The Boundary Dimension Of A Self-affine Set And The Group Of Isometries Of A Fractal Set

Fractal geometry is not only a discipline,but also an art.Although the dis-cipline was attached great importance in 1980s,but from it's development to the application is very fast.Fractal geometry not only rigorous theoretical knowledge,but also important practical value.It has an unpredictable role and value for the natural sciences and the social sciences in all areas.Therefore,this paper has written some of the relevant knowledge of fractal geometry,and research on fractal set.The introduction part of this paper describes the development process of fractal and the object of research.In the first chapter,some basic knowledge needed in this paper are introduced,such as Hausdorff measure,Hausdorff dimension,box dimension,self-similar dimension and self-affine dimension and so on.The second chapter computes the dimension of a class of self-affine and applies the result to calculate the dimension of a class of self-affine bounds.In the third chapter,we study the group of isometries on the fractal set,and it is concluded that the number of the group of isometries is finite when the fractal set is completely disconnected.The fourth chapter makes a summary of this thesis and puts forward some further questions that to be studied and solved.