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grgroup={{1,0}{5,1},{1,1}{5,0},{2,0}{1,0},{2,1}{3,1},{3,0}{1,0},{3,1}{4,1},{4,0}{5,0},{4,1}{2,1},{5,0}{5,0},{5,1}{5,1}};

Show[CellGraphics[NestList[(Last/@Rest[FAStep[grgroup,4,#]])&,PadRight[{1},50],30]]]

⁃Graphics⁃

Show[FAMapSpectrumGraphic[grgroup,5]];

Show[FAMapSpectrumGraphic[grgroup,6]];