'Inscribed rectangles,' is a way of mathematically proving that any continuous shape will always have four points along its perimeter that make up the vertices of a regular rectangle, though beyond that I don't pretend to understand the idea. In fact, the name of this experiment is a little misleading, as the method of generating audio is only vaguely related, I just couldn't think of another name.
The process of the aforementioned mathematical proof involves a step in which the distance between every two opposite points along the continuous shape is measured and then represented on a hypothetical third axis. This process is the basis of this experiment, but rather than plotting distances along a 'Z-Axis,' they are placed linearly along an X-axis. These then form a series of values that can be mapped according to the total possible distance range to the range of audio samples [-1,1]. The resulting waveform can then be resampled according to a chosen frequency and the sample rate, and ramped to the 0 crossing point at the beginning and end.
The timbres generated using this method were very promising, with a noticeably varied spectrum of harmonics, depending on the shape. One issue is that glitches can occur at higher frequencies, probably because the amount of samples per wave cycle is smaller and my resampling algorithm isn't sophisticated enough to deal with this. I plan to adapt this technique into JUCE to then apply various other processes to the signal. Another possible next step is to try and mathematically define these waveforms with a Fourier transform, which may make further signal processing easier in the long run.