The Dimensions Of The Self-affine Sierpinski Capets In Space

This paper consists of four parts. First chapter introduces the fractal knowledge profiles, including the emergence of fractal, the establishment of fractal and development of the course of fractal and the definition of the fractal. The second chapter describes the fractal dimension and its calculation method, including fractal dimension, two kinds of fractal dimension——Hausdoff dimension and Box dimension, and calculating the fractal dimension of the upper and lower bounds of the method——quality distribution principle and natural covering method. The third chapter is one of the main content of this paper, discussing a class plane self-affine fractal sets——Mc Mullen set as well as to its existing the Hausdoff of dimension and Box di-mension formula, and carries on the some promotion,making Mc Mullen set of dimension results more richon the plane. The fourth chapter is the main content of this paper. This paper dis-cusses a kind of self-affine fractal set on three dimensional space——and development present situation of dimension problem of Mc Mullen set. Promotion of on the basis of two-dimensional, we extends and gives the general Hausdoff dimension and Box dimension calculation formula of Mc Mullen set on the three dimensional space.