Comportamento fractal de tracos de fraturas na borda sul do macico granitico de itu, estado de Sao Paulo

Fractal geometry is relevant to understand and explain many natural complex geometries. Using the fractal set concept (fig. 1) many authors have shown that shorelines, landscapes and fractures follow a fractal behaviour. These authors have developed many methods, including the Cantor's Dust Method (CDM) (VELDE et al., 1992), a linear method of analysis adapted for the determination of two-dimensional phenomena. The Itu Granitic Complex (IGC) is a wide granitic body that that crops out at northwest of Cabreuva City, Sao Paulo State (fig. 2) and was affected in its south border by dextral Itu-Jundiuvira Shear Zone (IJSZ) that produced fractures and alignment of feldspars crystals. The different types of fractures (compression, distension and shear) was discriminated from the relationship between them and medium stress ellipsoid of IJSZ (fig. 3). A modified version of CDM was used to study a possible fractal behaviour of the fracture traces in the south border of IGC. The main modification was the use only one direction of analysis (NE/SW). Four parallel profiles were traced with lengths between 9.75km and 12.75km, each one them was divided into six classes of segments (x) with 375m, 500m, 750m, 1.000m, 1.250m and 1.500m. The parameter (N) is provided by he rate between profile length and choiced segment. For each x the number of intervals is counted with at least one event (fracture intersection) which supplied the parameter(n). The n/N rate provide the parameter (p) that represents the relationship between frequency of events and x. And finally the parameters p and x were plotted in a logarithmic graphics (fig. 4) that provide a line with such a declivity (1) which is related to effective dimension (De). In theory, granitics bodies are isotropics and they would have a same fractal dimension in all segments, but the logarithmic graphics (fig. 4) show that fracture traces of IGC has a fractal behaviour in a restrict interval. This fact probably occurs from the passage of a ductil-brittle deformation condition to a more brittle deformation condition of IGC.