Random Brown function method

It is difficult to describe the complex forms and status of natural fracture surfaces with ordinary functions. The fractal theory can be used to describe extremely irregular geometric patterns, and many researches have indicated that it is reasonable to simulate rough fracture surfaces with fractals theory. At present, the self-affine fractal model is regarded as the best fractal model to simulate fracture surface. In the following, random Brown function method (Weierstrass- Mandelbrot function) is used to simulate a fractal fracture surface. 

According to a certain D, the curved surface height z of an arbitary point can be obtained if A is given (commonly 1.0 fracture surface with fractal characteristics can be obtained by overall distribution (x,y). Fig. 1 shows a fracture surface generated by simulation using random Brown function method, the fractal dimensions is 2.3 and the parameter A = 1.25. 

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