Scaling group formulation of multifractals

Daniel E. Platt and Fereydoon Family
Phys. Rev. Lett. 58, 2786 – Published 29 June 1987
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Abstract

On the basis of the premise that scaling is defined by a set of scaling transformations which form a simple product group, a scaling group is constructed for simple fractal scaling and the scaling of multifractal sets. The singularity strengths and densities are shown to be corollary to the scaling-group formalism. Fractal dimension and other exponents are shown to be generators of infinitesimal transformations. Applications are made to self-affine fractals and the scaling log-normal distribution.

  • Received 10 March 1987

DOI:https://doi.org/10.1103/PhysRevLett.58.2786

©1987 American Physical Society

Authors & Affiliations

Daniel E. Platt and Fereydoon Family

  • Department of Physics, Emory University, Atlanta, Georgia 30322

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Issue

Vol. 58, Iss. 26 — 29 June 1987

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