Evaluate everything in this notebook...
Clear[RasterGraphics]
PixelPerfect[state_,colors_:2,size_:1]:=With[{dim=Reverse[Dimensions[state]]},Graphics[Raster[Reverse[1-state/(colors-1)]],AspectRatio->Automatic,PlotRange->{{0,dim[[1]]},{0,dim[[2]]}},ImageSize->size*dim+1]]
fa={{1,1}{1,0},{1,0}{2,1},{2,1}{2,1},{2,0}{1,0}};
FAApply[rule_,init_,list_]:=FoldList[{First[#1],#2}/.rule&,{init},list]
FAApply[rule_,s0_,list_]:=FoldList[{First[#1],#2}/.rule&,{s0},list]
FAStep[rule_,s0_,list_]:=Map[Last,Rest[FoldList[{First[#1],#2}/.rule&,{s0},list]]]
FAEvolveList[rule_,s0_,init_,t_]:=NestList[FAStep[rule,s0,#]&,init,t]
RasterGraphics[data_,lab_]:=Graphics[Raster[1-Reverse[data]],AspectRatioAutomatic,PlotLabellab]
Show[RasterGraphics[FAEvolveList[fa,1,Table[0,{100}],60]]];
PixelPerfect[FAEvolveList[fa,1,Table[0,{100}],60],2,3]//Show
⁃Graphics⁃
Export["H:/NewScience/FollowOnWork/Grigorchuk/ForumPost-01/automaton-60.gif",%29]
H:/NewScience/FollowOnWork/Grigorchuk/ForumPost-01/automaton-60.gif
ToFARule[n_Integer,{s_Integer,k_Integer}]:=Flatten[MapIndexed[{1,-1}#2+{0,k}Mod[Quotient[#1,{k,1}],{s,k}]+{1,0}&,Partition[IntegerDigits[n,sk,sk],k],{2}]]
RasterGraphics[data_,lab_]:=Graphics[Raster[1-Reverse[data]],AspectRatioAutomatic,PlotLabellab]
Show[GraphicsArray[Partition[Table[RasterGraphics[FAEvolveList[ToFARule[i,{2,2}],1,Table[0,{40}],30],i],{i,0,255}],8]]];
A simple heuristic to find "interesting" cases: