A multiplicative Cantor measure (branching with probabilities p and 1-p) has a multifractal spectrum. The Rényi entropy H_q = (1/(1-q))log∑pᵢq characterizes scaling: D_q = H_q/log(N) is the generalized dimension. The singularity spectrum f(α) is the Legendre transform of (q-1)D_q, giving the Hausdorff dimension of points with local scaling exponent α.