The Mandelbrot set Paradox a Potential Infinity
We have this paradox because the Mandelbrot Set is covered by a finite area, but has an infinite outer boundary. In fact, there are no two distinct points on the boundary of the Mandelbrot Set that can be reached from one another by moving a finite distance along that boundary.
This paradox can be explained by explaining a potential infinity of possibilities formed from a dynamic universal geometry that human mathematics itself is based upon. In this theory fractals are formed by the repetition of the quantum wave particle function or probability function of quantum mechanics continuously collapsing and reforming. A kind of geometrical and therefore mathematical repetition!
We have infinite complexity upon the boundary of a fractal like the Julia Sets. No matter how much we magnify a fractal we will still see new patterns new images emerging. In this theory this is because we have an interactive process the fractals are only relative to actions of the mathematician. We have a process of continuous creation or change creating an infinity of possibilities at every degree and angle of creation that we can interact with turning the possible into the actual!