In[]:=
ResourceFunction["NestGraphTagged"][n|->Table[an,{a,5}],1,5]
Out[]=
In[]:=
ResourceFunction["TokenEventGraph"][n|->Table[an,{a,3}],{1},3]
Out[]=
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
String Substitution Systems
Enumerate inequivalent rules....
In[]:=
ResourceFunction["EnumerateSubstitutionSystemRules"][{2->2},2]
Out[]=
{{AAAA},{AAAB},{AABB},{ABAA},{ABAB},{ABBA}}
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[]=
{{AAAA},{AAAB},{AABB},{ABAA},{ABAB},{ABBA}}
Explicitly complete rule sets
Explicitly complete rule sets
This does not include all cases.... (What about AABA ?) Equivalent under A↔B transformation
In[]:=
Union[Flatten[Outer[Rule,#,#]&[ResourceFunction["StringTuples"]["AB",2]]]]
Out[]=
{AAAA,AAAB,AABA,AABB,ABAA,ABAB,ABBA,ABBB,BAAA,BAAB,BABA,BABB,BBAA,BBAB,BBBA,BBBB}
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?
What kind of equivalencing picks out a particular rule?
Canonical rules only
Canonical rules only
Turing Machines
Turing Machines
Rulial MW WM ?
Rulial MW WM ?
https://www.wolframphysics.org/technical-introduction/typical-behaviors/the-number-of-possible-rules/#p-92
Limiting Process
Limiting Process
Rules
Rules
(Initial conditions)
(Initial conditions)
Time
Time
Given rules up to some size, what does time imply?
Given rules up to some size, what does time imply?
What is the significance of the geodesic-ball-dimension in the ruliad?
What is the significance of the geodesic-ball-dimension in the ruliad?
The Observer
The Observer
Located at a particular place in rulial space
Located at a particular place in rulial space