:Nice fractal indeed, but just thought I'd add that higher and lower powers produce aesthetically good results too (perhaps increasingly less so as one approaches power two). Power eight is only very approximately the 'sweet spot' perhaps (orders seven and nine are almost identical), so there's nothing particularly special about it. See here for examples: http://images.math.cnrs.fr/Mandelbulb.html (Mandelbulb article by Jos Leys)