|The Mandelbrot set is a mathematical object that has gained celebrity status through the many startling images created from the set's visualization. The fractal mathematics of the set is easy to understand in its basic form. It is also easy to write a computer program to visualize the set. The usual approach is to calculate a plane of points, each point being evaluated to an integer and then mapped into a color.
By selecting a line of points, instead of a plane, an array of values can be calculated from the set. Using Csound these values can be mapped into sonic dimensions such as frequency or amplitude. A mapping is realized as a collection of I-statements for a predefined Csound instrument. The Csound orchestra and score compile to make a sonic representation of the set. Creating sonic maps from multiple lines can build a multi-voice composition.
This method of generating sonic maps of a mathematical model is straightforward, derived from earlier MIDI-based efforts to generate fractal music as an accompanient to fractal visualization. The specific example using the Mandelbrot set can be generalized to the sonification of a variety of abstract or scientific data.