Accession Number : ADA266010


Title :   Generalized Mandelbrot Rule for Fractal Sections


Descriptive Note : Final technical rept.


Corporate Author : ARMY ARMAMENT RESEARCH DEVELOPMENT AND ENGINEERING CENTER WATERVLIET NY BENET LABS


Personal Author(s) : Meisel, L V


Full Text : https://apps.dtic.mil/dtic/tr/fulltext/u2/a266010.pdf


Report Date : Apr 1993


Pagination or Media Count : 14


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, Dn(q) = Dn-m(q) + m, where the Dr(q) are box-counting Hentschel and Procaccia generalized fractal dimensions of r-dimensional sections of homogeneous fractal point sets in Rn. The rule is shown to apply for finite 'thickness' sections as well as 'true' sections. A more general form of the rule applicable to inhomogeneous fractal sets is also presented. Fractals, Generalized dimensions, Box-counting, Fractal dimensions


Descriptors :   *FRACTALS , THICKNESS , BOXES , STANDARDS , STATISTICAL ANALYSIS , SELECTION


Subject Categories : Cybernetics


Distribution Statement : APPROVED FOR PUBLIC RELEASE