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Some self-similar constructions in two and three dimensions and their neighbor geometry

  • Self-similar sets are a class of fractals which can be rigorously defined and treated by mathematical methods. Their theory has been developed in n-dimensional space, but we have just a few good examples of self-similar sets in three-dimensional space. This thesis has two different aims. First, to extend fractal constructions from two-dimensional space to three-dimensional space. Second, to study some of the properties of these fractals such as finite type, disk-likeness, ball-likeness, and the Hausdorff dimension of boundaries. We will use the neighbor graph tool for creating new fractals, and studying their properties.
  • In dieser Arbeit werden verschiedene selbstähnliche Konstruktionen von zwei auf drei Dimensionen übertragen, und ihre Eigenschaften werden mittels Nachbar-Abbildungen untersucht.

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Metadaten
Author: Mai The Duy
URN:urn:nbn:de:gbv:9-000993-6
Title Additional (German):Einige selbstähnliche Konstruktionen in zwei und drei Dimensionen und ihre Nachbarschaftsgeometrie
Advisor: Karsten Keller, Christoph Bandt
Document Type:Doctoral Thesis
Language:English
Date of Publication (online):2011/05/30
Granting Institution:Ernst-Moritz-Arndt-Universität, Mathematisch-Naturwissenschaftliche Fakultät (bis 31.05.2018)
Date of final exam:2011/05/17
Release Date:2011/05/30
Tag:fractal, neighbor map, self-similarity
GND Keyword:Fraktal, Selbstähnlichkeit
Faculties:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik und Informatik
DDC class:500 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Classification:28-XX MEASURE AND INTEGRATION (For analysis on manifolds, see 58-XX) / 28Axx Classical measure theory / 28A80 Fractals [See also 37Fxx]