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)
f(x)
D(\alpha)=DF\{x,\alpha(x)=\alpha\}
Where
\alpha(x)
\alpha(x)
f(x)
x
DF\{ ⋅ \}