Animation with fractals from variations on the Mandelbrot set

The results of experimenting with a most interesting variation on the iteration formula which generates the Mandelbrot set are presented. Varying the power m of the generating function results in fractal surfaces exhibiting self-similarity and suggesting smooth evolution under animation. One such sequence led to a mathematical conjecture, which has since been mathematically proven (Hubbard et al. 1986), illustrating the interaction between computer graphics and fractal geometry. Finally, we offer an extension of adapting fractal graphics algorithms to massively parallel computers.