# 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

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SHOWING 1-10 OF 65 REFERENCES

An optimized box-assisted algorithm for fractal dimensions

- Physics
- 1990

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 near… Expand

The infinite number of generalized dimensions of fractals and strange attractors

- Mathematics
- 1983

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 rescaling… Expand

Measuring the Strangeness of Strange Attractors

- Mathematics
- 1983

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 v… Expand

How to calculate the fractal dimension of a complex network: the box covering algorithm

- Mathematics, Physics
- 2007

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. Considerable… Expand

Consistency of the Takens estimator for the correlation dimension

- Mathematics
- 1999

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 is… Expand

Generalized dimensions of strange attractors

- Physics
- 1983

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

- Mathematics, Computer Science
- Medical Image Anal.
- 2009

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

- Mathematics
- 2005

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 Lyapunov… Expand

Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems

- Mathematics
- 1992

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

- Mathematics
- Nature
- 1991

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