Linear Stars
Liked this design in a gif I found for Carnival of Mathematics 108, http://mathhombre.blogspot.com/2014/03/carnival-of-mathematics-108.html, so I had to play around with the underlying ideas. My first try was dilations, http://www.geogebratube.org/material/show/id/94415, which warps the kites much more quickly. (But is still pretty.) This keeps a linear pattern to the points that determine the kites. The spiral effect seems strongest around t=1.5, but I haven't thought much yet about why.