From graphic design to stock market predictions, applications of fractal geometry permeate fields in every way. The depiction of fractals also has substantial artistic intrigue. Mathematical graphs displaying multiple dimensions of self-similarity reveal highly evocative perceptions of depth and design. Such a fascination in sight can also be perceived in sound. This research explains the depiction of fractal geometry in music. It examines various compositional techniques used to employ the representation of fractal symmetry in music. Upon considering such representations entailed in the compositional process and realized in the structure of a musical work, we use our findings to engineer an original method that musically depicts the geometry of a fractal. This method has its ultimate realization in a musical composition that amalgamates our discoveries. This paper will discuss fractal representations in music and the compositional procedures that achieved them.