Fractal Music Gallery Enjoy Fractal Music Lab with Crescendo by LiveUpdate Music Gallery Contents | About Fractals | Music Software | Music Gallery Fractal Music Overview Fractal Window I by Forrest Fang Omar's Fractal (Bifurcation fractal) Example Sonification of Mandelbrot Set Examples Examples from Logistic Equation Chua's Oscillator Examples Anti-Odysseus, the Irreversibility of Time by Insook Choi Examples created using Iterated Function Systems Fractal Music While fractals are 'sets of points' having particular properties they are usually created by simple feedback processes. The term 'Fractal Music' typically refers to music composed wholly or in-part using the same types of mathematical feedback processes that are used to create fractal images. For fractal music composition the numerical outputs of the feedback process are mapped to musical parameters such as pitch, duration, volume, etc to produce melodies, harmonies, rhythms, and textures. A Sampling of Fractal Music on the Web Fractal Music by Bob Devore Fractal Window I by Forrest Fang One of my favorites, this composition, copyright 1996 by Forrest Fang, is background music at Sprott's Fractal Gallery Omar's Fractal MIDI Example This fractal music example was composed with Omar's Fractalby Charles Neville, the programs author. This program produces MIDI output by iterating the Bifurcation Fractal equation x' = x * (1-x) * a (where 'x' is a number less than 1 and greater than 0 and 'a' is a number between 3 and 4) and mapping the 'x' values to particular note numbers . The output of iteration is a series of numbers, 'x' values, that might be an ordered repeating pattern, a chaotic non-repeating pattern, or a mix of both depending on the value of 'a'. Find out about Fractal Jazz by visiting Omar's Basement . MandelBrot single voice example (325 KB) MandelBrot multiple voice example (704KB) These examples were produced by assigning numeric values to the image pixels for a portion of the Mandelbrot set and then mapping the values of linearly sequential pixels to pitches. For more info on Hearing the Mandelbrot set Example by Martin Guertner This example was created by iterating the the logistic equation x' = x*b*(1-x) and mapping the output values 'x' to different musical parameters such as pitch, duration, etc. More information and additional examples can be found at the Fractal Music Project. Chua's Oscillator Musical Example Chua's Oscillator is one of a few physical systems for which the presence of Chaos has been observed experimentally, verified by computer simulation, and proven mathematically. It has been used to generate both musical signals and compositions. You can find a full description of Chua's Oscillator here. Visit this site for additional musical examples. Anti-Odysseus, the Irreversibility of Time (Insook Choi, 1993) presented at the 1993 Asian Contemporary Music Festival used the Chua Circuit. Excerpt Additional information and excerpts can be found here. My particular interest is mappings which produce 'familiar' styles of music from fractal processes. This interest in mappings for fractal-based algorithmic composition goes back to an early article by Charles Dodge and Curtis Bahn in Byte called Musical Fractals, (June 1986, pp185-196). Three comments from that article have stuck with me: Self-similarity was a characteristic of all the fractals that they found to be musically interesting. Heinrich Schenker's classical music analytical techniques reflect the parts of a musical form as self-similar structures. Certain compositional procedures that make new musical material by systematically transforming previous materials, i.e. canon, fugue, and motivic development, can result in clearly self-similar musical structures. 'Music Theory 101' teaches that unity and coherence in music is often achieved by repetition and development of a smaller number of musical motifs or themes. The hierarchical structure of 'self-similar' fractals appears to inherently have some of these same qualities. This article suggested to me that with appropriate mappings a wide range of musical styles could be composed from fractals. My composition algorithms are currently all based on Iterated Function Systems. These systems are interesting because both the image (attractor) formed by plotting the successive iterates and the pattern formed by the number of times different points on the attractor are 'hit' (the measure) are fractals...and they are almost always self-similar fractals. More about Iterated Function Systems (IFS) can be found at: IFS Playground Sprott's Fractal Gallery Here are some of the ways that I use Iterated Function Systems for composition: Use the IFS measure in a fashion similar to that described in the article Iterated Functions System Music by Michael Gogins: Computer Music Journal 15(1): p40-48, 1991 MIT Press. Example 1.. Assign starting pitches to particular x,y coordinates on the attractor. Then follow the orbit of successive iterations along the attractor and map either the absolute values of the coordinates or the change in coordinate to a given pitch range. The sequence currently playing is an example of this technique. Example 2. Create a 'pattern-template' via the above techniques and apply different chord progressions. Create a 'background layer' by one of the above techniques and produce additional harmonic layers as described in the Musical Fractals article. Two short anthologies of original fractal music compositions utilizing some of the techniques mentioned above. Both anthologies contain several MIDI Format 1 files orchestrated for General MIDI; I used the SB AWE 32 sound card. You will need an unzipping program. Download Anthology I (FRACTAL1.ZIP - 12K) Download Anthology II (FRACTAL2.ZIP - 17K) If you have some fractal music or fractal music composition software that you would like to link to this site, composition ideas, or any comments please drop me a line. Update: 1/18/97 Copyright 1996 DTStrohbeen ÿ