While at Tufts University this summer I will be conducting research in theoretical computer science. There will be two parts to my research this summer. One, I will be reading different articles weekly about computational geometry and having group discussions on the reading. Two, I will be working on my own individual research.

The object of my individual research is to develop a method of creating autonomous oscillators and to explore properties of their behavior. An oscillator is a pattern of cellular automata that repeats a given pattern periodically. A cellular automaton is a infinite grid of cells that are capable of two states: alive or dead. Each cell has neighbors that based on a set of rules allow the cell to change its state. Through analyzing statistical data of existing oscillators in Cellular Automata using the Game of Life rule sets I hope to learn how to generate novel oscillators. I plan to concentrate on oscillators with low periods: those with cycles between two and fifty-seven. For each existing oscillator I plan to record the density of each step and plotted the results. To calculate the density I will take the number of active cells and divided it by the bounding box of the oscillator. I will compare the oscillators and divided them into categories based on their density plots, common sub-patterns, and any other identifiable commonalities. With this information I hope to be able to expand the current understanding oscillators and potentially find generative patterns that create new types of oscillators or more efficiently existing patterns.