About: 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.