Polar Coordinate "Fractal"

thecesspit:
It seems that "trochoid" and "roulette" indeed are the terms for this type of curve. Thank you for finding that out for me!

kubikulann:
Everything I have found has agreed with the notion that only one or two circles are involved in the creation of a trochoid. The original picture had no explanation to it; No formulas, no distances. I did some measuring, estimating, and guessing, and was able to figure out all of the associated radii and rotation speeds for each circle.

I haven't done any "zoomed in" versions of the curve, but want to look into it. I don't expect it to be a fractal per se (with repeating patterns), but I am interested in seeing what is happening near the compass points especially.

I am also working on a bit of a higher resolution, smoother animated gif of the curve, which might not come to fruition due to lack of tools in creating it.

I find it amusing that it is a type of (mathematical) roulette, based on the board you asked the question :)