Physical Sciences and Mathematics Commons^™

Recurrence Relations, Fractals, And Chaos: Implications For Analyzing Gene Structure, Sarah. M. Harmon

Honors Theses

The “chaos game” is a well-known algorithm by which one may construct a pictorial representation of an iterative process. The resulting sets are known as fractals and can be mathematically characterized by measures of dimension as well as by their associated recurrence relations. Using the chaos game algorithm, is it possible to derive meaningful structure out of our own genetic encoding, and that of other organisms? In this paper, I will present one method of applying the chaos game to biological data and subsequently will discuss both the mathematical and biological implications of the results.