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The Fractal Geometry of Nature (1983)
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Amazon.com Amazon.com Review (ISBN 0716711869, Hardcover)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.
(retrieved from Amazon Thu, 12 Mar 2015 18:11:35 -0400)
The complexity of natures shapes differs in kind, not merely degree, from that of shapes of ordinary geometry. To describe these shapes Mandelbrot conceived and developed a new geometry - the geometry of fractal shapes which this text discusses.
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