# Project Proposals

## Software Engineering & Technology

• Graduation project: Computational Formalisms and MDSE
• Graduation project: New Metamodeling Language
• Graduation project: MDSE approach to the solving of packing puzzles
• Bachelor/Honors/Master project (Mathemetics or Computer Science): Combinator Soup Experiment

Start off with a (predefined) mix of combinators, repeatedly apply one combinator to another, and analyze the resulting mix. In particular, it is interesting to see under what conditions and after how long self-replicating combinators appear. This resembles the primordial soup experiment by Miller and Urey.

• Bachelor/Master project (Mathematics): Zeros of Compound Trigonometric Functions (in particular, related to the next project)
• Bachelor/Master project (Mathematics): Classification of Regular Constant-Torsion Polygons in 3D

The torsion angle of a segment in a (3D) polygon is the angle between the two angle-spanning planes at each end of the segment (involving the two adjacent segments).

In a constant-torision polygon, all torsion angles are the same.

In a regular polygon, all segment lengths are the same and all joint angles are the same.

The classification of all regular 2D polygons is known. Regular polygons in 3D are too wild. Hence, the interest in regular constant-torsion polygons. See:

• Bachelor/Master Project (Mathematics or Computer Science): Implement (in Mathematica) Stachowiak's algorithm for generating Hamiltonian paths in neighbor-swap graphs of permutations.

G. Stachowiak. "Hamilton Paths in Graphs of Linear Extensions for Unions of Posets", SIAM J. Discrete Math., 5(2):199–206 (1992).

• Bachelor/Master Project (Mathematics or Computer Science): Design and implement (in Mathematica) algorithms to determine the symmetry group of a finite (2D or 3D) graphics object (collection of points, lines, polygonal faces).
• Bachelor/Master Project (Mathematics or Computer Science): Implement (in Mathematica) algorithms to determine equivalences and symmetries of 3D turtle programs.

Tom Verhoeff. "3D Turtle Geometry: Artwork, Theory, Program Equivalence and Symmetry". Int. J. of Arts and Technology, 3(2/3):288–319 (2010).

• Bachelor/Master project (Mathematics): Computer-supported interactive determination schema plus visualization of the 230 space groups