Parametric Equations

In the following graphs, t ranges from 0 to 100 and n is being varied.

In all of the graphs, the curve will have a maximum distance of 1 from the origin. But, in many of the graphs, a circle (smaller than radius of 1) is outlined by the curve with a center at the origin. This interior cirlce will become smaller until n reaches a certain value, and then it expands form just a plain circle of radius 1. After that, a new cycle begins of closing in on the origin and expanding back out. As you can see in the following picture, this parametric curve does not always outline a circle.