Our goal is that you can define domain-specific Style files--analogous to a .sty in LaTeX--that apply to whatever field of mathematics you want. We have prototyped this but there are still too many rough edges to recommend to outside users at this point.

Flowcharts are not on our initial list of domains, but we hope that the infrastructure will let any user add a Style extension to support them.

Might depend on what they've implemented so far. The simplex in figure 2 from the paper looks a lot like some of the simplex plots seen in Keenan Crane's work here: https://www.cs.cmu.edu/~kmcrane/

And the authors have at least that connection to the ``Carnegie Mellon Geometry Collective,'' (see their prior work on his page) so I'd include discrete differential geometry in your list. This has connections (eh hem) all over...

Edit: For some reason I missed the Penrose site at the link and skipped straight to the PDF short introduction. I am presenting somewhat redundant information above. Sorry!

From their paper, it seems you can write a 'style' file for anything you can possibly want. Users then write the declarative code you see which Penrose interprets with respect to that 'style' file to know what to actually do.

this is the exciting part to me; is there any constraint that the output has to be a 2-dimensional figure? I could imagine a style file that outputs a blender scene with a time dimension, or a VR scene that you can interact with in the same way they describe dragging one of the vector heads and having it recalculate the rest of the model.