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Box-counting dimensions of generalised fractal nests

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  • Miličić, Siniša

Abstract

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.

Suggested Citation

  • Miličić, Siniša, 2018. "Box-counting dimensions of generalised fractal nests," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 125-134.
    • Handle: RePEc:eee:chsofr:v:113:y:2018:i:c:p:125-134
    DOI: 10.1016/j.chaos.2018.05.025
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    References listed on IDEAS

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    1. Resman, Maja, 2013. "Invariance of the normalized Minkowski content with respect to the ambient space," Chaos, Solitons & Fractals, Elsevier, vol. 57(C), pages 123-128.
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