2,34,3

In[]:=
rules=Table[RandomWolframModelRule[{{2,3}}{{4,3}}],5000];
In[]:=
Select[rules,LeftConnectedRuleQ];
In[]:=
Length[%]
Out[]=
2618
In[]:=
res=ParallelMapMonitored[WolframModelTest[#,Table[{0,0,0},2]]&,%372];
In[]:=
cres=FilterConnected[res];
In[]:=
Length[cres]
Out[]=
495
In[]:=
495/2618.
Out[]=
0.189076
In[]:=
263/495.
Out[]=
0.531313
In[]:=
Counts[#["EvolutionObject"]["TerminationReason"]&/@cres]
Out[]=
MaxVertices135,FixedPoint263,MaxVertexDegree97
In[]:=
MakePicturesGS[Select[cres,#["EvolutionObject"]["TerminationReason"]=!="FixedPoint"&]]
Out[]=

3,34,3

3,35,3

2,43,4