The fractal geometry of nature - Mandelbrot, Benoit B. (New York : W.H. Freeman, 1983)
1. Introduction -- Theme -- The irregular and fragmented in nature -- Dimension, symmetry, divergence -- Variations and disclaimers -- 2. Three classic fractals, tamed -- How long is the coasts of Britain? -- Snowflakes and other Koch curves -- Harnessing the Peano Monster curves -- Fractal events and Cantor dusts -- 3. Galaxies and eddies -- Fractal view of galaxy clusters -- Geometry of turbulence; Intermittency -- Fractal singularities of differential equations -- 4. Scaling fractals -- Length-area-volume relations -- Islands, clusters and percolation; Diameter-number relations -- Ramification and fractal lattices -- 5. Nonscaling fractals -- Surfaces with positive volume, and flesh -- Trees; Scaling residues; nonuniform fractals -- Trees and the diameter exponent -- 6. Self-mapping fractals -- Self-inverse fractals, Apollonian nets and soap -- Cantor and fatou dusts; Self-squared dragons -- Fractal attractors and fractal (Chaotic) evolutions -- 7. Randomness -- Chance as a tool in model making -- Conditional stationarity and cosmographic principles -- 8. Stratified random fractals -- Random curds: contact clusters and fractal percolation -- Random chains and squigs -- Brownian motion and brown fractals -- Random midpoint displacement curves -- 9. Fractional brown fractals -- River discharges; scaling nets and noises -- Relief and coastlines -- The areas of Islands, lakes and cups -- Isothermal surfaces of homogeneous turbulence -- 10. Random tremas; Texture -- Interval tremas; Linear levy dusts -- Subordination; Spatial levy dusts; ordered galaxies -- Disc and sphere tremas: moon craters and galaxies -- Texture: gaps and lacunarity; Cirri and succolarity -- General tremas, and the control of texture -- 11. Miscellany -- Logic of fractals in statistical lattice physics -- Price change and scaling in economics -- Scaling and power laws without geometry -- Mathematical backup and addenda -- 12. Of men and ideas -- Biographical sketches -- Historical sketches -- The path to fractals.
Includes bibliographical references (p. [425]-443 and indexes.
Keywords: Geometry; Mathematical models; Stochastic processes; Fractals; Probability; Mathematics; Fractals; Geometry; Mathematical models; Stochastic processes