Symmetry is merely an expression of how something stands in relation to itself.

Mathematica code:

R[n_] := (SeedRandom[n]; RandomReal[])

Table[
Animate[
 Graphics[
  Table[
   {PointSize[.03], Opacity[Exp[-.8 (Mod[t - 5*R[Q*i], 5])]], 
    Point[
       Table[
        RotationTransform[k*2 Pi/8][{R[Q*2 i], R[Q*2 i + 1]}],
      {k, 0, 7, 1}]]},
   {i, 1, 100, 1}],
  PlotRange -> 1.33, ImageSize -> 500],
 {t, 0, 29/6, 1/6}, AnimationRunning ->False],
{Q, {5, 7, 10, 14}}]