view GIFs in hi-res here (700x700)
Mathematica code:
F[a_, L_, r_, s_, t_] :=
Table[
{-(r + s*Cos[t])^n*Sin[n*a], (r + s*Cos[t])^n*Cos[n*a]}, {n, 0, L}]
V :=
{{1.45631, 556, .995, .003}, {2.94712, 502, .998, .001},
{4.50891, 485, .9955, .0025}, {4.9367, 630, .997, .002}}
Table[
ListAnimate[
Table[
Graphics[
Polygon[
F[Part[Part[V, G], 1], Part[Part[V, G], 2], Part[Part[V, G], 3], Part[Part[V, G], 4], t]],
PlotRange -> 1, ImageSize -> 250],
{t, 0, 2 Pi, 2 Pi/40}]],
{G,1,4,1}