Fractal processes

Those who investigate the order that lies behind seemingly turbulent natural systems (clouds, water flows, air turbulence, epidemics, etc.) have come to contrast what they call fractal systems with linear systems. The key difference of relevance to us is the flexibility and sturdiness of fractal processes, which can survive perturbations and function over a wide range of frequencies—a quality com-... 

The salient property of mathematical random fractals processes is the existence of long-time correlations, here measured by the correlation index r, which can be related to the fractal dimension by [21]... 

In many if not most formation processes diffusion is rate- and shapedetermining, in which case the reaction path of the process rather than the driving forces determines the result. Diffusion of reactants may introduce fractality and fractal processes on fractal surfaces (see below). If diffusion is rate-limiting when solids are formed the temporal fluctuations are frozen in spatial structures. The direction of transport of the atoms or energy during the formation of the solid introduces anisotropy in the solid products. 

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