Box-counting dimensions of generalised fractal nests (CROSBI ID 251807)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Miličić, Siniša
engleski
Box-counting dimensions of generalised fractal nests
Fractal nests are sets defined as unions of unit n-spheres scaled by a sequence of k−α for some α>0. In this article we generalise the concept to subsets of such spheres and find the formulas for their box counting dimensions. We introduce some novel classes of parameterised fractal nests and apply these results to compute the dimensions with respect to these parameters. We also show that these dimensions can be seen numerically. These results motivate further research that may explain the unintuitive behaviour of box counting dimensions for nest-type fractals, and in general the class of sets where the box-counting dimension differs from the Hausdorff dimension.
box-counting dimension, Minkowski-Bouligand dimension, uniform Cantor set, fractal nests, (a, b)-bifractals
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Podaci o izdanju
113
2018.
125-134
objavljeno
0960-0779
1873-2887
10.1016/j.chaos.2018.05.025