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) : Meisel, L. V. ; Johnson, M. A.

PDF Url : ADA300068

Report Date : APR 1995

Pagination or Media Count : 19

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.

Descriptors :   *FRACTALS, *NUMERICAL METHODS AND PROCEDURES, ALGORITHMS, IMAGE PROCESSING, COMPUTATIONS, CHAOS, INTEGRALS, ACCURACY, CORRELATION, PRECISION, CONVERGENCE, LOGARITHM FUNCTIONS, PIXELS, SET THEORY, POINT THEOREM.

Subject Categories : Numerical Mathematics
      Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE