Generalized Mandelbrot Rule for Fractal Sections

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

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1993
Accession Number
ADA266010

Entities

People

  • Lawrence V. Meisel

Organizations

  • United States Army Armament Research, Development and Engineering Center

Tags

Communities of Interest

  • Weapons Technologies

DTIC Thesaurus Topics

  • Abstracts
  • Air Force
  • Cartesian Coordinates
  • Coordinate Systems
  • Engineering
  • Geometry
  • Information Security
  • Mathematics
  • Military Research
  • Physical Properties
  • Security
  • Sizes (Dimensions)
  • Systems Analysis
  • Thickness
  • Three Dimensional
  • Two Dimensional
  • United States Military Academy

Fields of Study

  • Mathematics

Readers

  • Aerospace Propulsion Engineering.
  • Fluid Dynamics.
  • Graph Algorithms and Convex Optimization.