John D. Cook shared this great curve: [url]http://www.johndcook.com/blog/2015/06/03/mystery-curve/[/url][br]exp(it) – exp(6it)/2 + i exp(-14it)/3[br]from the book Creating Symmetry: The Artful Mathematics of Wallpaper Patterns by Frank Farris.[br][br]I converted it to parametric, and was immediately wowed by the possible variations. [br][br]Brent Yorgey wrote about this curve today, too, with a nice gallery of variations. [url]http://mathlesstraveled.com/2015/06/04/random-cyclic-curves-5/[/url][br]He had the great idea to parameterize the values of the coefficients as well. That's a_2, b_2 and c_2 in the sketch. Great effects.[br][br]Give it a try!

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