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Find this document at An Investigation into Tessellating Three-Space with Quasicrystals


The purpose of this excersize is to create a program that generates an aperiodic lattice of three-dimensional quasicrystals. This was accomplished using the DeBruijn dual method, which involves taking a star of vectors, each with direction normal to a face of a dodecahedron, and imagining planes normal to those vectors at distances on intervlas of the golden ratio away from the origin. Then, at each point where three or more planes intersect, the vectors are transported and added, forming a quasicrystal. By cycling through all points of intersection, an aperiodic lattice is formed.


An oral presentation by the author will be given in the GraffiXlab in 102 Altgeld Hall on Monday, May 8, 2006 at 3:00 PM. The software will be demonstrated in the Beckman Institute Cube by the author on Wednesday, May 10 at 2:30 PM.


Here is a link to the paper. Here is a link to the source code.