## Mandelbrot Music

Stop the presses. A while ago, I figured it would make an amazing fractal if we could feed the equation for harmonic propagation into a fractal programme – because as we know, when harmonics propagate, the gap between your starting frequency and your ending frequency is always a harmonic of your starting frequency.

Well, I found this video where he shows how fractals can be shown to make music. If someone could just help me figure out what the equation is to represent:

* a starting frequency,
* multiplied by 3,
* multiplied by 11 to get us back nearly to where we started, where the difference nearly matches an octave of our starting frequency

* and the difference between that gap frequency and an octave of the starting frequency again becomes the input to the next iteration of the equation.

E.g.

0.9 Hz x 3 = 2.7 hz
X 11 = 29.7 hz
The ‘expected’ frequency is 28.8 hz (0.9 hz x 32, which is several octaves above our starting frequency).

And the difference between the starting octave and the ending frequency is 29.7 minus 28.8 = 0.9 hz, which in this case is our starting frequency, although sometimes it might be the 9th or the 5th harmonic, etc.

So, the gap is the part that makes it fractal because the gap is always a whole number harmonic of the starting frequency.
It would be a really amazing fractal because it would visualise how vibrational harmonics actually propagate, while also emitting the sounds of this process!

Can anyone help with the equation?!