fractalsselfsimilarity
Fractal self-similarity is a central idea in fractal geometry describing patterns that replicate themselves at different scales. An object is exactly self-similar when it can be decomposed into parts that are scaled copies of the whole. In mathematical constructions, this property is often produced by iterated function systems, a finite set of contraction mappings whose fixed point is a self-similar set. The level of scaling is captured by the fractal or similarity dimension, which tends to be non-integer and reflects how detail scales with magnification.
Exactly self-similar structures include classic examples generated by simple rules. The Cantor set consists of two
Not all self-similarity is exact. Many natural objects display statistical or finite self-similarity, meaning parts resemble
Dimensions and measurement techniques, such as box-counting and Hausdorff dimension, quantify self-similarity and complexity. Fractal self-similarity