The Fractal Geometry of Nature
Clouds 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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approximation attractors Besicovitch bounded branches Brown function Brown line-to-line Brown trail Brownian motion called Cantor dust Chapter circles coastline construction contact clusters converge cosmographic principle curd curdling D=log defined definition denote density described discs distribution Essay Euclidean example exponent fact finite Fournier fractal curves fractal dimension fractional Brown galaxies galaxy clusters gaps gasket Gaussian Hausdorff hence hyperbolic independent infinite integer interval intuitive involves islands Koch curve KOCH ISLAND lacunarity lattice Leibniz length limit linear Mandelbrot mass mathematical mathematicians measure mension noise observed Peano curve percolation physics plane Plate Poincare properties radius random variable ratio result river scaling self-affine self-avoiding self-contact self-similar self-squared sequence shape Sierpinski Sierpinski carpet Sierpinski gasket space square squig stage standard stationary statistical surface teragons term theory tion topological dimension tree trema triangle turbulence variant Weierstrass Weierstrass function yields zeroset Zipf law