The name fractal is given to images, landscapes, sounds, and any other pattern that is, if you look at one small part, you getting an idea of the entire picture. Fractals in music is one area of the overall study of fractals.
Relatively current research pertaining to fractals in music took place a few years ago. Mr. Harlan Brothers engaged in a mathematically precise treatment of fractal music. Mr. Brothers presented a lab and lecture concerning this study at the 2004 Fractal Geometry Summer Workshop at Yale.
Since that time, he has published a number of papers on the subject of fractals in music. Furthermore, he also produced a compilation of fractal music in honor of Benoit B. Mandelbrot; this was for Science Writers 2010. Mr. Mandelbrot was a mathematician. He developed the field of fractal geometry; he applied it to physics, biology, finance and several other fields. He passed away in 2010.
In a documentary entitled Bach & Friends, Mr. Brothers engaged in a discussion about Bach, mathematics, as well as fractal geometry.
In addition, Dmitry Kormann has composed music which incorporate fractals in music. He has developed a fractal music system that he utilizes. Compositions include the Coral Reef Symphony, Wind and Metal, and Anemonae.