ABSTRACT
Fractal theory is one of the important branches of nonlinear science. It studies the scale-invariant object at the structure level. It represents the behavioral characteristics of the nonlinear system by the self-affine characteristic of the study object. Fractal dimension is one of the important parameters that are used to characterize the singularity of a chaotic attractor quantitatively. The fractal dimensions of the profile curve are calculated by applying the general fractal dimension. Taking the general fractal dimension spectrum and singular spectrum as the characteristic parameters, the fractal dimension characteristic value of different shearing mark surfaces are found out. The fractal theory provides a theoretical basis for the description of the nonlinear behavior system. It is used to quantitatively characterize the singularity of chaotic attractor. The general fractal is used to describe the nonuniform random probability distribution of the fractal geometry on different layers.
