High-res: 800x800

Mathematica code:

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

ImageTransformation[
ImageCrop[
DensityPlot[
Sum[Cos[(Cos[n*2*Pi/5] + Sin[n*2*Pi/5])* x + (Cos[n*2*Pi/5] - Sin[n*2*Pi/5])*y],
{n, 0, 4, 1}], {x, -125, 125}, {y, -125, 125},
PlotPoints -> 200, Mesh -> False, Frame -> False,
ColorFunction -> GrayLevel, ImageSize -> 834],
800],
f[#[[1]], #[[2]]] &, DataRange -> {{-Pi, Pi}, {-Pi, Pi}}]