Graphics in Notebook Different from Graphics Expression?

Question

Consider the expression

TreeForm[a+b^2+c^3+d]

which displays as

This is a nice Graphics object, as I can prove by typing //FullForm after it, like this

and getting

Graphics[Annotation[
  GraphicsComplex[
   List[List[1.29777, 1.29777], List[0., 0.648886], 
   List[0.648886, 0.648886], List[0.324443, 0.], List[0.973329, 0.], 
   List[1.94 
... 
    List[Tooltip[
      Inset[Framed[Style[Plus, "StandardForm", "Output", Rule[LineColor, 

It has framed elements in it, as I can prove by either looking at the text above, or by typing

But, the TreeForm expression itself does not have any framed elements in it. For instance

TreeForm[a+b^2+c^3+d] /. (x_Framed :> Print[x])

produces the original graphic

Somehow, the Notebook is not allowing me to capture and rewrite the expression form of the graphic -- the only way I know to access it is by cutting and pasting the graphical form of the object manually by mouse into the places where I need to manipulate it. This is no good. I need SecretEvaluator, such that

SecretEvaluator[TreeForm[a+b^2+c^3+d]] /. (x_Framed :> Print[x])

produces the same output as

Answer 1

The reason your original code fails is that the TreeFrom object is only formatted as Graphics object, meaning that it converted for display rather that as part of the normal evaluation sequence.

You can convert to and from box form to recover your Graphics object:

tf = TreeForm[a + b^2 + c^3 + d];

gr = tf // ToBoxes // ToExpression

gr /. (x_Framed :> Print[x]);

Answer 2

From this answer

Network`GraphPlot`ExprTreePlot[a+b^2+c^3+d] /. (x_Framed :> Print[x])

Answer 3

Building on swish's answer, I would write

nodes = Cases[Network`GraphPlot`ExprTreePlot[a + b^2 + c^3 + d], _Framed, ∞];

This has the advantage of allowing you to work with the individual node objects; for example:

nodes[[2]]

If want output that looks like your printed output just evaluate

Column@nodes