In[]:=
With[{t=5},With[{ggg=MultiwayTuringMachine[{{{1,1}{1,0,-1}},{{1,0}{1,0,-1}},{{1,0}{1,1,1}}},{{1,t+1,0},Table[0,2t+1]},t,"StatesGraphStructure",AspectRatio1,GraphLayout"LayeredDigraphEmbedding"]},Graph[ggg,VertexLabels(#->ToExpression[#][[1,3]]&/@VertexList[ggg])]]]
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In[]:=
Table[With[{t=20},MultiwayTuringMachine[{{{1,1}{1,0,-1}},{{1,0}{1,0,-1}},{{1,0}{1,1,1}}},{{1,t+1,0},Table[0,2t+1]},tt,"BranchialGraphStructure"]],{tt,10}]
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
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
In[]:=
With[{t=3},ResourceFunction["BranchialHypergraph"][IndexGraph[MultiwayTuringMachine[{{{1,1}{1,0,-1}},{{1,0}{1,0,-1}},{{1,0}{1,1,1}}},{{1,t+1,0},Table[0,2t+1]},t,"StatesGraphStructure",AspectRatio1,GraphLayout"LayeredDigraphEmbedding"]]]]
Out[]=
{{2,3,6},{2,3,8},{2,3,12},{2,3,14},{2,4,6},{2,4,8},{2,4,12},{2,4,14},{5,7,6,12},{5,7,6,14},{5,7,8,12},{5,7,8,14},{5,7,10,12},{5,7,10,14},{5,7,13,12},{5,7,13,14},{6,8,2},{6,8,5},{6,8,12},{6,8,14},{7,5,8,12},{7,5,8,14},{7,5,9,12},{7,5,9,14},{7,5,11,12},{7,5,11,14},{8,6,2,9},{8,6,2,10},{8,6,2,11},{8,6,2,13},{8,6,5,9},{8,6,5,10},{8,6,5,11},{8,6,5,13},{8,6,7,9},{8,6,7,10},{8,6,7,11},{8,6,7,13},{9,11,7,8},{9,11,7,12},{9,11,7,14},{9,11,10,8},{9,11,10,12},{9,11,10,14},{9,11,13,8},{9,11,13,12},{9,11,13,14},{10,13,5,8},{10,13,5,12},{10,13,5,14},{10,13,9,8},{10,13,9,12},{10,13,9,14},{10,13,11,8},{10,13,11,12},{10,13,11,14},{11,9,7,8},{11,9,7,12},{11,9,7,14},{11,9,10,8},{11,9,10,12},{11,9,10,14},{11,9,13,8},{11,9,13,12},{11,9,13,14},{12,14,2,5},{12,14,2,7},{12,14,2,9},{12,14,2,10},{12,14,2,11},{12,14,2,13},{12,14,6,5},{12,14,6,7},{12,14,6,9},{12,14,6,10},{12,14,6,11},{12,14,6,13},{13,10,5,8},{13,10,5,12},{13,10,5,14},{13,10,9,8},{13,10,9,12},{13,10,9,14},{13,10,11,8},{13,10,11,12},{13,10,11,14},{3,2},{4,2},{14,12,2,5},{14,12,2,7},{14,12,2,9},{14,12,2,10},{14,12,2,11},{14,12,2,13},{14,12,6,5},{14,12,6,7},{14,12,6,9},{14,12,6,10},{14,12,6,11},{14,12,6,13},{1}}
In[]:=
ResourceFunction["WolframModelPlot"][%]
Out[]=
In[]:=
ResourceFunction["WolframModelPlot"][Take[#,UpTo[2]]&/@With[{t=3},ResourceFunction["BranchialHypergraph"][IndexGraph[MultiwayTuringMachine[{{{1,1}{1,0,-1}},{{1,0}{1,0,-1}},{{1,0}{1,1,1}}},{{1,t+1,0},Table[0,2t+1]},t,"StatesGraphStructure",AspectRatio1,GraphLayout"LayeredDigraphEmbedding"]]]]]
Out[]=
Requires 3 rule cases to be nontrivial....