"It is by manipulating on paper, or in the fancy, formulæ or other diagrams — experimenting on them, experiencing the thing. Such experience alone evolves the reason hidden within us and as utterly hidden as gold ten feet below ground — and this experience only differs from what usually carries that name in that it brings out the reason hidden within and not the reason of Nature, as do the chemist's or physicist's experiments." [CP 4.86]
This not to say diagrammatic thinking is necessarily experimental. Any of Peirce's means of fixing beliefs — tenacity, authority, discussion, and/or experimentation — can be used to measure the consequences being inferred from a diagram, and thereby assess the diagram itself. Even within the experimental means there are any number of criteria — truth, utility, beauty, goodness — that can be and have been applied. This is just to say there is a measure in using the diagram that has a bearing on the structuring of the diagram itself.