1998•Mathematical Proceedings of the Cambridge Philosophical SocietyRequires access

Measure and dimension for some fractal families

Boris Solomyak

Abstract

We study self-similar sets with overlaps, on the line and in the plane. It is shown that there exist self-similar sets that have non-integral Hausdorff dimension equal to the similarity dimension, but with zero Hausdorff measure. In many cases the Hausdorff dimension is computed for a typical parameter value. We also explore conditions for the validity of Falconer's formula for the Hausdorff dimension of self- affine sets, and study the dimension of some fractal graphs.

About this research paper

What this paper is about

Why it matters

OpenAlex reports 187 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

Key concepts: Hausdorff dimension, Effective dimension, Minkowski–Bouligand dimension, Mathematics, Hausdorff measure, Packing dimension, Dimension function, Outer measure