Infinite detail or 'invariance to scaling' is not limited to visual phenomena. Certain types of sounds do not change when played at different sample rates; Mandelbrot called these 'scaling noises' (The Fractal Geometry of Nature).
The term 'Fractal Music' typically refers to music composed wholly or in-part using the same types of iterative or recursive processes used to create fractal images.
Often fractal music is composed directly from fractal images. Creating music from fractals is an example of 'algorithmic' music composition. Algorithmic composition refers to the process of using a formula or recipe (an algorithm) for creating music. Musical 'recipes' can be formal or informal depending upon how precisely the compositional steps are specified.
Though fractal music can be composed without a computer, currently most is composed with the aid of a computer.

Computer composed fractal music always uses a formal 'recipe' - the software program - to produce music. During computer-based fractal music composition inputs from the fractal image or fractal generating process are converted to musical parameters to create melodies, harmonies, rhythms, textures, etc. The process of converting from the 'fractal' value type into a musical parameter is called 'mapping'. There are numerous, if not infinite, ways to map numerical values to musical parameters. While fractal music generators will not make a musician out of a lay person, I nonetheless find the process of discovering "sound" through fractals endlessly inspiring. The software I have found easy to use is the following:

Koan X
Oblivion
Gingerbread
FractMus2000