Algorithm to estimate the Hurst exponent of high-dimensional fractals

Details Algorithm to estimate the Hurst exponent of high-dimensional fractals Algorithm to estimate the Hurst exponent of high-dimensional fractals

2007-11-19

arxiv.org/abs/0711.2892v1

Phys. Rev. E 76, 056703 (2007)

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1103/PhysRevE.76.056703

We propose an algorithm to estimate the Hurst exponent of high-dimensional fractals, based on a generalized high-dimensional variance around a moving average low-pass filter. As working examples, we consider rough surfaces generated by the Random Midpoint Displacement and by the Cholesky-Levinson Factorization algorithms. The surrogate surfaces have Hurst exponents ranging from 0.1 to 0.9 with step 0.1, and different sizes. The computational efficiency and the accuracy of the algorithm are also discussed.

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