Self-similarity independent of scale: that's fractal behavior.
Besides clouds, trees, shorelines, earthquake magnitudes, mammalian circulatory systems ...
There are human creations that are also fractal, especially music (and not just fabricated "fractal" music). A Bach fugue is fractal. The typical form a popular song (ABAA) is fractal. A phrase (A or B) may be four measures (sixteen measures comprise a chorus). Within each measure (in 4/4) there are full, half, quarter ... notes. Look at the musical patterns, and quite often there is repetition (not only A and A or B and B) of note sequences at different rhythms.
Then there's a chord. A major chord includes harmonically consistent notes, with compatible harmonic vibrations. They "fit" together.
Then, consider an arrangement. Say, Nelson Riddle of Fifties Sinatra. There's the repetition, and then background melodies that contrast with the primary melody, but a fractal content is very much there.
