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Accuracy of the box-counting algorithm for noisy fractals
https://doi.org/10.1142/S0129183116501126Cited by:2 (Source: Crossref)
Abstract
The box-counting (BC) algorithm is applied to calculate fractal dimensions of four fractal sets. The sets are contaminated with an additive noise with amplitude γ=10−5−10−1. The accuracy of calculated numerical values of the fractal dimensions is analyzed as a function of γ for different sizes of the data sample. In particular, it has been found that even in case of pure fractals (γ=0) as well as for tiny noise (γ≈10−5) one has considerable error for the calculated exponents of order 0.01. For larger noise the error is growing up to 0.1 and more, with natural saturation limited by the embedding dimension. This prohibits the power-like scaling of the error. Moreover, the noise effect cannot be cured by taking larger data samples.
Keywords:
PACS Nos.: 05.45.Df
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