A Dynamical System on Polygons:
Start with an initial configuration of points z_1, z_2, ..., z_n.
Perform a flip in the following way: choose a point z_j at random. Draw the perpendicular bisector of its two neighboring points, and reflect z_j across this line.
This defines an operation on the configuration of points.
This python script visualizes the behavior of this operation on any initial configuration.