intothecontinuum:

view GIFs in high-res (700x700) here

Mathematica code:

Table[
 ListAnimate[
  Table[
   Graphics[
    {White, Line[
     Table[
      {-.99^n*Sin[n*a], .99^n*Cos[n*a]},
     {n, 0, 700}]]},
   PlotRange -> 1, ImageSize -> 250, Background -> Black],
 {a, 2 Pi/p, 2 Pi/(p + 1), (2 Pi/(p + 1) - 2 Pi/p)/75}]],
{p, 3, 6, 1}]