2,2  3,2

In[]:=
rules=Select[Table[RandomWolframModelRule[{{2,2}}{{3,2}}],1000],FullyConnectedRuleQ];
In[]:=
Length[%]
Out[]=
205
In[]:=
res=ParallelMapMonitored[WolframModelTest[#,{{0,0},{0,0}}]&,rules];
In[]:=
cres=FilterConnected[res];
In[]:=
Length[cres]
Out[]=
64
In[]:=
MakePictures2[Select[cres,#["EvolutionObject"]["TerminationReason"]==="MaxVertices"&]]
Out[]=
{},
Clear
Copy

In[]:=
MakePictures2[Select[cres,#["EvolutionObject"]["TerminationReason"]==="MaxEdges"&]]
Out[]=
In[]:=
rules=Select[Table[RandomWolframModelRule[{{2,2}}{{3,2}}],10000],FullyConnectedRuleQ];
In[]:=
Length[%]
Out[]=
2097
In[]:=
res=ParallelMapMonitored[WolframModelTest[#,{{0,0},{0,0}}]&,rules];
In[]:=
cres=FilterConnected[res];
In[]:=
Length[cres]
Out[]=
715
In[]:=
MakePictures2[Select[cres,#["EvolutionObject"]["TerminationReason"]==="MaxVertices"&]]
Out[]=
In[]:=
MakePictures2[Select[cres,#["EvolutionObject"]["TerminationReason"]==="MaxEdges"&]]
Out[]=

Different initial conditions

2,2  4,2

Alternative Initial Conditions

514 to 547 stay connected....
Many fewer stay connected....
514 to 547 stay connected....