log-polar transforms

shown with increasing wave amplitude from top to bottom

Mathematica code:

WfPlot[ s_, t_] :=
 Graphics[
  Table[
   {AbsoluteThickness[1.5], 
    Line[
     Table[
      {i + If[Mod[i, 2] == 0, s*Sin[j*2 Pi/66 + i*2 Pi/6 + t], 0],
       (-1)^i*.5 + .4*j},
     {i, 1, 19}]]},
   {j, 1, 69, 1}],
  PlotRange -> {{1, 19}, {.8, 27.2}}, 
  ImageSize -> {500, 500}]

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

Manipulate[
  ImageTransformation[
   WfPlot[s, t],
  LogPolar[#[[1]], #[[2]]] &, DataRange -> {{-Pi, Pi}, {-Pi, Pi}}],
{s, 0, 1}, {t, 0, 2Pi}]