Definition¶

Separation hypothesis on an iterated function system: there exists a nonempty bounded open set U with the union of the maps' images of U contained in U and those images pairwise disjoint. When it holds for similarities, the similarity dimension log N / log(1/r) equals the Hausdorff dimension (Moran 1946; Hutchinson 1981). It is the precise condition that licenses the closed-form dimension formulas for the classical self-similar fractals.

Aliases¶

osc, moran condition, moran open set condition

Related concepts¶

• Iterated Function System
• Hausdorff Dimension
• Self-Similarity
• Fractal

Citations¶

[1] Fractal Notebooks glossary (Chapter 4) — docs/foundations/glossary.md

[2] fractal_rag concept seed (seed.yaml) — fractal_rag/src/fractal_rag/concepts/seed.yaml