Rényi Entropy & Multifractal Spectrum

A multifractal measure has singularities of varying strength α. The spectrum f(α) gives the fractal dimension of the set of points with Hölder exponent α. The generalized dimensions D_q = lim τ(q)/(q−1) are related by a Legendre transform to the (α, f(α)) singularity spectrum.

Controls

Multiplier p₁: 0.70 Cascade levels: 8 q range max: 5

Binomial cascade: interval split with weights (p, 1-p). As p→0.5 measure becomes uniform, D_q=1 for all q. Asymmetric p creates multifractal with f(α) parabola-like spectrum.