Paint can cardioids

As I looked into a nearly empty paint can, I noticed a familiar heart-shaped graph:

I'm used to seeing the cardioid-shaped region of the Mandelbrot set (what my students have sometimes called "the butt crack"), but also noticed it in my Spirograph program, where a family of graphs can be generated that seem similar to the paint can cardioids (or caustics):

You can get the same cardioid graph by drawing a cycloid around a circle of the same diameter (an epicycloid):


  1. [...] the cardioid, whose name comes from it’s heart-like shape, there are some cool graphs out there that [...]


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