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.
Keywords:
2D fractal dimension / generalisation of Higuchi's fractal dimension / fractal dimension of a planar curve
TY - JOUR
AU - Spasić, Slađana
PY - 2014
UR - http://rimsi.imsi.bg.ac.rs/handle/123456789/781
AB - 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.
PB - Pergamon-Elsevier Science Ltd, Oxford
T2 - Chaos Solitons & Fractals
T1 - On 2D generalization of Higuchi's fractal dimension
EP - 187
SP - 179
VL - 69
DO - 10.1016/j.chaos.2014.09.015
ER -
@article{
author = "Spasić, Slađana",
year = "2014",
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.",
publisher = "Pergamon-Elsevier Science Ltd, Oxford",
journal = "Chaos Solitons & Fractals",
title = "On 2D generalization of Higuchi's fractal dimension",
pages = "187-179",
volume = "69",
doi = "10.1016/j.chaos.2014.09.015"
}
Spasić, S.. (2014). On 2D generalization of Higuchi's fractal dimension. in Chaos Solitons & Fractals
Pergamon-Elsevier Science Ltd, Oxford., 69, 179-187.
https://doi.org/10.1016/j.chaos.2014.09.015
Spasić S. On 2D generalization of Higuchi's fractal dimension. in Chaos Solitons & Fractals. 2014;69:179-187.
doi:10.1016/j.chaos.2014.09.015 .
Spasić, Slađana, "On 2D generalization of Higuchi's fractal dimension" in Chaos Solitons & Fractals, 69 (2014):179-187,
https://doi.org/10.1016/j.chaos.2014.09.015 . .
