Fractal logic

For an accessible introduction to the fractal logic of living processes, see James Gleick, Chaos Making a New Science (New York Penguin, 1988). 

Fractal Logic This was introduced into fine particles science by Kaye and coworkers (Kaye, op. cit., 1981), who show that the noneuchd-ean logic of Mandelbrot can be applied to describe the ruggedness of a particle profile. A combination of fractal dimension and geometric shape factors such as the aspect ratio can be used to describe a population of fine particles of various shapes, and these can be related to tne functional properties of the particle. 

Several forms of the modified Stake s law have been used in a series of studies concerning aggregates in the liquid phase (Li and Yuan, 2002). In these studies, the particle-liquid density difference has been further modified and adopted for the cases of impermeable bio-logical/microbial aggregates, permeable aggregates, and fractal aggregates. 

Fractal models for soil structure and rock fractures are becoming increasingly popular (e.g., Sahimi, 1993 Baveye et al., 1998). The primary appeal of these models is their ability to parsimoniously parameterize complex structures. Scale symmetry or scale invariance, in which an object is at least statistically the same after magnification, is a fundamental property of fractals and can also be observed in numerous natural phenomena. Thus, it is logical that some investigators have examined theoretical transport in known prefractals. 

Zhang, L. Xi, L. F. (2007). A Novel Fractal Image Coding Based on Quadtree Partition of the Adaptive Threshold Value. Theoretical Advances and Applications of Fuzzy Logic and Soft Computing, 504-512. 

Fig. 6 Fractal analysis of the porosity from cornea data (Fig. 5d with Q = 0) abscissa X = logic MR. (a) Fitting function y=kBa...

A.G. Flook. The use of dilation logic on the quantinet to achieve fractal dimension characterization of textured and structured profile. Powder Technol, 21 (2), 295-298,1978. 

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