Multifractal Spectrum

A fractal is multifractal when its local scaling exponent varies across space — different regions have different Hölder exponents α, described by the singularity spectrum f(α).

f(α) is the Hausdorff dimension of the set of points with Hölder exponent α. For a monofractal, f(α) is a delta function. For a multifractal, it is a concave arc.
Measure distribution (depth d)
Singularity spectrum f(α)
τ(q) — mass exponent function
Generalized dimensions D(q)
Computing...