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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.
Author: | Mai The Duy |
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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] |