When a quadrilateral undergoes a certain infinite folding process, an intricate curve is traced out by its transformed vertices. The curve possesses attractive symmetry properties. We study the folding as a dynamical system in $\C^4$, which is partially described by a billiard-like dynamical system on the bounded component of an elliptic curve associated with the squared diagonal lengths.
"The dynamics of quadrilateral folding." Experiment. Math. 2 (3) 209 - 222, 1993.