A Modified Box-Counting Method to Estimate the Fractal Dimensions
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%.
J. Xu and G. Lacidogna, "A Modified Box-Counting Method to Estimate the Fractal Dimensions", Applied Mechanics and Materials, Vols. 58-60, pp. 1756-1761, 2011