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}]





![intothecontinuum:
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}]](http://25.media.tumblr.com/4be8160470f71bea55bc5dab850dfe40/tumblr_mmb7i9VYqc1qfjvexo1_500.gif)


