Reviews
5.0 out of 5 stars Excellent
I very much enjoyed reading this book. The math and science in it is fascinating, and even if you do not manage to understand all of it with all the details.
Published 2 months ago by KT
5.0 out of 5 stars Who couldn't love Mandelbrot
Mandelbrot... R.I.P. my friend... he was an angel sent from infinity to infinity and beyond... although he is gone from the known human world, Mandelbrot is a fractal of the... Read more
Published 3 months ago by Wquilliam
5.0 out of 5 stars Classic of fractal geometry
This book could be regarded as a starting point to investigate fractal geometry. Supporting material may be required. Read more
Published 6 months ago by Albert
1.0 out of 5 stars Quality issues with Kindle edition
Some formulas are not reproduced in pristine quality, in some whole symbols are even replaced with squares. Read more
Published 12 months ago by sonic7406
5.0 out of 5 stars Classic book
This is Mandelbrot's original work which introduced fractal geometry to the world. An essential read for those interested in the topic
Published 12 months ago by James M. Todd
5.0 out of 5 stars A Great Book.
I entered fractals for the first time in the early 90s after a had read about them in a fantastic book called Excursions in Modern Mathematics. Read more
Published 12 months ago by TheNigerian
4.0 out of 5 stars Approachable
I was afraid this would be over my head mathematically. But really it isn't. Anyone with college level mathematics can gain some understanding here.
Published 13 months ago by kfractal
5.0 out of 5 stars The classic opus of a new mathamtics
This is Mandelbrot's standard work on interpreting nature in a way that other branches of mathematics could not achieve. Read more
Published 15 months ago by Michael Kolmet
5.0 out of 5 stars A fractal is by definition
A set for which the Hausdorff Besicovitch dimension strictly exceeds the topological dimension.

The definition of a fractal pretty much sets the tone for the book. Read more
Published 16 months ago by bernie
5.0 out of 5 stars The book that popularized fractal geometry.
For the general public, this book helped set in motion the concepts of, and the potential to understand natures' geometry. Read more
Published 17 months ago by Kenneth R. Bolser
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