A hypotrochoid generated by a fixed point on a circle rolling inside a fixed circle.
The curves above correspond to values of 
, 0.2, ..., 1.0.
Additional attractive designs such as the one above can also be made by superposing individual spirographs.
The Season 1 episode "Counterfeit Reality" (2005) of the television crime drama NUMB3RS features spirographs when discussing Guilloché patterns.
