It is often useful to view mathematical sequences in nonstandard ways to improve our understanding of them. This project is an attempt to present a well-known mathematical sequence, the Thue-Morse sequence, in a musical format. Information on the sequence can be found at http://en.wikipedia.org/wiki/Thue%E2%80%93Morse_sequence. I have created a program that generates values from the sequence and then uses a cipher I made to convert the values into a musical representation. The values of the sequence are reflected in the melody, chords, and rhythms of the piece. The piece is generated entirely from a portion of the sequence. I have also included a pictorial representation of the sequence. Both presentations draw attention to the so-called "self-similarity" of the sequence; this means that we can find copies of the sequence within itself, much like we can find copies of a fractal within itself. My hope is that this musical representation can bring to light previously-unseen patterns and properties of the sequence.