Star Slinky
Saw a gif called Star Slinky on Tumblr and that got me playing around with modulated spirals today.
Original link and some of the designs I made with it: http://mathhombre.tumblr.com/post/126374797224/star-slinky-saw-a-gif-called-star-slinky-on-tumblr
You can make the parametric function anything you want, and this sketch uses that for how far to go in the t (as an angle) direction. If your function is t +/- some regular or periodic bit, you get rounded stars. Add a little shift or make the values non-multiples of pi, and you get shifting with each revolution.
More GeoGebra at bit.ly/mh-ggb.