John D. Cook shared this great curve: [url]http://www.johndcook.com/blog/2015/06/03/mystery-curve/[/url]
exp(it) – exp(6it)/2 + i exp(-14it)/3
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.
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]
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.
Give it a try!
