Try speed Y = 4 and speed X = 3, amplitude X = 200 amplitude Y = 100 also try amplitude X = 133 (results in 4x3 size) Try speed X = 2 and speed Y = 3, amplitude X = 150 amplitude Y = 100 (3x2 in size) Try your own for unique Irish (or Celtic) knots (whole number ratios work best) Two lines oscillate following a sine function. Yellow line goes up and down (Y position) at speed Y. The red line goes sideways (X position) at speed X. When ratio of speed Y to speed X is 4/3, a pattern much like a Celtic knot results. Works well also for ratio of 3/2. Set ratio of amplitude X to amplitude Y is 4/3 to 2. Change ratio of speeds for different patterns. At a ratio 1 you just get a line (change one sine to cosine and you get a circle). Other ratios yield interesting Lissajous figures. Whole number ratios yield knots, meaning the ends are connected. Such knots repeat. Sometimes these are called Lissajous knots. Generates Lissajous patterns of coupled harmonic motion.
These are "Lissajous figures" in a form that looks like Irish or Celtic knot, or "endless knot." They use whole number ratios so ends connect. My earlier version (shared separately) included a drawn background, but this one looks good with only the pen. I varied brightness & saturation with the sine. I change the brightness every third time step to create a rope effect. Pen matches the X position of the red line and the Y of of the yellow line. This generates a type of harmonic motion that creates Lissajous figures. Usually the presentation of Lissajous is complex, with sine or cosine functions, but the underlying principle is simple. Two circling motions can generate these Lissajous patterns.
