Select higher speed to better see patterns. Set dot X to Neptune's X or Pluto's X (Y is set to other planet). Try different starting angles before clicking flag. Can color dots to Plu-Nep distance. "K" for Celtic knot.
Puts dots at the X of one planet and the Y of the other. Traces a (Lissajous) knot, despite planets' orbits being very circular (a bit ovoid). It's like a Celtic knot, but slightly asymmetrical due to planets' relative motions. I discovered all this while playing with my Scratch models. Kathy and I drew the Celtic knot. Patterns depend upon which planet is X and upon the starting angle (yields Lissajous knot variants). Neptune's orbit is 3/2 times faster that of Pluto (Neptune's year is 2/3 as short as Pluto's). Note tones highlight this 3:2 orbital resonance. A higher note plays when Neptune is just North of Sun. Lower note plays when Pluto is North of Sun. Neptune's note has 3/2 the frequency of Pluto's, just as the orbital ratio is 3/2, corresponding to a "perfect fifth." I set the ratio of planets' distances from Sun to be 4/3, which is close to accurate. Spacebar hides variables. Used clones so that I could fade over time at different rates for pen, and each planet. Variant of my project from a few days ago, adding sliders, fading clones, and drawn lines for clarity. That required recoding.
