Darboux evolution is a pretty cool way to morph a curve. Basically, you take a polycurve and find the midpoint of each segment composing that closed polycurve. Create a new polycurve by connecting these midpoints and repeat. It is a simple procedure with pretty nice results. The more iterations, the more the curve begins to resemble an ellipse after a while.
Darboux Evolution by Luis Gil is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.