In[]:=
ResourceFunction["NestGraphTagged"][n|->Table[an,{a,5}],1,5]
Out[]=
In[]:=
ResourceFunction["TokenEventGraph"][n|->Table[an,{a,3}],{1},3]
Out[]=
[◼]
TokenEventGraph
[Function[n,Table[an,{a,3}]],{1},3]
In[]:=
TokenEventGraph[{{n_}:>{n+1,n+2}},{1,2},2]
Out[]=
In[]:=
TokenEventGraph[{{n_}:>{n+1},{n_}->{n+2}},{1,2},2]
Out[]=

String Substitution Systems

Enumerate inequivalent rules....
In[]:=
ResourceFunction["EnumerateSubstitutionSystemRules"][{2->2},2]
Out[]=
{{AAAA},{AAAB},{AABB},{ABAA},{ABAB},{ABBA}}
In[]:=
ResourceFunction["MultiwaySystem"][Flatten[ResourceFunction["EnumerateSubstitutionSystemRules"][{2->2},2]],ResourceFunction["StringTuples"]["AB",4],4,"StatesGraph"]//LayeredGraphPlot
Out[]=
In[]:=
Graph3D[ResourceFunction["MultiwaySystem"][Flatten[ResourceFunction["EnumerateSubstitutionSystemRules"][{2->2},2]],ResourceFunction["StringTuples"]["AB",4],5,"StatesGraph"]]
Out[]=
In[]:=
ResourceFunction["MultiwaySystem"][Flatten[ResourceFunction["EnumerateSubstitutionSystemRules"][{2->2},2]],ResourceFunction["StringTuples"]["AB",2],5,"StatesGraph"]
Out[]=
In[]:=
ResourceFunction["MultiwaySystem"][Flatten[ResourceFunction["EnumerateSubstitutionSystemRules"][{2->2},2]],ResourceFunction["StringTuples"]["AB",2],5,"StatesGraph","IncludeEventInstances"->True]
Out[]=
In[]:=
ResourceFunction["EnumerateSubstitutionSystemRules"][{2->2},2]
Out[]=
{{AAAA},{AAAB},{AABB},{ABAA},{ABAB},{ABBA}}

Explicitly complete rule sets

This does not include all cases.... (What about AABA ?) Equivalent under A↔B transformation
In[]:=
Union[Flatten[Outer[Rule,#,#]&[ResourceFunction["StringTuples"]["AB",2]]]]
Out[]=
{AAAA,AAAB,AABA,AABB,ABAA,ABAB,ABBA,ABBB,BAAA,BAAB,BABA,BABB,BBAA,BBAB,BBBA,BBBB}
In[]:=
ResourceFunction["MultiwaySystem"][Union[Flatten[Outer[Rule,#,#]&[ResourceFunction["StringTuples"]["AB",2]]]],ResourceFunction["StringTuples"]["AB",2],4,"StatesGraph"]
?? Related to DeBruijnGraph

What kind of equivalencing picks out a particular rule?

Canonical rules only

Turing Machines

Rulial MW WM ?

https://www.wolframphysics.org/technical-introduction/typical-behaviors/the-number-of-possible-rules/#p-92

Limiting Process

Rules

(Initial conditions)

Time

Given rules up to some size, what does time imply?

What is the significance of the geodesic-ball-dimension in the ruliad?

The Observer

Located at a particular place in rulial space