A small circle rolls inside a fixed outer circle. The traced path is a hypocycloid. Integer radius ratios produce perfect closed curves.
Parametrically: x=(R−r)cos(t)+r·cos((R−r)t/r), y=(R−r)sin(t)−r·sin((R−r)t/r). When k=R/r is an integer, you get a k-pointed star curve: deltoid (k=3), astroid (k=4), etc. Non-integer ratios create quasi-periodic open curves that eventually fill an annulus.