Abstract: We extend the Pickover and Carlson static trap technique,put forward circularity trap, dynamic trap technique and escape rendering method. At the same time, based on the virtual 3D quasi Mandelbrot set of F(z)=z⁴+(c-1)z²-c, we construct and study the quasi Mandelbrot-Julia set (M-J set) of F(z)=z^α+(c-1)z^β-c(α,β∈R, α>β≥2) by respective method (static, dynamic, trap and escape). The study demonstrates the following points: (1)No matter which positive integer α and β take you may always find the standard Mandelbrot structure formed by “ bad ” points in the 3D M-set. (2)In M-J set, there is various 3D self-similarity color cell that corresponds to the shape of trap unit. (3)When α and β are positive decimal, M-J set evolutions depend on the choice of the principal range of the phase angle.