Mandelbrot fractal geometry

B.M. Mandelbrot, Fractal Geometry of Nature. Freeman, San Francisco... 

B. B. Mandelbrot, The Fractal Geometry of Nature, Freeman, New York, 1982 Fractals Form, Chance, arul Dimension, Freeman, New York, 1977. 

Mandelbrot, BB, The Fractal Geometry of Nature WH Freeman San Francisco, 1983. 

Mandelbrot, B.B. (1982) The fractal geometry of nature. Freemarm, San Francisco Mann, H. Tazaki, K. Fyfe,W.S. Kerrich, R. (1992) Microbial accumulation of iron and manganese in different aquatic environments An electron optical study. In Skinner, H.C.W. Fitzpatrick, R.W. (eds.) Biomineralization processes of iron and manganese. Catena Verlag, Cremlingen-Destedt, Catena Suppl. 21 115-132... 

B.B. Mandelbrot The Fractal Geometry of Nature. W. H. Freeman and Company, NewYork (1982)... 

For a limited discussion of fractal geometry, some simple descriptive definitions should suffice. Self-similarity is a characteristic of basic fractal objects. As described by Mandelbrot 58 When each piece of a shape is geometrically similar to the whole, both the shape and the cascade that generate it are called self-similar. Another term that is synonymous with self-similarity is scale-invariance, which also describes shapes that remain constant regardless of the scale of observation. Thus, the self-similar or scale-invariant macromolecular assembly possesses the same topology, or pattern of atomic connectivity, 62 in small as well as large segments. Self-similar objects are thus said to be invariant under dilation. 

Simulations may be grouped according to the general uses for which they were developed. As such, the first to be developed, and the simplest simulation techniques, are those investigating the structure of aggregates. These models first appeared in 1963 [18], and after Mandelbrot s seminal work on fractal geometry [45], development of these types of simulations increased dramatically, spurred by the well-known Witten-Sander model [46]. 

Mandelbrot BB (1982) The fractal geometry of nature. WH Freeman, New York... 

Refs. [i] Mandelbrot BB (1982) The fractal geometry of nature. Freeman, San Francisco [ii] Pajkossy T (1995) Heterogen Chem Rev 2 143... 

Since Mandelbrot s original description (1977,1983), fractal geometry has found relevance in a number of scientific disciplines including aerosol technology and science [e.g., see Lovejoy (1982), Meakin (1983), Kaye (1984), Sheaffer (1987), Reist et al. (1989)]. Many applications are covered in some detail by Kaye (1989), so only a brief description of fractals is given here. 

Mandelbrot, Benoit. The Fractal Geometry of Nature. San Francisco Freeman, 1977. Mandell, Arnold J., and Charles E. Spooner. Psychochemical Research Studies in Man. Science 162(1968) I442ff. 

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