Abstract: Fractal images from mapping f 1（z）=z 2+c in the complex C plane and complex Z plane are attracting attention of many researchers. Moreover, scholars are investigating the fractals constructed by mapping f 2（z）=z α+c （α∈R 1） The M fractal images generated by mapping f 3（z）=z w+c（w=α+iβ;α,β∈R 1） are explored. And then the basic mathematic features of f 3 are analyzed, the image characteristics of M sets of f 3 and the arrangement orders of attracting period buds adsorbed on the boundary of the main M sets are studied, and several conjectures about general M sets of complex mapping f 3 are suggested.