Rényi Entropy & Multifractal Spectrum f(α)

H_q = log(Σ pᵢ^q)/(1−q) · τ(q) = (q−1)D_q · Legendre transform gives f(α) singularity spectrum

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Multifractal analysis quantifies how the local scaling exponent α = log(μ_i)/log(ε) varies across a measure. The singularity spectrum f(α) = dim_H{x : α(x)=α} is obtained via Legendre transform of τ(q). D_0 = Hausdorff dimension, D_1 = information dimension, D_2 = correlation dimension. Drag the q slider to highlight which part of the spectrum is probed at each moment order.