This video shows continuous variation in angle (from 0 to Pi) of the connect-the-dots algorithm while keeping all other parameters fixed. Each instant is a valid 2-coloring.

Music: “Derbyshire” by Nerve

Mathematica code:

Manipulate[
  ImageCrop[
   Graphics[
    GraphicsComplex[
     Table[
      {-(.96)^n*Sin[n*.001 f], .96^n*Cos[n*.001 f]}, 
     {n, 0, 300}],
    Polygon[Table[i, {i, 1, 300, 1}]]], 
  PlotRange -> .1, ImageSize -> 640],
 {640, 480}],
{f, 1, 3145, 1}]