Singularity spectrum
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  of a function, , is defined as:

Where  is the function describing the Hölder exponent,  of  at the point .   is the Hausdorff dimension of a point set.

See also
 Fractal
 Fractional Brownian motion
 Hausdorff dimension

References
 .

Fractals