Convergence of Numerical Box-Counting and Correlation Integral Multifractal Analysis Techniques.

Abstract

A systematic study of the rate of convergence for a numerical box-counting and a numerical correlation integral algorithm applied to Euclidean point sets, Koch constructions, and a symmetric chaotic mapping is described. The number of points N(5) required for 5 percent convergence of the box-counting (for 0 < or = q < or = 25) and correlation integral (for q between -25 and 25) algorithms for the fractal sets studied is determined by the generalized dimension D(q) and is given by log10(N5) approx. equals to 2.54 D(q)-O.11. Approximately 25 times as many points are required for 1 percent convergence. The box-based correlation integral(BBCI) algorithm employed in the present studies, which is well suited to the analysis of large data sets, is also described.

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1995
Accession Number
ADA300068

Entities

People

  • Lawrence V. Meisel
  • Marc A. Johnson

Organizations

  • United States Army Armament Research, Development and Engineering Center

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Construction
  • Convergence
  • Data Sets
  • Integrals

Readers

  • Aerospace Propulsion Engineering.
  • Computer Programming and Software Development.
  • Operations Research