Mark is currently an undergraduate at Princeton University, studying mathematics. He is interested in exploring deep mathematical concepts and applied mathematics, and is also interested in chemistry and materials science. In his free time, he enjoys playing chess, playing piano, ballroom dancing, fencing, and traveling, as well as hiking and other outdoor-type activities.
Project: Determining Dense Nonperiodic Packing on 2D Lattice
Context of my PhD work
In 2011 Dan Shechtman was awarded the Nobel Prize in chemistry for his findings on quasicrystals, an ordered, non-periodic structure. His work is closely related to the mathematical discovery of aperiodic tilings, which has been studied since the 1960s. Aperiodic tiling is a non-periodic grouping of tiles, such as the well-known Penrose tiling. The goal of the project is as follows: given an arbitrary tile, determine the optimal packing of many copies of the tile on a two-dimensional square lattice. In addition, I will be exploring tiles whose optimal packing is nonperiodic.
Favorite Outer Totalistic r=1, k=2 2D Cellular Automaton