Fractal Geometry
Geometry of Euclidean Sets II: Analytical, Random, and Hypertopological Aspects

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Fractal Geometry


Geometry of Euclidean Sets II: Analytical, Random, and Hypertopological Aspects

Author : Jean-Charles PINOLI

Publication date: June 10, 2026 | Lire en français

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5. Fractal Geometry

The twelfth general mathematical framework is that of fractal geometry, which deals with fractal sets—that is, fractional subsets of 2n 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.”

5.1 Definitions and Properties

Informally, a subset of 2n...

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