SetDirectory@NotebookDirectory[];
QuantizeBits[x_,bits_,dither_:0]:=Clip[Round[x*(Power[2,bits]-1)+dither]/(Power[2,bits]-1)]
remaptri[v_]=({{\[Piecewise], ({{(Sqrt[2v])-1, v≤1/2}, {1-(Sqrt[2-2v]), v>1/2}})}});

SampleArrayWithWrap[arr_,x_,y_]:=Module[{dims=Dimensions[arr]},arr[[Mod[x,dims[[1]],1],Mod[y,dims[[2]],1]]]]
origSignal = Table[x/128,{y,0,127},{x,0,127}];
ArrayPlot[origSignal,ColorFunction->GrayLevel]

ArrayPlot[QuantizeBits[#1,3]&/@origSignal,ColorFunction->GrayLevel]

ditheredWhite=Map[QuantizeBits[#1,3,RandomReal[]-0.5]&,origSignal,{2}];
ArrayPlot[ditheredWhite,ColorFunction->GrayLevel]

ArrayPlot[Map[QuantizeBits[#1,3,(RandomReal[]-0.5)*2]&,origSignal,{2}],ColorFunction->GrayLevel]

ArrayPlot[Map[QuantizeBits[#1,3,(RandomReal[]+RandomReal[]-1)]&,origSignal,{2}],ColorFunction->GrayLevel]

Bayer[x_,y_,level_]:=Mod[Mod[BitShiftRight[x,level],2]+1+2*Mod[BitShiftRight[y,level],2],4]+If[level==0,0,4*Bayer[x,y,level-1]]
bayer3=Table[Bayer[x,y,2],{y,0,7},{x,0,7}]/63;
bayer6=Table[Bayer[x,y,5],{y,0,63},{x,0,63}]/(64*64-1);

ditheredBayer=MapIndexed[QuantizeBits[#1,3,SampleArrayWithWrap[bayer3,#2[[1]],#2[[2]]]-0.5]&,origSignal,{2}];

ArrayPlot[bayer3,ColorFunction->GrayLevel]

ArrayPlot[ditheredBayer,ColorFunction->GrayLevel]

InterleavedGradientNoise[x_,y_]:=FractionalPart[52.9829189*FractionalPart[0.06711056*x+0.00583715*y]]

ArrayPlot[Table[InterleavedGradientNoise[x,y],{y,0,63},{x,0,63}]]

ditheredInterleaved=MapIndexed[QuantizeBits[#1,3,InterleavedGradientNoise[#2[[1]],#2[[2]]]-0.5]&,origSignal,{2}];
ArrayPlot[ditheredInterleaved,ColorFunction->GrayLevel]

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ArrayPlot[blueNoise64,ColorFunction->GrayLevel]

ditheredBlue=MapIndexed[QuantizeBits[#1,3,SampleArrayWithWrap[blueNoise64,#2[[1]],#2[[2]]]-0.5]&,origSignal,{2}];
ArrayPlot[ditheredBlue,ColorFunction->GrayLevel]

GraphicsGrid[{{ArrayPlot[ditheredWhite,ColorFunction->GrayLevel],ArrayPlot[ditheredBlue,ColorFunction->GrayLevel]},{ArrayPlot[ditheredBayer,ColorFunction->GrayLevel],ArrayPlot[ditheredInterleaved,ColorFunction->GrayLevel]}}]
Export["2dditheringalltechniquescompared.gif",{ArrayPlot[ditheredWhite,ColorFunction->GrayLevel],ArrayPlot[ditheredBlue,ColorFunction->GrayLevel],ArrayPlot[ditheredBayer,ColorFunction->GrayLevel],ArrayPlot[ditheredInterleaved,ColorFunction->GrayLevel]},"DisplayDurations"->2];

Export["2dditheringquandizecomparisongrid.png",GraphicsGrid[{{ArrayPlot[ditheredWhite,ColorFunction->GrayLevel],ArrayPlot[ditheredBlue,ColorFunction->GrayLevel]},{ArrayPlot[ditheredBayer,ColorFunction->GrayLevel],ArrayPlot[ditheredInterleaved,ColorFunction->GrayLevel]}}]];

ListAnimate[{ArrayPlot[Abs[ditheredWhite-origSignal],ColorFunction->GrayLevel],ArrayPlot[ditheredWhite,ColorFunction->GrayLevel],ArrayPlot[origSignal,ColorFunction->GrayLevel]}]

Export["2dditheringwhitebands.gif",{ArrayPlot[Abs[ditheredWhite-origSignal],ColorFunction->GrayLevel],ArrayPlot[ditheredWhite,ColorFunction->GrayLevel],ArrayPlot[origSignal,ColorFunction->GrayLevel]},"DisplayDurations"->2];

