Researches on Some Internal Structures of the General Mandelbrot Sets for Negative Real Index Number

In order to reveal some internal structures of the Mandelbrot set，Pickover and Hooper have put forward “epsilon cross” and “star trails” methods respectively．These two methods were extended，and a series of internal structure images of the general Mandelbrot sets for negative real index number were given out．The researches showed the following results：（1） The internal structure images of the general Mandelbrot sets for negative real index number have the fractal feature．（2） The internal structure images for negative integer index number are symmetry；while for negative decimal index number are asymmetry and their different evolution results came from the different choice of principal range of phase angle．