Complex mapping with the interpolated Julia set and Mandelbrot set

Julia set and Mandelbrot set are very famous fractals (self-similar) with the iteration of a function of a complex variable f. These two sets provide a most striking illustration of how an apparently simple process can lead to highly intricate set. There are numbers of preceding studies about properties of the two sets and how to implement them in computer graphics. Different to the existing results we introduce color interpolation according to the diverging speed into the flat images of Julia set and Mandelbrot set for making shading-reflecting like effect and apply the proposed method into the stereographic projection of complex space to obtain a kind of uneven and shaded surfaces on Riemann sphere without any curved surface modeling and texture mapping.