2012•Unpublished venueRequires access

FRACTAL DIMENSION:BOX DIMENSION, HAUSDORFF DIMENSION, AND POTENTIALTHEORY

Maria Anestasia

Abstract

The concept of dimension has many aspects and meanings in mathematics, and there are a number of di�erent de�nitions of the dimension of a set. In this thesis, 2 de�nitions of fractal dimension will be discussed, i.e. box-dimension and Hausdor� dimension. The relation between box-dimension and Hausdor� dimension, and methods to determine upper bound and lower bound of Hausdor� dimension will also be studied. In the last part, examples of how to apply mass distribution principle and potential theory to determine the lower bound will be given on middle third Cantor set and Cantor dust. Keyword: Box dimension, Hausdor� dimension, Mass Distribution Principle, Potential Theoretic Method

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Key concepts: Hausdorff dimension, Minkowski–Bouligand dimension, Packing dimension, Dimension function, Mathematics, Effective dimension, Dimension (graph theory), Inductive dimension