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.
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.
Customer Reviews:
Avg. Customer Rating: 4.0 / 5.0
It's OK but....:
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... more info
A seminal work:
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... more info
Nice coffee table book? Not much else.:
The BOOK by the MAN who coined the name fractal and brought them
to the general public. (Actually an enhanced version of an
earlier book with a slightly different title, same publisher.) This book has historical value I suppose. But there are now
prettier picture books if you want those or you can easily create
your own. And if you are interested in the maths then you should
definitely look elsewhere (Devaney perhaps?). I think there is a
nice collection of papers by... more info
Essential classic book for everyone's library:
Mandelbrot presents unique and infinitely deep look at nature. The emerging theory of interaction shows that his notion of fractal turned to be more fruitful than anyone could guess. Savov's theory of interaction rigorously proves that nature is one self-reproducing and therefore self-similar fractal like interaction. Its oscillating sources remain always finite and synchronize to eject smaller similar ones.
