The Dimensions Of Fractals With Overlaps

This paper mainly study the dimension of several kinds fractal sets with overlaps. The related parameter of a class Cantor sets with overlaps is classified according to the difference of overlaps structure.First, we briefly address the significance of this research as well as current domestic and foreign regarding this topic research present situation and the trend of development. Then, we briefly review the foundation of fractal geometry, introduce some basic concepts and related proposition about fractals, dimension and some classes sets. Next, in Chapter 3, we study a class of Cantor sets with overlaps. The related parameter of them is classified according to the difference of overlaps structure. In Chapter 4, we construct a class of self-conformal sets based on related self-similar sets, and obtain the formula for their Box dimensions. Finally, in concluding remarks, we propose the ideas of work in the next step.