Pseudo-3D Generalized Mandelbrot-Julia Sets

This paper extends Peitgen,Pickover and Carlson's technique and presents actangent method, 3-D stalks method and bubble method.Based on these three methods,a series of pseudo-3D generalized Mandelbrot-Julia sets (M-J sets) are constructed.Using the experimental mathematics method combining the theory of analytic function of complex variable with computer drawing,the paper studies the structure topological inflexibility and the fission of evolution law for pseudo-3D generalized M-J sets.The results show that the pseudo-3D generalized M-J set has fractal character,fission and collapse occur in the pseudo-3D generalized M-J sets for decimal index number,and their fission and evolutions depend on the choice of the principal range of the phase angle.