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TakeLargestByNormal,Last,20
In[]:=
nogrowbits[{k_,r_}]:=nogrowbits[{k,r}]=Complement[Range[k^(2r+1)],Flatten[Position[Tuples[Reverse[Range[0,k-1]],2r+1],{1,0,0}|{0,0,1}]]]
In[]:=
nogrowbits[{3,1}]
Out[]=
{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,27}
In[]:=
ResourceFunction["RandomCA"][{3,1},"Quiescent"->True,"Type"->"Symmetric"]
Out[]=
RuleNumber7440773953329,Colors3
In[]:=
Tuples[{2,1,0},3]
Out[]=
{{2,2,2},{2,2,1},{2,2,0},{2,1,2},{2,1,1},{2,1,0},{2,0,2},{2,0,1},{2,0,0},{1,2,2},{1,2,1},{1,2,0},{1,1,2},{1,1,1},{1,1,0},{1,0,2},{1,0,1},{1,0,0},{0,2,2},{0,2,1},{0,2,0},{0,1,2},{0,1,1},{0,1,0},{0,0,2},{0,0,1},{0,0,0}}
In[]:=
With[{rus=Table[FromDigits[Lookup[Association[Join[Catenate[Map[Thread[#->RandomInteger[2]]&,Keys[KeyDrop[GroupBy[Tuples[{2,1,0},3],Union[{#,Reverse[#]}]&],{{{0,0,0}},{{0,1,0}},{{0,0,1},{1,0,0}},{{0,0,2},{2,0,0}}}]]]],Thread[{{0,0,2},{2,0,0}}->RandomChoice[{0,1}]],Thread[{{0,0,1},{1,0,0}}->RandomChoice[{0,2}]],{{0,1,0}->2,{0,0,0}->0}]],Tuples[{2,1,0},3]],3],100]},ArrayPlot[CellularAutomaton[{#,3,1},{{1},0},20]]&/@rus]
Out[]=
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