ToFARule[62,{2,2}]
{{1,1}{1,0},{1,0}{2,1},{2,1}{2,1},{2,0}{2,0}}
FAEvolveList[ToFARule[62,{2,2}],1,Table[0,{5}],10]//TableForm
0 | 0 | 0 | 0 | 0 |
1 | 0 | 0 | 0 | 0 |
0 | 1 | 0 | 0 | 0 |
1 | 1 | 0 | 0 | 0 |
0 | 0 | 1 | 0 | 0 |
1 | 0 | 1 | 0 | 0 |
0 | 1 | 1 | 0 | 0 |
1 | 1 | 1 | 0 | 0 |
0 | 0 | 0 | 1 | 0 |
1 | 0 | 0 | 1 | 0 |
0 | 1 | 0 | 1 | 0 |
ToFARule[54,{2,2}]
{{1,1}{1,0},{1,0}{2,1},{2,1}{1,1},{2,0}{2,0}}
FAEvolveList[ToFARule[54,{2,2}],1,Table[0,{5}],10]//TableForm
0 | 0 | 0 | 0 | 0 |
1 | 0 | 0 | 0 | 0 |
0 | 1 | 0 | 0 | 0 |
1 | 1 | 1 | 0 | 0 |
0 | 0 | 0 | 1 | 0 |
1 | 0 | 0 | 1 | 1 |
0 | 1 | 0 | 1 | 0 |
1 | 1 | 1 | 1 | 1 |
0 | 0 | 0 | 0 | 0 |
1 | 0 | 0 | 0 | 0 |
0 | 1 | 0 | 0 | 0 |
GroupQ[rule_]:=Apply[And,Apply[UnsameQ,Table[Cases[rule,({i,_}{_,y_})y],{i,Min[#[[1,1]]&/@rule],Max[#[[1,1]]&/@rule]}],{1}]]
GroupQ[ToFARule[54,{2,2}]]
True
Select[Range[0,255],GroupQ[ToFARule[#,{2,2}]]&]
{17,19,20,22,25,27,28,30,49,51,52,54,57,59,60,62,65,67,68,70,73,75,76,78,97,99,100,102,105,107,108,110,145,147,148,150,153,155,156,158,177,179,180,182,185,187,188,190,193,195,196,198,201,203,204,206,225,227,228,230,233,235,236,238}
Length[%]
64
{#,Table[ElementOrder[ToFARule[#,{2,2}],1,w,10],{w,4}]}&/@%70
{{17,{2,2,2,2}},{19,{2,2,2,2}},{20,{2,2,2,2}},{22,{2,2,2,2}},{25,{2,2,2,2}},{27,{2,2,2,2}},{28,{2,2,2,2}},{30,{2,2,2,2}},{49,{2,2,2,2}},{51,{2,2,2,2}},{52,{2,4,8,LCM[diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}]]}},{54,{2,4,4,8}},{57,{2,2,2,2}},{59,{2,2,2,2}},{60,{2,4,4,8}},{62,{2,4,8,LCM[diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}]]}},{65,{1,1,1,1}},{67,{1,1,1,1}},{68,{1,1,1,1}},{70,{1,1,1,1}},{73,{1,1,1,1}},{75,{1,1,1,1}},{76,{1,1,1,1}},{78,{1,1,1,1}},{97,{1,2,2,2}},{99,{1,2,4,4}},{100,{1,1,1,1}},{102,{1,1,1,1}},{105,{1,2,4,4}},{107,{1,2,2,2}},{108,{1,1,1,1}},{110,{1,1,1,1}},{145,{2,2,2,2}},{147,{2,2,2,2}},{148,{2,4,8,LCM[diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}]]}},{150,{2,4,4,8}},{153,{2,2,2,2}},{155,{2,2,2,2}},{156,{2,4,4,8}},{158,{2,4,8,LCM[diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}],diff[{{1}}]]}},{177,{2,2,2,2}},{179,{2,2,2,2}},{180,{2,2,2,2}},{182,{2,2,2,2}},{185,{2,2,2,2}},{187,{2,2,2,2}},{188,{2,2,2,2}},{190,{2,2,2,2}},{193,{1,2,2,2}},{195,{1,2,4,4}},{196,{1,1,1,1}},{198,{1,1,1,1}},{201,{1,2,4,4}},{203,{1,2,2,2}},{204,{1,1,1,1}},{206,{1,1,1,1}},{225,{1,2,2,2}},{227,{1,2,4,8}},{228,{1,1,1,1}},{230,{1,1,1,1}},{233,{1,2,4,8}},{235,{1,2,2,2}},{236,{1,1,1,1}},{238,{1,1,1,1}}}