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An exploration of fractal dimension

Master of Science / Department of Mathematics / Hrant Hakobyan / When studying geometrical objects less regular than ordinary ones, fractal analysis becomes a valuable tool. Over the last 30 years, this small branch of mathematics has developed extensively. Fractals can be de fined as those sets which have non-integral Hausdor ff dimension. In this thesis, we take a look at some basic measure theory needed to introduce certain de finitions of fractal dimensions, which can be used to measure a set's fractal degree. We introduce Minkowski dimension and Hausdor ff dimension as well as explore some examples where they coincide. Then we look at the dimension of a measure and some very useful applications. We conclude with a well known result of Bedford and McMullen about the Hausdor ff dimension of self-a ffine sets.

Identiferoai:union.ndltd.org:KSU/oai:krex.k-state.edu:2097/16194
Date January 1900
CreatorsCohen, Dolav
PublisherKansas State University
Source SetsK-State Research Exchange
Languageen_US
Detected LanguageEnglish
TypeReport

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