The Fractal Geometry of Nature
by Benoit B. Mandelbrot
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Book Summary Information
Author: Benoit B. MandelbrotBrand: Baker and Taylor
Edition: Hardcover
Audio: English (Unknown); English (Original Language); English (Published)
Published: 1982
ISBN: 0716711869
Number of pages: 460
Publisher: W. H. Freeman
Book Reviews of The Fractal Geometry of Nature
Book Review: A seminal work
Summary: 5 Stars
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.
Summary of The Fractal Geometry of Nature
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.
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.
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.
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