Fibonacci

[ From -01 ]
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Clear[f]
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f[n_]:=f[n-1]+f[n-2]
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f[1]=f[2]=1;
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ResourceFunction["TraceGraph"][f[8],_f]
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In[]:=
Graph[EdgeList[ResourceFunction["TraceGraph"][f[10],_f]],GraphLayout->"LayeredDigraphEmbedding"]
Out[]=
In[]:=
LineGraph[EdgeList[ResourceFunction["TraceGraph"][f[10],_f]],GraphLayout->"LayeredDigraphEmbedding"]
Out[]=
In[]:=
ResourceFunction["TraceGraph"][f[8],HoldPattern[_f+_f]]
Out[]=
In[]:=
ResourceFunction["TraceGraph"][f[8],_f|HoldPattern[_f+_f]]
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In[]:=
ResourceFunction["TraceGraph"][f[8],_Integer|_f|HoldPattern[_f+_f]]
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(in here, e.g. f[6] subtrees are all the same...)
Each layer has Fibonacci[t] nodes [with breadth-first evaluation]

Factorial

Multiply recursive

Each event here is the evaluation of f[n] in terms of its RHS....
Include no indirect calls:

General Operation of Evaluator

Take defined transformations, and apply them by substitution

Trivial Spatially Extended

Multievaluation

This represents all evaluation orders......

Fibonacci

Factorial

Combinators

Simpler Multiway Evaluation

String-Based Evaluator...