On Some Dimension Problems for Self-Affine Fractals

  • M.P. Bernardi

    Università di Pavia, Italy
  • C. Bondioli

    Università di Pavia, Italy


We deal with self-affine fractals in . We examine the notion of affine dimension of a fractal proposed in [26]. To this end, we introduce a generalized affine Hausdorif dimension related to a family of Borel sets. Among other results, we prove that for a suitable class of self-affine fractals (which includes all the so-called general Sierpiñski carpets), under the "open set condition", the affine dimension of the fractal coincides - up to a constant - not only with its Hausdorif dimension arising from a non-isotropic distance in , but also with the generalized affine Hausdorff dimension related to the family of all balls in . We conclude the paper with a comparison between this assertion and results already known in the literature.

Cite this article

M.P. Bernardi, C. Bondioli, On Some Dimension Problems for Self-Affine Fractals. Z. Anal. Anwend. 18 (1999), no. 3, pp. 733–751

DOI 10.4171/ZAA/909