Fractals and Fugues: How Self-Similarity Emerges in Musical Structure

Fractals refer to mathematical structures that exhibit self-similarity, i.e., the recursive repetition of identical structures, with complex patterns being created under simple parameters. This paper investigates the emergence of fractal patterns in the music of Johann Sebastian Bach, who was known for his repetitive modifica-tion of motifs, especially in his work The Art of Fugue. Although his compositions are not strictly fractal, they serve to highlight a unique relationship between math-ematics and music, exemplifying the use of recursive processes to create complexity in music.