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The Fractal Geometry of Nature
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The Fractal Geometry of Nature

4.12  ·  Rating Details  ·  766 Ratings  ·  32 Reviews
Clouds are not spheres, mountains are not cones, and lightning 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
Hardcover, 480 pages
Published August 15th 1982 by Times Books (first published 1977)
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Jan 01, 2009 Jack rated it it was amazing
More a reference than a read, Mandelbrot was the first mathematician and naturalist to embrace fractals, second citizen equations that turned out to be elegant expressions of much of the patterns, sequences, arrangements we can see in molecules, simple life forms, organ systems, complex life forms, environments, ecosystems.... Some of it is user friendly, some needs to be skimmed by those who don't care about the math, but Mandelbrot is supportive of both kinds of readers.
I have to admit that this book has been sitting on my shelves half-read and gathering dust. Mandelbrot's a fairly good speaker (from what I've seen of him on documentaries), but a trying and tedious writer.

If you're looking for pretty pictures of fractals, there are some. If you're looking for the formula for the Mandelbrot set, it's here. If you want to understand the theory behind fractals, this is not the best introduction.
John E. Branch Jr.
Dec 04, 2011 John E. Branch Jr. rated it really liked it
Shelves: mathematics, geometry
I believe this is where I first encountered such oddities of geometry and math, some of which were once thought to be monsters, as Cantor dust, Sierpinski triangles, Koch snowflakes, Peano curves, and the like. More important, it's where I first found explicated the idea of fractional dimensionality, from which I believe Mandelbrot derived the term "fractal." (The concept itself comes from a German mathematician named Hausdorff, but Mandelbrot generalized it). A solid understanding of the book i ...more
Apr 02, 2012 JenniferRuth rated it really liked it
Shelves: science, non-fiction
Mandlebrot does a good job of writing for both mathematicians and those who simply have a passing interest. He makes it easy to skip over the in-depth mathematical sections whilst still providing solid explanations of the concepts being discussed. I will admit that some of it was way over my head and there were sections that could be quite dry. However, it was thrilling to gain a greater understanding of fractals like the Menger sponge, Koch snowflakes and Cantor Dust along with how they can be ...more
Ami Iida
Nov 21, 2015 Ami Iida rated it it was amazing
Recommends it for: chaos and fractal theory
the essential reading for chaos and fractal
Elio Nakouzi
Jan 13, 2015 Elio Nakouzi rated it really liked it
A modern classic. The style of writing lurks between the literary and the scientific, very much like the topic itself.
A. Merlocks
Dec 17, 2014 A. Merlocks rated it it was amazing
Shelves: useful
I have to admit it: I simply love this book. However, this book is quite out of the ordinary. If you are a linear reader, this book is definitely not for you. The book is about fractals, but the book is fractal. Its structure, the way topics are introduced and developed, everything in it resembles a fractal. But the book is useful, very useful: it has thousands of ideas. Most of them still unexplored. It asks many, many questions and let you find the answers. If you are a researcher, you will fi ...more
Jul 09, 2014 Kaethe rated it really liked it
Amazing images and a very cool concept, well explained. Fractal make sense out of nature.
Alex Lee
Sep 17, 2015 Alex Lee rated it really liked it
Shelves: 2015, mathematics
This beautiful book is about Mandelbrot's love of science, mathematics and all forms of knowing. He is humorous at times, dense, and waxing on about fractals and changes that are self similar. It is through the figure of a difference that something is known. Fractals are unique in that they are that difference regardless of scale, that is, as Mandelbrot said of Leibniz, that Leibniz first recognized a straight line as being a curve whose arbitrary measure was universally applicable by itself by ...more
Dr Marco Bitetto
Aug 31, 2015 Dr Marco Bitetto rated it it was amazing
Recommends it for: College Engineering and Science majors...
Recommended to Dr Marco by: A Friend
This is a well written book...
But, it is not for the mathematically intimidated...
Nevertheless, with some basic understanding of at
least a third year level of scientific and
engineering based mathematics, this book will prove
to be quite readable and understandable.
C. Marcos
Aug 15, 2014 C. Marcos rated it it was amazing
What a book! Unlike anything you may have read before. The book itself has fractal structure. Truly a master piece. It covers almost everything from a strictly geometrical point of view. Linear readers beware, you may get really annoyed by this book.
