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Singularity spectrum

Mathematical function

Wikipedia contributorsAdapted for Fathomly · View authors
1 min read
Source updated May 8, 2023

The singularity spectrum is a function used in multifractal analysis to describe the fractal dimension of a subset of points of a function belonging to a group of points that have the same Hölder exponent. Intuitively, the singularity spectrum gives a value for how "fractal" a set of points are in a function.

More formally, the singularity spectrum D(\alpha ) of a function, f(x), is defined as:

D(\alpha )=D_{F}\{x,\alpha (x)=\alpha \}

Where \alpha (x) is the function describing the Hölder exponent, \alpha (x) of f(x) at the point x. D_{F}\{\cdot \} is the Hausdorff dimension of a point set.

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This article is adapted from the Wikipedia article “Singularity spectrum”, written by its contributors and licensed under CC BY-SA 4.0. Fathomly has changed the layout, removed citation markers, navigation and maintenance notices, and adjusted punctuation. This adapted version is shared under the same license. For references, see the original article.

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