Article citationsMore>>

Moran, M. and Rey, J.-M. (1998) Singularity of Self-Similar Measures with Respect to Hausdorff Measures. Transactions of the American Mathematical Society, 350, 2297-2310.
https://doi.org/10.1090/S0002-9947-98-02218-1

has been cited by the following article:

• TITLE: Combining Fractals and Box-Counting Dimension

  AUTHORS: M. Ndiaye

  KEYWORDS: Box-Counting Dimension, Combining Fractals

  JOURNAL NAME: Applied Mathematics, Vol.12 No.9, September 30, 2021

  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.