John Schneider
Jul 23, 2015 John Schneider rated it it was amazing
"The Fractal Geometry of Nature" is a book to be skimmed by many but read closely by few because its excellences are so uneven. On the one hand Mandelbrot creates truly wonderful images that allow most people to see how nature can be described by fractals. On the other hand he freely engages in formulas that any non-mathematician reads but fails to grasp. In all honesty I probably understood all of his images, 4/5 of his prose, and perhaps a 1/4 of his formulae. Still, I am far richer intellectu ...more
Alan Bower
Nov 19, 2015 Alan Bower rated it it was ok
Very technical and repetitive. I read about half of it.
Paul Hardisty
Aug 17, 2015 Paul Hardisty rated it it was amazing
Erudite, impenetrable but very cool.
Thomas A Wiebe
I read the first few chapters of this book, and the concept of the fractal was fascinating; it describes a partial dimensionality. The early chapter on the coastline of Britain was very stimulating - the idea that the perimeter of an object can have a significantly different length depending on the scale it is measured was surprising. The remainder of the book delved into various mathematical structures that can describe fractal states, something that put me rapidly to sleep.
Ron Moreland
May 23, 2008 Ron Moreland rated it really liked it
Recommends it for: Anyone
This book may just provide a hunger in a student to learn more about what fractals are in math. It is something I have studied for quite sometime and I hope to incorporate in my future math classes as a teacher. The images and mathematical properties of fractals are fascinating! Even if someone doesn't understand the mathematics behind fractals they can use technology to create some interesting fractals.
Chuck Weiss
Dec 27, 2011 Chuck Weiss rated it it was amazing
The complexity of nature as explained by the genius behind the study of fractals. I can never look at a fern leaf the same way again. The illustrations alone in this gem of a book are worth its purchase price. Gaussian curves, the Julia Set, all explained - albeit a little technical for me in many chapters.
Jul 12, 2008 Krystal rated it liked it
After seeing the author lecture I bought this book, which is completely over my head but illustrated with some of the most beautiful fractal representations I've seen. For anyone interested in fractal geometry, specifically in nature, its a great place to get inspired.
Oct 25, 2008 Kami rated it did not like it
Shelves: skimmed
I didn't really read this. More like glance through. I thought it would be a book of pretty pictures of patterns in nature. Its not. It is like a mathmeticians text book. Oops.
David Hunt
Dec 23, 2007 David Hunt rated it liked it
Recommends it for: math fans.
Technical and, in fact, not my favorite book on the topic. Nonetheless, sometimes it is good to get your story straight from the horse's mouth.
Mar 04, 2016 Jim marked it as to-read-tier-2
Aug 12, 2013 Philski rated it it was amazing
breezed over most of the math in the last 20 chapters except for the chapters on turbulence and finance, my primary interests.
Jenson Stevens
Apr 09, 2016 Jenson Stevens rated it liked it
Tedious read. More information than I care to know about fractals. Good examples and illustrations.
Mar 22, 2015 Justin rated it it was amazing
Beautiful in its unfolding
Insightful in its message
An essay to be enjoyed!
Dec 29, 2010 Bruce rated it really liked it
Pretty pictures...ooooo! Oh yeah, and math that fits nature...aaaaah!
Carmen Mandel
Jan 14, 2010 Carmen Mandel rated it it was amazing
Shelves: fractals
"As with Fibonacci numbers, nature holds surprises as fractals"
Feb 07, 2014 Wylz rated it it was amazing
an immensely pertinent epistemological text..
Oct 09, 2007 Jimmy rated it it was amazing
Shelves: mathematics
A classic written by the Father of Fractals.
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Benoît B. Mandelbrot was a French mathematician, best known as the father of fractal geometry. He was Sterling Professor of Mathematical Sciences, Emeritus at Yale University; IBM Fellow Emeritus at the Thomas J. Watson Research Center; and Battelle Fellow at the Pacific Northwest National Laboratory. He was born in Poland, but his family moved to France when he was a child; he was a dual French a ...more
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“Why is geometry often described as ""cold" and ""dry?" One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline, or a tree. Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.” 0 likes
“Weierstrass, Cantor, or Peano! In physics, an analogous development threatened since about 1800, since Laplace’s Celestial Mechanics avoided all illustration. And it is exemplified by the statement by P. A. M. Dirac (in the preface of his 1930 Quantum Mechanics) that nature’s “fundamental laws do not govern the world as it appears in our mental picture in any very direct way, but instead they control a substratum of which we cannot form a mental picture without introducing irrelevancies.” The wide and uncritical acceptance of this view has become destructive. In particular, in the theory of fractals “to see is to believe.” 0 likes
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