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
.
