There is something special about rotations of 137.5 degrees.

This is an attempt at replicating Seeds by Jared Tarbell of Levitated and Complexification.

Mathematica code:

d[x_, y_, r_, c_, s_, F_, n_] :=
 {Disk[
    RotationTransform[n*2.4][{x*c^n, y}], r*c^n],
  Table[
   {White,
    Disk[
     RotationTransform[k*2 Pi/F, RotationTransform[n*2.4][{x*c^n, y}]]
     [RotationTransform[n*2.4][{x*c^n, y}] + c^n {r - s, 0}], s*c^n]},
  {k, 0, F - 1, 1}]}

Manipulate[
 ImageCrop[
  Graphics[
   Table[
     d[3, 0, 1 - .1*Sin[t + n*Pi/110]^2, 1.025, .03, 24, n],
   {n, 0, 110, 1}],
  PlotRange -> 30, Background -> Black, ImageSize -> 700],
 {500, 700}],
{t, 0, 39 Pi/40, Pi/40}]

Manipulate[[
 ImageCrop[
  Graphics[
   Table[
     d[3, 0, 1 - .1*Sin[t*3 Pi/40 + n*2 Pi/110]^2, 1.025, .03, 24, n],
   {n, If[t < 66 , 0, 2 (t - 65)], If[t < 56, 2 t, 110], 1}],
  PlotRange -> 30, Background -> Black, ImageSize -> 700],
 {500, 700}],
{t, 0, 120, 1}]