Rényi Entropy & Fractal Dimension

H_q = log(Σpᵢq)/(1−q) · D_q = lim[log C(q,ε)/log ε]/(q−1) · multifractal spectrum

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Rényi entropy: H_q = (1/(1−q)) log(Σᵢ pᵢ^q). Special cases: q→1 gives Shannon entropy, q=2 gives collision entropy, q=0 gives Hartley entropy (log of support size). The multifractal spectrum f(α) vs α describes how the Hölder exponents of a fractal measure are distributed. Generalized dimensions D_q connect: D_0 = Hausdorff dim, D_1 = information dim, D_2 = correlation dim. For a monofractal: all D_q are equal.