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Combining Fractals and Box-Counting Dimension
Mathematics and Computer Sciences Department, Marist College, Poughkeepsie, NY, USA
- 1 Mathematics and Computer Sciences Department, Marist College, Poughkeepsie, NY, USA
Applied Mathematics·Volume 12 (2021)·Pages 818–834·Published 2 September 2021·DOI10.4236/am.2021.129055
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Abstract
In this paper, the box-counting dimension is used to derive an explicit formula for the dimension of a fractal constructed using several contractions or by combining fractals. This dimension agrees with the Hausdorff dimension in the particular case when the scales factors considered are all the same. A more general sufficient condition for the box-counting dimension and the Hausdorff dimension to be the same is given. It is also shown that the dimension of the fractal obtained by combining two fractals is the weighted average of the dimensions of the two fractals.
KeywordsBox-Counting DimensionCombining Fractals
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