Self similarity
An object exhibit exact self-similarity across all spatial or temporal scales, such that successive magnifications reveal an identical structure. A self-similar object is composed of N copies of itself (with possible translations and rotations), each of which is scaled down by a scale ratio in all directions of the dimensional available space.
Consider a set S of points at positions in Euclidean space of dimension Under a similarity transform with a scale ratio , the set becomes with points at positions . A bounded set S is self-similar when S is the union of N nonoverlapping subsets, each of which is identical (under translations and rotations) to .