Die Penrose-Parkettierung mit Drachen und Pfeil.

This thesis investigates whether a tiling of the Euclidean plane exists, with kite and dart comprising the set of prototiles, and if this tiling is aperiodic. To this end, two opposing algorithms are deployed, termed composition and decomposition, and a further algorithm, inflation, that is closely related to the latter. It can be shown that the aperiodic Penrose tiling, despite its aperiodicity, demonstrates a surprisingly high level of structure. This can be assigned to a less strict translation symmetry that was shown to occur.