I thought (long time ago, I guess 2011 or earlier) that traditional lissajous rendering with oscilloscopes are kind of distorted, so I created a processing version for simulation. Have fun tweaking the formulas and parameters ;)
Maybe some further refinement for changing parameters and moving the graph would make sense. Feel free to contribute!
PS 20210113: The code was hiding in my linked git, attached the pde for use in processing.