Type 4) form constant: square lattice

Mathematica code:

SquareLattice[t_] :=
 Graphics[{
   Table[
     Rectangle[{i + t, j + t}],
    {i, -2, 42, 2}, {j, -2, 42, 2}],
   Table[
    Rectangle[{i + 1 + t, j + 1 + t}],
    {i, -2, 42, 2}, {j, -2, 42, 2}]},
  PlotRange -> {{0, 40}, {0, 40}}, ImageSize -> 500]

ListAnimate[
  Table[
    SquareLattice[t],
  {t, 0, .9, .1}]]

f[x_, y_] := {Log[Sqrt[(x)^2 + (y)^2]], ArcTan[x, y]}

ListAnimate[
  Table[
   ImageTransformation[
     SquareLattice[t],
   f[#[[1]], #[[2]]] &, DataRange -> {{-Pi, Pi}, {-Pi, Pi}}],
  {t, 0, .9, .1}]]