p[{x_, y_, z_}, t_] := (
   With[{p2 = 
      RotationMatrix[
        2 Pi t, {0, 0, 1}].RotationMatrix[-2 Pi t, {1, 1, 0}].{x, y, 
        z}},
    p2[[;; 2]]/(p2[[3]] + 2 n + 2)
    ]
   );
n = 5;
frame[t_] := (Graphics[{
     (*PointSize[Medium],*)
     Point[
      Flatten[
       Table[
        p[{x, y, z}, t],
        {x, -n, n},
        {y, -n, n},
        {z, -n, n}],
       2]
      ]
     }
    , PlotRange -> 1.2 {{-1, 1}, {-1, 1}}]);
Manipulate[frame[t],
 {{t, 0.2}, 0, 1}]