An Introduction to Fractals and Hausdorff Measures
نویسندگان
چکیده
It is possible for one to define fractals as those sets which have non-integral Hausdorff Dimension. This paper defines Hausdorff Dimension and rigorously introduces the necessary theory to prove that one such set is indeed a fractal. The first chapter includes a proof of Banach’s Fixed Point Theorem. The Hausdorff Metric is defined and it is mentioned how one produces ‘generators’ for creating self-similiar fractals. The second chapter defines Hausdorff Dimension and proves some characteristics regarding it, including its invariance under different Lp metrics. Frostman’s lemma is introduced as a tool for calculating the Hausdorff Dimension of sets, and examples of fractals are introduced in order to illustrate how one proceeds in calculating the dimension of fractals.
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