A Framework for GPU-Assisted Generation and Composition of Inductive Rotation Patterns

Information

• Publication Type: Master Thesis
• Workgroup(s)/Project(s):
  • Visualization Group
• Date: August 2015
• First Supervisor: Eduard Gröller

Abstract

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.

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BibTeX

@mastersthesis{Sippl_Sebastian_EFG,
  title =      "A Framework for GPU-Assisted Generation and Composition of
               Inductive Rotation Patterns",
  author =     "Sebastian Sippl",
  year =       "2015",
  abstract =   "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.",
  month =      aug,
  address =    "Favoritenstrasse 9-11/E193-02, A-1040 Vienna, Austria",
  school =     "Institute of Computer Graphics and Algorithms, Vienna
               University of Technology ",
  URL =        "https://www.cg.tuwien.ac.at/research/publications/2015/Sippl_Sebastian_EFG/",
}