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| The Fractal Geometry of Nature | 
 enlarge | Author: Benoit B. Mandelbrot
Publisher: W. H. Freeman
Category: Book
Buy New: $30.55
New (7) Used (15) from $29.49
Avg. Customer Rating:  13 reviews
Media: Hardcover
Edition: Updated
Number Of Items: 1
Pages: 468
Shipping Weight (lbs): 2.2
Dimensions (in): 9.3 x 8.2 x 1.1
ISBN: 0716711869
Dewey Decimal Number: 516.15
EAN: 9780716711865
Publication Date: 1983
Availability: Usually ships in 1-2 business days
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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.
Product Description
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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| Customer Reviews: Read 8 more reviews...
 It's OK but.... June 4, 2008
1 out of 1 found this review helpful
Benoit 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.
 A seminal work September 7, 2005
19 out of 21 found this review helpful
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.
Nice coffee table book? Not much else. March 29, 2005
15 out of 30 found this review helpful
The BOOK by the MAN who coined the name fractal and brought them
to the general public. (Actually an enhanced version of an
earlier book with a slightly different title, same publisher.)
This book has historical value I suppose. But there are now
prettier picture books if you want those or you can easily create
your own. And if you are interested in the maths then you should
definitely look elsewhere (Devaney perhaps?). I think there is a
nice collection of papers by early 20th century pioneers
available too.
Now I wonder is Mandelbrot really the mathematician he is reputed
to be in popular imagination? It seems to me there is little here
that was not thought of before in the early 20th century by
Hausdorff, Poincare, Julia, Lebesgue, Bachelier and others. And
the whole fractal idea seems to have a life of its own in popular
imagination that does not to be justified according to the (much
smaller) importance in physics and other sciences.
Essential classic book for everyone's library November 9, 2004
4 out of 13 found this review helpful
Mandelbrot presents unique and infinitely deep look at nature. The emerging theory of interaction shows that his notion of fractal turned to be more fruitful than anyone could guess. Savov's theory of interaction rigorously proves that nature is one self-reproducing and therefore self-similar fractal like interaction. Its oscillating sources remain always finite and synchronize to eject smaller similar ones.
A dated but still fascinating book August 26, 2002
13 out of 17 found this review helpful
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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