Mathematica is great for producing graphics, but sometimes you have to resort to good old-fashioned Java and Python.
Evolutes of the (2,3) Lissajous curve emerge by computing the unit normal at each point and multiplying by the time. This is a smooth map from the curve to S1. As the curve flows outwards, 6 singularities emerge but eventually only 2 survive. evolutes.m
The billiard flow on regular polygons is throught to be quasi-integrable. Here we have two 200 iterations on some pentagons and a heptagon, generated by a python script. The aliasing in the first image comes from rounding error in my computer program. The orbit should be periodic.
The billard flow is equivalent to the geodesic flow on translation surfaces - flat surfaces with conical singularities.
