[Zurück]

S. Sippl:
"A Framework for GPU-Assisted Generation and Composition of Inductive Rotation Patterns";
Betreuer/in(nen): E. Gröller; Institut für Computergraphik und Algorithmen, 2015.

The Inductive Rotation Method, developed by the artist Hofstetter Kurt, is a strategy for generating elaborate artistic patterns by applying translations and rotations repeatedly to a copy of a so called prototile. The method has been inspired by aperiodic tilings such as the popular Penrose tilings. The Inductive Rotation Patterns and their nonperiodic structure is interesting from both a mathematical and from an artistic point of view. In the scope of a previous thesis different algorithms for the generation of such patterns were already implemented and researched which resulted in a program called the "Irrational Image Generator". However, this software prototype provides only few features which support Hofstetter in designing patterns, and can only produce patterns with limited size. The limited size results from a property of the patterns: The number of tiles grows exponentially with each iteration.

The Inductive Rotation Framework, a software framework for the generation of Inductive Rotation Patterns, was developed in the course of this thesis and unites new generation algorithms with an extended tool-set, like a graphical prototile editor which supports Hofstetter in his pattern design process. One of the existing algorithms was successfully parallelized and now allows the artist pattern generation via GPGPU methods.

Depending on the implementation this can increase either pattern generation speed or the maximum pattern-size. In order to research the advantages and disadvantages of a recently developed tile substitution method for the creation of Inductive Rotation Patterns, the framework was extended by an algorithm which is based on this new discovery. Following the definition of the Inductive Rotation Method from Hofstetter, this tile-substitution method produces only a subset of Inductive Rotation Patterns.

By varying the definition of Hofstetter´s Inductive Rotation Method only slightly, the Sierpinski gasket, a fractal pattern, emerges. The similarity between the Inductive Rotation Method and fractals can be observed further by comparing the parallel generation algorithm´s matrix scheme to Iterated Function Systems (IFSs), which are used to generate fractals.

http://publik.tuwien.ac.at/files/PubDat_241786.pdf