Abstract
We study the L\'evy 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 L\'evy 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.
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