Animated GIF (700x700)

• Choose 300 random points in some region of the plane over some time interval.

• For each point, create 7 copies obtained by consecutive rotations around the origin by 45º.

• Let each set of 8 points decrease exponentially in opacity starting at some random time in that interval.

In the animation above the time interval loops about every 3 seconds, and there are 2400 points in total.

Mathematica code:

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

Animate[
 Graphics[
  Table[
   {PointSize[.015], Opacity[Exp[-.8 (Mod[t - 5*R[14*i], 5])]], 
    Point[
       Table[
        RotationTransform[k*2 Pi/8][{R[14*2 i], R[14*2 i + 1]}],
      {k, 0, 7, 1}]]},
   {i, 1, 300, 1}],
  PlotRange -> 1.4, ImageSize -> 500],
 {t, 0, 29/6, 1/6}, AnimationRunning ->False]