The Fractal Geometry of NatureClouds 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 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. 
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I'm a nonmathematician  art and logic background  but I *love* how Mr. Mandelbrot is so explicit in his narrative. Except for some odd Greek alphabet characters and a few strange math symbols (which I'll look up), Mandelbrot makes this an exciting narrative voyage into math, through Fractals, but as he examines the common relationships of fields of math, he makes this a broader, and very enjoyable journey.
I only had high school physics, and never entered Calculus, yet the base in geometric fundamental the author uses make this material more easily comprehensible than I think the publishers realize. It really reads like a travel log narration, and I'd love to see a more fully illustrated film of the journey. (and I aspire to contribute to such an illustrated and animated edition!)
G. Rice 12014