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.
Descriptors:
Subject Categories:
- Numerical Mathematics
- Theoretical Mathematics