Varies the ratio of two superimposed perpendicular harmonic motions to generate new patterns (Lissajous figures). You'll see ribbons, something like a Mobius strip, taking the form of those patterns. Spacebar changes from ribbon to simple line, both following Lissajous patterns. The ratio of musical pitch frequencies correspond to the xy ratio, e.g. one octave is a ratio of 2 to 1. Tones are played each time x position reaches the maximum amplitude. If xy ratio = 1 and xy phase difference set to 0 you get a straight line. If xy phase difference = 90 degrees you get a circle. Ratios of something other than 1 for more interesting curves called Lissajous figures. Whole number ratios yield figures that connect and repeat in simpler figures.
3D effect enhanced using line costume and coloring. These patterns (Lissajous figures) result from superposition of two perpendicular simple harmonic motions, one along x and one y: x = amplitude * sine(ratio * time + phase) y = amplitude * sine(time) We model that with just a few code blocks. It's a special case of the harmonic motion seen in many physical phenomena. This code simplifies my previous lissajous patterns and uses a standard set of variables (except instead of greek terms omega, delta, I use plain language terms). Put motion in a separate sprite from pen for conceptual simplicity. For many settings, these patterns are enclosed by rectangular boundaries as seen in real pendulums with two axes, like Barton's pendulums knocked sidewise, or a harmonograph. But if you set the ratio to 1 and the phase difference to 90 degrees, you get a circle. The frequency of a simple harmonic oscillator like this one, or a vibrating guitar string, is independent of amplitude. These oscillate with the same frequency whether swung gently or hard or, if a vibrating string, plucked gently or hard. (We don't vary angular frequency, ω = dθ/dt. We treat the period (T, time it takes to go around and back to original position) as constant, so the angular frequency is 2π divided by the period, ω=2πT, but here we just varied time. The patterns come out the same).
