Last edited 09dec13 by firstname.lastname@example.org
Find this document at http://new.math.uiuc.edu/math198/MA198-2013/semibra2/
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Overall, I intend to study the relationship between fractals and grain boundaries. If you are interested, please take a look at my pre-proposal or proposal.
Created a weekly progress report and added a draft abstract, available here.
Created a weekly progress report and added pseudo-code for the stellation of a tetrahedron and cube, available here.
Created an iterative process that stellates one side of a tetrahedron (a triangle). Unfortunately, the process is extremely inefficient.
Created a cube.
Created first level extrusions on the cube, using an iterative method. The cube extursion is an "anti-Menger Sponge." It is based on a stellation which extrudes the central of nine squares generated by dividing each side of a cube into three equal-sized portions.
Built a recursive program that stellates tetrahedra.
Unfortunately, there are still loads of errors. For example, the extrusion method does not quite work right, so the tetrahedra lean towards the outside. Also, if the height given is too much, the tetrahedra rapidly become needles.
Fixed the extrusion for the tetrahedron and built a recursive method for the cube. Researched and computed the fractal dimensions for the cube and tetrahedron stellations.
The tetrahedron stellation. Stage 2
The cube stellation. Stage 2
An interesting observation: the tetrahedron stellation approaches a cube. Stage 4 is pictured below.
Optimized the project to run using display lists. There is now a printout of the keyboard controls at the top of the program.