Phase Art: The picture above is of the Wikipedia 3:2 phase modulation example 1 and corresponding comparison with frequency modulation as displayed by an oscilloscope in X-Y mode.2 This is a mode typically used for testing phase relationships between signals and is well known as the method for displaying Lissajous curves – a sine wave on the X axis and a cosine wave on the Y creates a perfect circle, for example.
What I hadn’t realized is that a phase modulated signal against the same (unmodulated) reference frequency could create the kinds of shapes above. (The frequency modulated signal against the same unmodulated reference frequency produces a rotating oval.3) In this case the phase and (linear) frequency modulated signals are presented simultaneously, resulting in the bands of lines that look something like a staff in music notation.