Ready.
In the following text box, there is the include file I use to prepare my Petri net graphs with POV-Ray. You may copy it to the clipboard and save it on your harddisk, with the name "petri.inc", later to be included in the scene-rendering *.pov files.
I crafted it POV-Ray version 3.1, which says the macros are a new feature with it. POV-ray is freeware, and you may download it for a variety of platforms.
I am planning to improve this further, while using it. Currently, it may take a few trial-and-errors to set the figures as desired. I may consider to make it more automatized.
And here is an example usage of it. You may save the text in the next box in a file with pov extension, e.g: "pn_kitable.pov". POV-Ray for windows generates a bmp file. I later convert that to the png (Protable Network Graphics) format, for it to take less space.
You may also render the graph and the token set separately. That way, on a web page, different token sets may be put on a layer over the graph, interactively with the user.