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Beschreibung:
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.