# Fractal Music

Much music includes themes that repeat themselves. Sometimes a phrase is repeated exactly, and sometimes it is slightly changed. These types of patterns can be seen not only in fractal images, but also in fractal music. In fractal music, numbers produced by equations are not converted to pixel colors, as they are in images, but into musical notes. Musical concepts can be expressed mathematically. For example, transposing music (playing it in a different key) can be accomplished by translating numbers along a position axis. Augmentation and dimunution, respectively the lengthening and shortening of notes, can be accomplished by expanding and compressing along the axis of position vs. time.

Fractal music can be created in a number of different ways. Probably the best known is the Morse-Thue method. This method involves a sequence of complementary binary digits. The sequence is calculated using a recursive algorithm. Transforms are defined as being one 'event' of the recursion. These transforms are then converted into musical notes. Thus, the sequences of numbers become sequences of notes.

In addition to the Morse-Thue method, there are at least 8 other mathematical methods for creating fractal music. Many of these methods can be used for composing music with the program FractMus.

Here is a simple piece of fractal music I created using the Morse-Thue algorithm with FractMus.
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There is another interesting program which creates music through fractals. It is called ArtSong. The user inputs a bitmap image, and the program traces over it in a fractal pattern, creating music. Here are two pieces I created using a picture of my dog.

Here is my dog, played using a Sierpinski Triangle algorithm in a major key:Using a jazz orchestration option
Now here he is again, played using a spiral type of algorithm in a harmonic minor key: Using a string trio orchestration option