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- W2014603229 startingPage "654" @default.
- W2014603229 abstract "Mandelbrot's rule for sections is generalized to apply to the Hentschel and Procaccia fractal dimension at arbitrary q and on arbitrary sections. It is shown that for almost all (n-m)-dimensional sections, ${mathit{D}}^{mathit{n}}$(q)=${mathit{D}}^{mathit{n}mathrm{ensuremath{-}}mathit{m}}$(q)+m, where the ${mathit{D}}^{mathit{r}}$(q) are box-counting, Hentschel, and Procaccia generalized fractal dimensions of r-dimensional sections of homogeneous fractal point sets in ${mathit{R}}^{mathit{n}}$ and ${mathit{D}}^{mathit{n}mathrm{ensuremath{-}}mathit{m}}$(q)>0. The rule applies for finite ``thickness'' sections as well as ``true'' sections and can be interpreted for inhomogenous fractal sets." @default.
- W2014603229 created "2016-06-24" @default.
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- W2014603229 date "1992-01-01" @default.
- W2014603229 modified "2023-10-14" @default.
- W2014603229 title "Generalized Mandelbrot rule for fractal sections" @default.
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- W2014603229 doi "https://doi.org/10.1103/physreva.45.654" @default.
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