Nested Stars
I love rotationally symmetric patterns on a circle! (See the previous http://www.geogebratube.org/material/show/id/57320, or http://www.geogebratube.org/material/show/id/116885, or http://www.geogebratube.org/material/show/id/55541...)
This came from experiments thinking about how to nest expanding patterns of what I think of as polystars. It has p levels, where the kth level has n*k vertices, and poly lines that move through skipping 1 to m vertices for its edges.