WOLFRAM NOTEBOOK

{{1,2}}->{{2,2}}

In[]:=
allrules12=EnumerateWolframModelRules[{{1,2}}{{2,2}}];
In[]:=
Length[allrules12]
Out[]=
73
In[]:=
lens=ParallelMapMonitored[(Length[WeaklyConnectedComponents[Graph[Rule@@@#]]]&/@WolframModel[#,{{0,0}},8,"StatesList"])&,allrules12];
In[]:=
Counts[lens]
Out[]=
{1,1,1,1,1,1,1,1,1}33,{1,1}10,{1,1,2,4,8,16,32,64,128}20,{1,1,1,2,4,8,16,32,64}6,{1,1,3,7,15,31,63,127,255}4
In[]:=
Keys[%]
Out[]=
{{1,1,1,1,1,1,1,1,1},{1,1},{1,1,2,4,8,16,32,64,128},{1,1,1,2,4,8,16,32,64},{1,1,3,7,15,31,63,127,255}}
In[]:=
Counts[ParallelMapMonitored[(Length[WeaklyConnectedComponents[Graph[Rule@@@#]]]&/@WolframModel[#,{{1,2}},8,"StatesList"])&,allrules12]]
Out[]=
{1}15,{1,1,1,1,1,1,1,1,1}27,{1,2,2,2,2,2,2,2,2}1,{1,2,3,5,9,17,33,65,129}4,{1,1,2,4,8,16,32,64,128}16,{1,1,1,2,4,8,16,32,64}6,{1,2,4,8,16,32,64,128,256}4
In[]:=
27+15
Out[]=
42
In[]:=
xlens=ParallelMapMonitored[{#,(Length[WeaklyConnectedComponents[Graph[Rule@@@#]]]&/@WolframModel[#,{{0,0}},8,"StatesList"])}&,allrules12];
In[]:=
First/@GatherBy[xlens,Last]
Out[]=
In[]:=
First/@%124
Out[]=
{{{1,1}}{{1,1},{1,1}},{{1,1}}{{1,2},{1,2}},{{1,2}}{{1,1},{2,3}},{{1,2}}{{2,3},{2,3}},{{1,2}}{{1,3},{2,4}}}
In[]:=
EvolutionPicture2[#,{{0,0}},5]&/@%127
Out[]=
In[]:=
Counts[ParallelMapMonitored[((Sort[Length/@WeaklyConnectedComponents[Graph[Rule@@@#]]])&/@WolframModel[#,{{0,0}},8,"StatesList"])&,allrules12]]
Out[]=
In[]:=
xxlens=ParallelMapMonitored[{#,((Length/@WeaklyConnectedComponents[Graph[Rule@@@#]])&/@WolframModel[#,{{0,0}},8,"StatesList"])}&,allrules12];
In[]:=
First/@GatherBy[xxlens,Last]
Out[]=

{{1,2}}->{{3,2}}

Tracking largest component size

{{2,2}}->{{3,2}}

Larger Rules

Finding a disconnection

Larger case

The {2,2}->{4,2} case

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