Fractal Music works much like the random music discussed on the previous page, with one significant difference. Like random music, a variety of mappings between numerical values and pitches may be used with varying results, but the numerical values are generated using fractals, rather than random numbers. A number of different fractals can be used for the purpose, including Iterated Function Systems (IFS), strange attractors (such as the Lorenz attractor), and the Mandelbrot set and Julia sets.
Using a system like the Henon attractor, we can generate pitches by beginning with a particular value of our choosing and then using its iterates to generate further values. A similar method can be used with Iterated Function Systems.
The applet below uses the equations of the Henon Attractor, x(n+1) = 1 + y(n) - a*x(n)^2 and y(n+1) = b*y(n) with starting values of 0.0 for both x and y, and values of 1.4 and 0.3 for a and b respectively. Each x and y value is normalized and then scaled to give a pitch value within a two-octave range. For this example, we've used the minor scale, just for some variety. Since there are two values, x and y, we can generate two different pitches at the same time, resulting in harmony (or dissonance, as the case may be).