Mathematica code:
Ce[r_, k_, N_, n_] := r^n {Cos[2 Pi*k/N], Sin[2 Pi*k/N]}
f[n_, N_] := 2 Pi*n/N
G[op_, P_, c_, d_, r_, N_, s_, t_, IS_] :=
Graphics[
Table[
{Opacity[op],
Rotate[
Disk[
Ce[r, k, N, n],
d*c^n],
f[n, N]*t, {0, 0}]},
{k, 1, N, 1}, {n, 1, s, 1}],
ImageSize -> IS, PlotRange -> P]
ListAnimate[
Table[
G[.175, 1.3, .95, .3, 1, 4, 100, t, 500],
{t, 0, 1, .02}]]