As an example I build this pseudo phase space generator. A pseudo-phase-space allows a 1 dimensional data-series to be converted into a 2D (or higher) representation. It is used in non-linear systems to look for periodicity or stability within a data-series.
For a 1D dimemsional data-series, such as:
s(0), s(1), s(2), s(3), ..., s(n), ...,
A 2D representation of the data can be produced by plotting s(i) against s(i+1).
In TouchDesigner this is easily done by using the Delay CHOP and after delaying the signal merging it with the original. I used the resulting channels as the input to a Limit SOP to create the geometry. I also delay the signal to create channels then used as point colors on the geometry.
The attached component makes 2 different uses of the PPS - in 1 it uses the current timeslice of an audio signal via the AudioIn CHOP and the other one creates the PPS from a static Waveform (G1 note of a marimba in the attached image).