1. A fern is like a fern

Fractals are based on the notion of self-similarity. Self-similarity is when things are like themselves. One example is a fern. The branch of a fern looks like a whole fern. The leaf of a fern looks like the branch of a fern, which looks like a whole fern. Fractals are objects which are self-similar at all levels.

2. A mathematical fern

The self-similarity of a real fern is limited. But the fact that a fern has self-similar characteristics means that we can create a fern-like object with a few mathematical rules, such as the Barnsley fern. Fractal Music Machine is based on math similar to the Barnsley fern.

3.A simple fractal

Start with a simple line drawing (drawn by hand):

Replace each of the lines with the entire drawing, at the scale of that line:

Do that again...

Keep going...

And eventually you will have an object which is self-similar at many scales. These objects tend to have a certain naturalness or harmony about them.

4.Fractals in time

If we use a linear fractal, such as the Cantor Set,
then we can read off the points of the fractal as rhythmic elements, as if
it were a score over time. By varying the length, number, and direction
of the original lines, we can create more interesting rhythms. These rhythms have
fractal properties over time. This is the core of fractal music.

Cantor Set: try reading off the bottom line as a rhythm.