In orderlo stody the iatefior strcture of the Mandelbrot (M) set. Pickover and Hooper have ad-wwed the epsilon cross method and the star trails method. respectively. In order to reveal the exterior structure of the Mset. Philip has proposed the regional decomposition method and the angle-slicing decompoaition method. In this pa-per. these methods-are extended. and the equipolenfial line method and the color adjustment method are proposod to study the exterior struture of the M set. A series of the non-boundary region structure images of the generalized M sets is generated by using the above-mentioned methode. The results show that the non-boundary regions of the generalized M sets for intexer index number have the fraetal feature; while those for decimal index number have diseontlnuity and col-lapse, and their erolutions depend on the choice of the principal range of the phase angle.