Epicycloids and Hypocycloids
Negative frequencies let the circle role inside

The curves are defined by these equations:
c(t) = RR * [ cos(t), sin(t) ] +
sticklength * [ cos(frequency*t), sin(frequency*t)];
The curve and ists tangents are obtained
from a rolling construction.
If sticklength = RR/|frequency| (stick = 1), the curves are called hypocycloids - which roll inside - and epicycloids - which roll outside.
For other sticklengths these curves are called hypotrochoids resp. epitrochoids.