Corpus ID: 237492015

Estimating the fractal dimension: a comparative review and open source implementations

@inproceedings{Datseris2021EstimatingTF,
  title={Estimating the fractal dimension: a comparative review and open source implementations},
  author={Georoge Datseris and Inga Kottlarz and Anton P. Braun and Ulrich Parlitz},
  year={2021}
}
Estimating the fractal dimension: a comparative review and open source implementations George Datseris,1, a) Inga Kottlarz,2, 3 Anton P. Braun,2, 3 and Ulrich Parlitz3, 2 1)Max Planck Institute for Meteorology, 20146 Hamburg, Germany 2)Institute for the Dynamics of Complex Systems, University of Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany 3)Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany 

References

SHOWING 1-10 OF 65 REFERENCES
An optimized box-assisted algorithm for fractal dimensions
Abstract We present an optimized algorithm for estimating the correlation dimension of an attractor based on very long time sequences. The main idea is to use a mesh in order to count only nearExpand
The infinite number of generalized dimensions of fractals and strange attractors
Abstract We show that fractals in general and strange attractors in particular are characterized by an infinite number of generalized dimensions Dq, q > 0. To this aim we develop a rescalingExpand
Measuring the Strangeness of Strange Attractors
We study the correlation exponent v introduced recently as a characteristic measure of strange attractors which allows one to distinguish between deterministic chaos and random noise. The exponent vExpand
How to calculate the fractal dimension of a complex network: the box covering algorithm
Covering a network with the minimum possible number of boxes can reveal interesting features for the network structure, especially in terms of self-similar or fractal characteristics. ConsiderableExpand
Consistency of the Takens estimator for the correlation dimension
Motivated by the problem of estimating the fractal dimension of a strange attractor, we prove weak consistency of U-statistics for stationary ergodic and mixing sequences when the kernel function isExpand
Generalized dimensions of strange attractors
Abstract It is pointed out that there exists an infinity of generalized dimensions for strange attractors, related to the order-q Renyi entropies. They are monotonically decreasing with q. For q = 0,Expand
Fractal and multifractal analysis: A review
TLDR
The aim of this review is to explain and to categorize the various algorithms into groups and their application in the field of medical signal analysis. Expand
A comparison of correlation and Lyapunov dimensions
This paper investigates the relation between the correlation ( D2) and the Kaplan–Yorke dimension (DKY) of three-dimensional chaotic flows. Besides the Kaplan–Yorke dimension, a new LyapunovExpand
Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems
We show that values of the correlation dimension estimated over a decade from the Grassberger-Procaccia algorithm cannot exceed the value 2 log10N if N is the number of points in the time series.Expand
Dimension of weather and climate attractors
A PROCEDURE for estimating the correlation dimension of the attractor of a dynamical system1 has been applied to a number of data sets that are representative of weather or climate variations.Expand
...
1
2
3
4
5
...