Fractals

The space of compact subsets of a bounded subset of Euclidean space is a compact metric space under the Hausdorff metric. One can view certain self-similar fractals as fixed points of contractions on this metric space. Below are approximations of such a fractal of. Amazingly, one may begin with any compact subset of Euclidean space and iterate through this contraction to obtain the fractal. See the difference between lines and squares below!