Brad Klee holds a bachelor's degree in physics. He has been outside of the academic world for one year now, conducting original research with plane tiling and the polyhedra, completely alone. Here, a married person would write a sentence thanking his or her spouse for the gift of constant love and support. The conflicts and revolutions in the Middle East concern him, and he hopes that Islamic math and science will someday in the future regain the importance and respect that they garnered in the past.
Project: Tiling by Constraint
Constraints on patterns apparent in a subspace of a regular lattice have been shown to affect patterns on the entire lattice, at least in the case of the square lattice (p. 210) and the hexagonal lattice. The symmetries of different lattices may or may not affect the type of patterns that satisfy local constraints. This project takes steps toward creating the scaffolding for constraint-based pattern searches on any of the three regular plane tilings. Some simple patterns have already been found on the hexagonal lattice.
Constraint Tiling on a Truncated Icosahedron
Favorite Four-Color Totalistic Cellular Automaton