TY - THES
U1 - Dissertation / Habilitation
A1 - Duy, Mai The
T1 - Some self-similar constructions in two and three dimensions and their neighbor geometry
N2 - 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.
N2 - In dieser Arbeit werden verschiedene selbstähnliche Konstruktionen von zwei auf drei Dimensionen übertragen, und ihre Eigenschaften werden mittels Nachbar-Abbildungen untersucht.
KW - Fraktal
KW - Selbstähnlichkeit
KW - fractal
KW - self-similarity
KW - neighbor map
Y2 - 2011
U6 - https://nbn-resolving.org/urn:nbn:de:gbv:9-000993-6
UN - https://nbn-resolving.org/urn:nbn:de:gbv:9-000993-6
ER -