Self-Similarity: mathematics
Self-similarity is a rigorous statistical property:
- there is a lot more to it than just the pretty ‘‘fractal-like’’ pictures
Precisely:
- A process X is called (exactly second-order) self-similar with self-similarity parameter H = 1 – ß/2 if:
- for all m = 1, 2, …, Var(X(m)) = ?² m-?
- r(m)(k) = r(k), k = 0
- X(n) is wide-sense stationary.