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On 2D generalization of Higuchi’s fractal dimension

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  • Spasić, Sladjana

Abstract

We propose a new numerical method for calculating 2D fractal dimension (DF) of a surface. This method represents a generalization of Higuchi’s method for calculating fractal dimension of a planar curve. Using a family of Weierstrass–Mandelbrot functions, we construct Weierstrass–Mandelbrot surfaces in order to test exactness of our new numerical method. The 2D fractal analysis method was applied to the set of histological images collected during direct shoot organogenesis from leaf explants. The efficiency of the proposed method in differentiating phases of organogenesis is proved.

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  • Spasić, Sladjana, 2014. "On 2D generalization of Higuchi’s fractal dimension," Chaos, Solitons & Fractals, Elsevier, vol. 69(C), pages 179-187.
    • Handle: RePEc:eee:chsofr:v:69:y:2014:i:c:p:179-187
    DOI: 10.1016/j.chaos.2014.09.015
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    Cited by:

    1. Karimui, Reza Yaghoobi, 2021. "A new approach to measure the fractal dimension of a trajectory in the high-dimensional phase space," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).

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