VFF: Nonperiodic structures: tiling theory and materials physics

Physical materials are collections of one or a few types of "particles" (atoms, molecules, or bigger units) that are arranged in some sort of pattern. I am interested in the processes by which such patterns form and in the fundamental question of what types of structure are accessible in natural physical systems. The most familiar patterns are crystalline arrangements in which a simple unit is repeated in a regular way, but there are other possibilities. Investigating the more exotic ones requires visualization of candidate patterns along with development of algebraic descriptions. I will describe some of these nonperiodic structures, show computer generated pictures of the patterns of interest, and explain how the pictures are generated.