Diamond Illusion

n = 6;
gradient = Graphics[
   Rotate[
    Inset[ContourPlot[y, {x, 0, 1}, {y, 0, 1}, Axes -> None,
      Frame -> None, Contours -> 100, ContourLines -> False,
      ColorFunction -> (GrayLevel[0.1 + #1/1.2] &)], {0, 0}, {0,
      0}, {1, 1}]
    , Pi/4]
   ,
   PlotRange -> {{0.2, 0.7}, {0.2, 0.7}}];
piece = Graphics[{Texture[gradient],
    Polygon[{{0, 0}, {1/2, -1}, {1, 0}, {1/2, 1}},
     VertexTextureCoordinates -> {{0, 0}, {1, 0}, {1, 1}, {0, 1}}]}];
bg = Rasterize[Graphics[
    Table[
     {Translate[
       Inset[piece, {0, 0}, {0, 0}, {2.1, 2.1}], {xshift +
         If[EvenQ[yshift], 0.5, 0], yshift}]},
     {xshift, n}, {yshift, n}
     ]
    , Background -> GrayLevel[0.9],
    PlotRange -> {{2, n + 1}, {1, n + 1}}]];
frame[t_] := Graphics[{Inset[bg, {0, 0}, {0, 0}, n {1.1, 1.1}],
    Translate[
     Inset[piece, {0, 0}, {0, 0}, {2.2, 2.2}], {1.65 + 0.5 t,
      1 + t}]}
   , PlotRange -> {{0, n - 1}, {0, n + 0.5}}];
Manipulate[frame[t], {t, 0, n - 1}]