R.J. Gambino, N.R. Stemple, et al.
Journal of Physics and Chemistry of Solids
A new notion of fractal dimension is defined. When it is positive, it effectively falls back on known definitions. But its motivating virtue is that it can take negative values, which measure usefully the degree of emptiness of empty sets. The main use concerns random multifractals for which f(α) < 0 for some α's. The positive f(α) are show to define a "typical" distribution of the measure, while the negative f(α) rule the sampling variability. Negative dimensions are best investigated using "supersamples." Applications are to turbulence and to DLA. © 1990.
R.J. Gambino, N.R. Stemple, et al.
Journal of Physics and Chemistry of Solids
Ranulfo Allen, John Baglin, et al.
J. Photopolym. Sci. Tech.
Sang-Min Park, Mark P. Stoykovich, et al.
Advanced Materials
Surendra B. Anantharaman, Joachim Kohlbrecher, et al.
MRS Fall Meeting 2020