These patterns of sine-cosine intersection are most interesting at whole number ratios, about 1/2, 1/3, 1, 3/2, 2, 2.5, and so on. So watch the patterns at around those ratios. They are called "Lissajous" patterns. You'll see a parabola at 1/3 and 1/5, and see variants of a circle around the ratio of 1. I tried this with a real pendulum with paint and often got the same pattern as with ratio = 1. With a Barton's pendulum I got a pattern that looked like ratio 0.5.
Code redraws the waves after each gradual increase of the ratio of two variables for the x and y coordinates, using the sine and cosine of course. I was inspired by the opening of the 1958 film Vertigo. The title sequence by Saul Bass featured spiraling patterns called Lissajous figures using a pendulum. It looked like the patterns in this project around ratio = 1. But back in 1958 they couldn't animate them like we can now. What I'm showing here I think is a rather complete runthrough of possible Lissajous patterns. Credit: Bernard Hermann composed the score for Vertigo. Here I use a midi version of the title sequence music by Hermann.
