Crack patterns in rocks - Anisotropy and fractal aspects

A Scale-Space Information Flux Approach to Natural Irregular Patterns: Methods and Applications

“…What distinguishes the scale space information flux from other modes of characterizing irregular features consists mainly of its interpretation in terms of its relation to the size of the informational backbone, and the way in which it is used. There are numerous methods for the evaluation of a fractal dimension, characterized by strengths and weaknesses regarding their capability of grasping properties of the analyzed features (Feder, 1988); however, their numerical equivalency -even if established, in theory, for mathematical patterns -is not always true in the case of real-world systems (Ioana et al, 1997;Takayasu, 1991); therefore, the statements made here about the information flux may not always correspond to other "equivalent" fractal dimensions. From a practical point of view, the information flux v provides a way to determine quickly and in a simple way the expected information storage and transfer effort implied by a change in scale.…”

“…In accordance to the format proposed in section 3.1, the scale space information flux is written as: g = (2, 0.85 ± 0.01, 256); the round parentheses show that neither the lower nor the upper limit of the scaling interval have been reached for these resolution values. Brownian walks have been studied in detail from the point of view of their mathematical properties (Malamud and Turcotte, 1999), and have been used for the testing and evaluation of time series analysis methods (Ioana et al, 1997). For this study, the data were generated as running sums over series of time series representing white noise; an example of one of the analyzed Brownian walks is provided in Figure 9.…”