Lévy dusts, Mittag-Leffler statistics, mass fractal lacunarity, and perceived dimension

Raphael Blumenfeld and Benoit B. Mandelbrot
Phys. Rev. E 56, 112 – Published 1 July 1997
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Abstract

We study the Lévy dusts on the line on two accounts: the fluctuations around the average power law that characterizes the mass-radius relation for self-similar fractals, and the statistics of the intervals between strides along the logarithmic axis (their tail distribution is related to the dust’s fractal dimension). The Lévy dusts are suggested as a yardstick of neutral lacunarity, against which non-neutral lacunarity can be measured objectively. A notion of perceived dimension is introduced. We conclude with an application of the Mittag-Leffler statistics to a nonlinear electrical network.

  • Received 12 June 1996

DOI:https://doi.org/10.1103/PhysRevE.56.112

©1997 American Physical Society

Authors & Affiliations

Raphael Blumenfeld1 and Benoit B. Mandelbrot2

  • 1Theoretical Division and CNLS, Mail Stop B262, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
  • 2Mathematics Department, Yale University, New Haven, Connecticut 06520-8283

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Vol. 56, Iss. 1 — July 1997

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