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The Fractal Geometry of Nature
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63 of 69 people found the following review helpful
on September 7, 2005
Format: 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.
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148 of 170 people found the following review helpful
on August 26, 2002
Format: 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.
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94 of 120 people found the following review helpful
Format: 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.
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22 of 27 people found the following review helpful
on July 31, 1998
Format: Hardcover
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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20 of 25 people found the following review helpful
on August 26, 2002
Format: Hardcover
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
on June 14, 1998
Format: Hardcover
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
on October 14, 2009
Format: Hardcover
This book is the latest version of a book the famous Benoit Mandelbrot wrote back in the mid-1970s, in which he coined the term "fractal". The subsequent version was released around 1980 and had, among other pictures, a black blotchy image on a white background which he called "the µ-map". Then some joker started calling it "The Mandelbrot Set" and he had to change the book again.

It is true that this is not the best-written book on fractal geometry. However, for a time it was the ONLY book on fractal geometry, and as such has incredible historic value. Imagine in ancient Greece where people had to borrow one of Euclid's latest scrolls to read about things found in no other work.

Personally, this book has taught me only a few things. I had already learned about fractals from articles in 1980s issues of Scientific American, and computer programs in Compute! magazine.

Many black-and-white images suffuse this tome, though there are some color plates which are by no means as complex as today's fractallographies, but will serve as an introduction to the genre.

The only Mandelbrot Set image is the blotchy one mentioned earlier. That's because Dr. Mandelbrot, though he discovered the set, wasn't the first to color the complement, and it was Heinz-Otto Peitgen's 1984 book "The Beauty of Fractals" that has the first color Mandelbrot pictures.

I wholeheartedly recommend this book for a glimpse into history, and the uninitiated may learn something as well; though I wouldn't demand that much of it.
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2 of 2 people found the following review helpful
on February 17, 2010
Format: HardcoverVerified Purchase
This is a great book for someone looking to discover what all the hullabaloo is about fractals. It provides a wonderful insight into the mind of one of the great mathematical geniuses of our time, Benoit Mandelbrot. I think some people will find his writing style a bit too stodgy, almost arithmetical, but I find it interesting. I especially appreciate how marks off when he's going to be tangential with special brackets. Mandelbrot doesn't delve into too many rigorous mathematical proofs of the various topics he discusses. He broaches each subject in such a way that should be accessible to people from a wide array of sciences and disciplines. I don't recommend this book if you're trying to figure out how to create simple fractal programs. But I enthusiastically recommend it if you want to learn more about fractals, discover a new way to think about and understand nature, or are simply looking for a good bit of erudition.
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5 of 6 people found the following review helpful
on July 11, 2013
Format: Kindle EditionVerified Purchase
Some formulas are not reproduced in pristine quality, in some whole symbols are even replaced with squares.
The b/w graphics are reproduced far worse that technically possible today.
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7 of 10 people found the following review helpful
on June 4, 2008
Format: Hardcover
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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