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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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"A rarity: a picture book of sophisticated contemporary research ideas in mathematics."--Douglas Hofstadter, author of Godel, Escher, Bach
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Most helpful customer reviews
3 of 3 people found the following review helpful
2.0 out of 5 stars
A review on the book -- not on Mandelbrot,
By Assela Pathirana (Japan) - See all my reviews
This review is from: The Fractal Geometry of Nature (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.
2 of 2 people found the following review helpful
3.0 out of 5 stars
Not as good as I expected,
This review is from: The Fractal Geometry of Nature (Hardcover)
After having studied fractals in school and reading numerous books on chaos and fractals on my own, I figured that Mandelbrot's book would be the pinnacle, surpassing everybody else's interpretations and getting the information "straight from the horse's mouth". I was wrong. Mandelbrot, while he may be a brilliant mathematician, has not quite mastered the English language. The topics that he speaks of in this book are basic, not exactly what you would expect from the leader in his field. He doesn't even go into real specifics, or not the specifics that I wanted to see going into this book. In fact, I didn't even bother finishing it. There was nothing new, no powerful insights that other books may have missed. Mandelbrot, it seems is much better at mathematics then at writing. My suggestion is to buy a different book on the subject.
3.0 out of 5 stars
beauty does not equate to depth or thoroughness,
By
This review is from: The Fractal Geometry of Nature (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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