Convergence of numerical box-counting and correlation integral multifractal analysis techniques

✍ Scribed by L.V. Meisel; M.A. Johnson

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 458 KB
• Volume: 30
• Category: Article
• ISSN: 0031-3203
• DOI: 10.1016/s0031-3203(96)00162-8

✦ Synopsis

Abstraet--A systematic study of the rate of convergence for a numerical box-counting and a numerical correlation integral algorithm for determining the generalized fractal dimension D(q) are described. The algorithms are applied to Euclidean point sets, Koch constructions, and a symmetric chaotic mapping. The results provide a basis for estimating the size of a fraetal subset needed for measurement of the generalized dimension D(q). In particular, the number of points N5 required to assure 5% convergence of the algorithms is given within a factor of 4 by logl0(Ns) --~ 2.54D(q) -0.11 for the fractal sets studied here. Approximately 25 times as many points are needed for 1% convergence. Approximately 0.1 times as many points are needed for 25% convergence. The box-based correlation integral algorithm employed in the present studies, which is well suited to the analysis of large data sets, is also described. ~.~' )