Accession Number:

ADA300068

Title:

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

Descriptive Note:

Final rept.,

Corporate Author:

ARMY ARMAMENT RESEARCH DEVELOPMENT AND ENGINEERING CENTER WATERVLIET NY BENET LABS

Personal Author(s):

Report Date:

1995-04-01

Pagination or Media Count:

19.0

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 N5 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 Dq and is given by log10N5 approx. equals to 2.54 Dq-O.11. Approximately 25 times as many points are required for 1 percent convergence. The box-based correlation integralBBCI algorithm employed in the present studies, which is well suited to the analysis of large data sets, is also described.

Subject Categories:

  • Numerical Mathematics
  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE