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Ed Pegg Jr
This picture starts with the greatest common denominator of the coordinates, then applies a Fourier transform. The complete code for this picture is as follows: With[{n = 512}, ListDensityPlot[ Abs[ Fourier[ Table[ GCD[i, j], {i,n}, {j, n}]]], ColorFunction -> Hue, Mesh -> False, Frame -> False]]



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