Type 2) form constant: spiral

Mathematica code:

Diagonals[t_] :=
 ImageCrop[
   DensityPlot[
     Cos[x + y - t*Pi/5],
   {x, -20 Pi, 20 Pi}, {y, -20 Pi, 20 Pi},
   PlotPoints -> 100, Mesh -> False, Frame -> False, 
   ColorFunction -> GrayLevel, ImageSize -> 522],
 500]

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

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

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