MyTwoDimPeriodogram[arr_]:=ArrayPlot[Abs[RotateLeft[Fourier[arr],Dimensions[arr]/2]],ColorFunction->GrayLevel]

MyTwoDimPeriodogram[bayer6-0.5]

ArrayPlot[Log[0.01+Abs[RotateLeft[Fourier[bayer6-0.5],Dimensions[bayer6]/2]]],ColorFunction->GrayLevel]

MyTwoDimPeriodogram[Table[InterleavedGradientNoise[x,y],{y,0,63},{x,0,63}]-0.5]
ListPlot3D[Abs[RotateLeft[Fourier[Table[InterleavedGradientNoise[x,y],{y,0,63},{x,0,63}]-0.5],{32,32}]],PlotRange->{0,2},ColorFunction->"Rainbow"]

MyTwoDimPeriodogram[blueNoise64-0.5]

ListPlot3D[Abs[RotateLeft[Fourier[blueNoise64-0.5],Dimensions[bayer6]/2]],ColorFunction->"Rainbow"]

ListAnimate[{MyTwoDimPeriodogram[blueNoise64-0.5],MyTwoDimPeriodogram[Table[RandomReal[],{x,0,63},{y,0,63}]-0.5]}]

Export["2dwhitenoisevsbluenoise.gif",{MyTwoDimPeriodogram[blueNoise64-0.5],MyTwoDimPeriodogram[Table[RandomReal[],{x,0,63},{y,0,63}]-0.5]},"DisplayDurations"->2];

ListAnimate[{ArrayPlot[ditheredWhite,ColorFunction->GrayLevel],ArrayPlot[ditheredBlue,ColorFunction->GrayLevel]}]

Export["2dwhitenoisevsbluenoise.gif",{ArrayPlot[ditheredWhite,ColorFunction->GrayLevel],ArrayPlot[ditheredBlue,ColorFunction->GrayLevel]},"DisplayDurations"->2];

GraphicsRow[{GaussianFilter[Image[ditheredWhite],2],GaussianFilter[Image[ditheredBlue],2]}]

ListAnimate[{ArrayPlot[Map[QuantizeBits[#1,3,(RandomReal[]+RandomReal[]-1)]&,origSignal,{2}],ColorFunction->GrayLevel],ArrayPlot[MapIndexed[QuantizeBits[#1,3,remaptri[SampleArrayWithWrap[blueNoise64,#2[[1]],#2[[2]]]]]&,origSignal,{2}],ColorFunction->GrayLevel]}]

Export["2dwhitenoisevsbluenoisetriangle.gif",{ArrayPlot[Map[QuantizeBits[#1,3,(RandomReal[]+RandomReal[]-1)]&,origSignal,{2}],ColorFunction->GrayLevel],ArrayPlot[MapIndexed[QuantizeBits[#1,3,remaptri[SampleArrayWithWrap[blueNoise64,#2[[1]],#2[[2]]]]]&,origSignal,{2}],ColorFunction->GrayLevel]},"DisplayDurations"->2];

ditheredInterleavedRemap=MapIndexed[QuantizeBits[#1,3,remaptri[InterleavedGradientNoise[#2[[1]],#2[[2]]]]]&,origSignal,{2}];

ditheredBayerRemap=MapIndexed[QuantizeBits[#1,3,remaptri[SampleArrayWithWrap[bayer3,#2[[1]],#2[[2]]]]]&,origSignal,{2}];
ditheredWhiteRemap=Map[QuantizeBits[#1,3,remaptri[RandomReal[]]]&,origSignal,{2}];

ditheredBlueRemap=MapIndexed[QuantizeBits[#1,3,remaptri[SampleArrayWithWrap[blueNoise64,#2[[1]],#2[[2]]]]]&,origSignal,{2}];

GraphicsGrid[{{ArrayPlot[ditheredWhiteRemap,ColorFunction->GrayLevel],ArrayPlot[ditheredBlueRemap,ColorFunction->GrayLevel]},{ArrayPlot[ditheredBayerRemap,ColorFunction->GrayLevel],ArrayPlot[ditheredInterleavedRemap,ColorFunction->GrayLevel]}}]

Export["2dditheringallfourcomparedtriangular.gif",{ArrayPlot[ditheredWhiteRemap,ColorFunction->GrayLevel],ArrayPlot[ditheredBlueRemap,ColorFunction->GrayLevel],ArrayPlot[ditheredBayerRemap,ColorFunction->GrayLevel],ArrayPlot[ditheredInterleavedRemap,ColorFunction->GrayLevel]},"DisplayDurations"->2];