John D. Cook shared this great curve: [url]http://www.johndcook.com/blog/2015/06/03/mystery-curve/[/url]
[math]e^{it} – e^{6it}/2 + i e^{-14it}/3[/math]
from the book Creating Symmetry: The Artful Mathematics of Wallpaper Patterns by Frank Farris.
I converted it to parametric, and was immediately wowed by the possible variations. Give it a try!