What does it mean to sample “random” points in a fractal? In practice you’re probably sampling in terms of numbers at some specific precision (e.g. the limit of your floating point type for the range in question). This is still going to be points in some particular discrete lattice. Depending on the way the fractal is constructed, this could bias your picture.

Again, I’m not sure that the color of an “area” is meaningful for a fractal. But yeah, I think fsloth has the right idea: if the purpose of the images is to be pretty, then do it in whichever way gets you results you prefer.