Application of rotational spectrum for correlation dimension estimation. (June 2017)

• Record Type: Journal Article
• Authors: Dlask, Martin; Kukal, Jaromir
• Is Part Of: Chaos, solitons and fractals. Volume 99(2017)
• Page Start: 256
• Page End: 262
• Publication Date: 2017-06
• Subjects: Point set -- Correlation dimension -- Power spectrum -- Rotation -- Monte Carlo; 28A80 -- 65P20; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2017.04.026
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: Correlation dimension is one of the many types of fractal dimension. It is usually estimated from a finite number of points from a fractal set using correlation sum and regression in a log-log plot. However, this traditional approach requires a large amount of data and often leads to a biased estimate. The novel approach proposed here can be used for the estimation of the correlation dimension in a frequency domain using the power spectrum of the investigated fractal set. This work presents a new spectral characteristic called "rotational spectrum" and shows its properties in relation to the correlation dimension. The theoretical results can be directly applied to uniformly distributed samples from a given point set. The efficiency of the proposed method was tested on sets with a known correlation dimension using Monte Carlo simulation. The simulation results showed that this method can provide an unbiased estimation for many types of fractal sets.