Fractal Geometry
Geometry of Euclidean Sets: Analytical, Stochastic and Hypertopological Aspects

The twelfth general mathematical framework is that of fractal geometry, which deals with fractal sets—that is, fractional subsets of ${ℝ}_2^n$ that have a spatial structure following a deterministic or probabilistic rule involving internal self-similarity. A fractal set is “infinitely fragmented,” with details that are observable at any arbitrarily chosen scale. By zooming in on a part of such a subset, it is possible to reproduce the entire subset, which is then said to be “self-similar.”