Composing Music with Computers

4  Iterative algorithms: chaos and fractals

4.1  Iterative processes

An iterative process is the repeated application of a mathematical procedure where each step is applied to the output of the preceding step (Figure 4.1).

Figure 4.1 An iterative process whereby the output is fed back to the input.

Mathematically, an iterative process is defined as a rule that describes the action that is to be repeatedly applied to an initial value X₀. The outcome of an iterative process constitutes a set, technically referred to as the orbit of the process; the values of this set are referred to as the points of the orbit. Thus, the orbit O that arises from ...