A Modified Box-Counting Method to Estimate the Fractal Dimensions

Jie Xu; Giusepe Lacidogna

doi:10.4028/www.scientific.net/AMM.58-60.1756

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vols. 58-60A Modified Box-Counting Method to Estimate the...

A Modified Box-Counting Method to Estimate the Fractal Dimensions

Abstract:

A fractal is a property of self-similarity, each small part of the fractal object is similar to the whole body. The traditional box-counting method (TBCM) to estimate fractal dimension can not reflect the self-similar property of the fractal and leads to two major problems, the border effect and noninteger values of box size. The modified box-counting method (MBCM), proposed in this study, not only eliminate the shortcomings of the TBCM, but also reflects the physical meaning about the self-similar of the fractal. The applications of MBCM shows a good estimation compared with the theoretical ones, which the biggest difference is smaller than 5%.

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Periodical:

Applied Mechanics and Materials (Volumes 58-60)

Pages:

1756-1761

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.58-60.1756

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Online since:

June 2011

Authors:

Jie Xu, Giusepe Lacidogna

Keywords:

Box-Counting, Fractal, Fractal Dimension, MBCM, Self-Similar, TBCM

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