Multifractal analysis of imprecise data: Badii-Politi and correlation integral approaches

Analytic and numerical implementations of the correlation integral and the Badii-Politi multifractal analysis algorithms are described and applied to machine precision and imprecise model multifractal data. The correlation integral technique yields good results for machine precision data and for data with 1% random errors. The standard numerical Badii-Politi algorithm did not yield satisfactory results for data with 0.05% or larger random errors. However, the present results suggest that a natural generalization of the Badii-Politi approach along the lines suggested by Kostelich and Swinney [Phys. Scr. 40, 436 (1989)] can be applied to the analysis of imprecise fractal data.