In[]:=
ArrayPlot[#,ColorRules->{0->White,1->Lighter[Orange],2->Darker[Orange]}]&@ResourceFunction["BlockCellularAutomaton"][{{2,2}{1,1},{1,1}{2,2},{1,2}{1,2},{2,1}{2,1},{2,0}{0,2},{1,0}{1,0},{0,2}{2,0},{0,1}{0,1},{0,0}{0,0}},RandomChoice[{0,2},200],400]
Out[]=
In[]:=
ResourceFunction["BlockCellularAutomaton"][{{2,2}{1,1},{1,1}{2,2},{1,2}{1,2},{2,1}{2,1},{2,0}{0,2},{1,0}{1,0},{0,2}{2,0},{0,1}{0,1},{0,0}{0,0}},RandomChoice[{0,2},200],400]//Last
Out[]=
{2,2,2,2,0,1,1,0,2,0,0,1,1,2,0,2,2,0,1,2,2,1,0,2,2,0,0,0,0,2,2,2,0,2,2,0,2,0,0,0,0,0,0,1,1,2,0,2,0,2,0,0,2,0,0,0,2,0,1,1,1,1,0,2,1,1,0,0,0,2,0,0,0,2,0,0,0,0,0,2,0,0,0,0,0,0,2,2,2,0,0,2,2,0,0,2,0,0,0,0,0,0,0,0,0,0,2,0,0,0,2,1,2,2,2,2,2,2,1,2,0,0,1,1,1,1,0,0,2,0,0,0,0,0,0,0,0,1,1,0,2,2,2,2,0,1,2,2,1,0,0,2,0,0,0,0,2,0,0,2,0,2,2,2,0,0,2,0,0,2,0,0,0,2,2,0,0,1,1,2,0,0,2,2,0,0,1,1,0,0,2,2,2,0,2,0,1,1,0,2}
In[]:=
ArrayPlot[#,ColorRules->{0->White,1->Lighter[Orange],2->Darker[Orange]}]&/@Partition[ResourceFunction["BlockCellularAutomaton"][{{2,2}{1,1},{1,1}{2,2},{1,2}{1,2},{2,1}{2,1},{2,0}{0,2},{1,0}{1,0},{0,2}{2,0},{0,1}{0,1},{0,0}{0,0}},ReplacePart[RandomChoice[{0,2},300],Table[i->2,{i,135,165}]],800],400]
Out[]=

,

In[]:=
ArrayPlot[#,ColorRules->{0->White,1->Lighter[Orange],2->Darker[Orange]}]&/@Partition[ResourceFunction["BlockCellularAutomaton"][{{2,2}{1,1},{1,1}{2,2},{1,2}{1,2},{2,1}{2,1},{2,0}{0,2},{1,0}{1,0},{0,2}{2,0},{0,1}{0,1},{0,0}{0,0}},With[{h=1},Join[RandomChoice[{0,2},150-h],Flatten[{1,2,Table[0,2h],1}],RandomChoice[{0,2},150-h]]],800],400]
Out[]=

,

In[]:=
Join[{{1}},Table[Flatten[{1,2,Table[0,n],1}],{n,0,5}]]
Out[]=
{{1},{1,2,1},{1,2,0,1},{1,2,0,0,1},{1,2,0,0,0,1},{1,2,0,0,0,0,1},{1,2,0,0,0,0,0,1}}
Join[{{1}},Table[Flatten[{1,2,Table[0,n],1}],{n,0,5}]]