Fractal Geometry, Graph and Tree Constructions
Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
In the 18th and 19th centuries the branch of mathematics that would later be known as fractal geometry was developed. It was the ideas of Benoˆıt Mandelbrot that made the area expand so rapidly as it has done recently, and since the publication of his works there have for fractals, and most commonly the estimation of the fractal dimension, been found uses in the most diverse applications. Fractal geometry has been used in information theory, economics, flow dynamics and image analysis, among many different areas.
This thesis covers the foundations of fractal geometry, and gives most of the fun- damental definitions and theorems that are needed to understand the area. Concepts such as measure and dimension are explained thoroughly, especially for the Hausdorff di- mension and the Box-counting dimension. An account of the graph-theoretic approach, which is a more general way to describe self-similar sets is given, as well as a tree- construction method that is shown to be equivalent to the graph-theoretic approach.
Place, publisher, year, edition, pages
2008. , 101 p.
IdentifiersURN: urn:nbn:se:umu:diva-51347OAI: oai:DiVA.org:umu-51347DiVA: diva2:479178
UppsokPhysics, Chemistry, Mathematics