Meghana Ranganathan, Mathematics

How a Sentence is like a Potato: A Mathematical Study of Patterns

The concept of a pattern is something we learn at a very young age, and colloquially it refers to the repetition of some element (a phrase, a geometric design, a letter, a number). Pattern theory is a branch of mathematics that seeks to understand what a pattern is, what it consists of, and then analyze patterns as a way of examining the complexity in our world. Its central tenet is an assumption that everything is a pattern at some level. My senior paper was a discussion of the fundamental attributes of pattern theory through examples we interact with on a daily basis. I use the construction of a simple sentence using English language syntax to define the core facets of a pattern: generators and bonds. This is compared to an example of creating a model of a potato image to demonstrate that we can use this same terminology created by pattern theory in different media, as well as to show that pattern theory is useful in many respects. Ultimately, this discussion of patterns demonstrates that we can use the same simple model to create very complex patterns and processes that we see every day.