Made in response to a recent question posted at the Mathematica Stack Exchange.

Mathematica code:

`img = ImageCrop@DensityPlot[ Sin[2 x - 20 Log[2 (Sin[y]^2 + 1), 2]], {x, 0, 16 Pi}, {y, 0, 32 Pi}, PlotPoints -> 250, ColorFunction -> "SunsetColors", Frame -> False, ImageSize -> 600]`

LogPolar[x_, y_] := {Log[Sqrt[x^2 + y^2]], ArcTan[x, y]}`d = ImageDimensions[img][[1]]`

Manipulate[ ImageResize[ ImageTransformation[ ImageTake[ img, {1, 14*d/16}, {1 + (2 - 2 t)*d/32, (32 - 2 t)*d/32}], LogPolar[#[[1]], #[[2]]] &, DataRange -> {{-Pi, Pi}, {-Pi, Pi}}], 500], {t, 0, 6/7, 1/7}]