An exploration of fractal dimension
dc.contributor.author | Cohen, Dolav | |
dc.date.accessioned | 2013-08-07T12:27:42Z | |
dc.date.available | 2013-08-07T12:27:42Z | |
dc.date.graduationmonth | August | en_US |
dc.date.issued | 2013-08-07 | |
dc.date.published | 2013 | en_US |
dc.description.abstract | 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. | en_US |
dc.description.advisor | Hrant Hakobyan | en_US |
dc.description.degree | Master of Science | en_US |
dc.description.department | Department of Mathematics | en_US |
dc.description.level | Masters | en_US |
dc.identifier.uri | http://hdl.handle.net/2097/16194 | |
dc.language.iso | en_US | en_US |
dc.publisher | Kansas State University | en |
dc.subject | Fractals | en_US |
dc.subject | Hausdorff | en_US |
dc.subject | Minkowski | en_US |
dc.subject | Dimension | en_US |
dc.subject | McMullen | en_US |
dc.subject | Cantor | en_US |
dc.subject.umi | Applied Mathematics (0364) | en_US |
dc.title | An exploration of fractal dimension | en_US |
dc.type | Report | en_US |