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Measure and dimension for some fractal families

Published online by Cambridge University Press:  01 November 1998

BORIS SOLOMYAK
Affiliation:
University of Washington, Department of Mathematics, Box 354350, Seattle, WA 98195-4350, USA

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.

Type
Research Article
Copyright
© Cambridge Philosophical Society 1998

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