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