The Dimension Of The Complete Family Of Fractals Derived By The Function System Matrix

This paper mainly contains there chapters. In the first chapter, we introduce the basic knowledge of fractal geometry, including the definition of fractal, and all kinds of fractal di-mensions. We also introduce the different methods in calculating the upper and lower bounds of fractal dimension——natural covering and quality distribution theory. In the second chap-ter, we introduce fractal space, contraction mapping based on fractal space, and an important method in forming fractals——iterate function system. Moreover, we introduce a category of fractal——self-similar set, and its extension by Marion——A-complete set, and their formulas in calculating dimensions. The third chapter is the main part of this paper. We perfect the basic theory of A-complete set further. We define the function system matrix, which is the extension of the function system, and its calculation rules. Using strictly contracted function system ma-trix, we construct the complete family of fractals, and determine the Hausdorff dimension and Box dimension of similar contracted function system matrix with the open set condition satisty.