{{Short description|Mathematical function}} {{no footnotes|date=January 2012}} {{one source|date=January 2012}} 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 <math>D(\alpha)</math> of a function, <math>f(x)</math>, is defined as:
:<math>D(\alpha) = D_F\{x, \alpha(x) = \alpha\}</math>
Where <math>\alpha(x)</math> is the function describing the Hölder exponent, <math>\alpha(x)</math> of <math>f(x)</math> at the point <math>x</math>. <math>D_F\{\cdot\}</math> is the Hausdorff dimension of a point set.
==See also== * Fractal * Fractional Brownian motion * Hausdorff dimension
==References== * {{citation |last=van den Berg |first=J. C. |year=2004 |title=Wavelets in Physics |publisher=Cambridge |isbn=978-0-521-53353-9}}.
Category:Fractals
{{fractal-stub}}