Application of rotational spectrum for correlation dimension estimation

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.