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}}]