Research on high-periodic attracting points in Mandelbrot set

The ordering of high-periodic attracting points and their periodic buds in Mandelbrot set have been analyzed. Using the method of computer mathematic experiments, the five-periodic attracting points are solved and the topology distribution images of five-periodic attracting points and six-period attracting points are gained. Furthermore, the reasons of the bottleneck solved high-periodic attracting points in Mandelbrot set are analyzed. In this paper, we study the distributing discipline of high-periodic attracting points and their characteristic, and we have focused on the ordering of attracting points and the periodic buds in the Mandelbrot set and created a recurrence formula between numbers of attracting points and numbers of periodic buds in Mandelbrot set. As a result, it provides a useful discussion on internal structure of Mandelbrot set.