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John Baez and Jacob Biamonte have mentioned Feynman diagrams several times in their Network Theory series. Part 7 includes a model of interactions between amoebas, using a stochastic Petri net and a Feynman diagram. I've implemented a version of the model as a simple online app.
While running, the app generates the instructions for a Unified Modeling Language (UML) sequence diagram. UML is used by software analysts and developers. UML sequence diagrams specify and capture sequences of runtime interactions between objects over time, also known as histories. The instructions can be fed to the web sequence diagrams online tool which will generate the diagram. My goal in generating these sequence diagrams is to test my sense that Feynman diagrams and UML sequence diagrams have a lot in common, based on my reading of the Network Theory posts.
I'd like to ask this group a few questions:
(1) To those of you who are more familiar with Feynman diagrams, does this UML sequence diagram fill essentially the same function as a Feynman diagram? Does it look similar? What are the similarities and differences?
(2) I know of at least four tools, each with its own syntax, that I could use in place of websequencediagrams.com to draw a sequence diagram. Are there similar tools in the world of Feynman diagrams?
To get a better sense of how similar and different these two diagram types are, I would like to write out two streams of text while the Amoeba app is running. One stream of text would contain instructions to build a sequence diagram - this is what I'm doing now. The other stream would contain instructions to build a Feynman diagram. In both cases the instructions would be in the syntax of a tool that knows how to display that type of diagram. As much as possible, the two streams of instructions should both be written out from the same parts of the code in the Amoeba app. The semantics should be the same, but the syntax would be radically different.
The following is a representative set of instructions, generated by the Amoeba app, that can be fed to the online tool to generate a UML sequence diagram:
title Amoebas Amoeba_2->Amoeba_3: fission Amoeba_2->Amoeba_3: compete Amoeba_2->Amoeba_3: compete destroy Amoeba_3 Amoeba_2->Amoeba_4: fission Amoeba_4->Amoeba_2: compete Amoeba_2->Amoeba_4: compete Amoeba_4->Amoeba_5: fission Amoeba_4->Amoeba_2: compete Amoeba_4->Amoeba_5: compete Amoeba_2->Amoeba_4: compete Amoeba_2->Amoeba_5: compete Amoeba_4->Amoeba_2: compete Amoeba_4->Amoeba_5: compete Amoeba_5->Amoeba_2: compete Amoeba_5->Amoeba_4: compete Amoeba_2->Amoeba_4: compete Amoeba_2->Amoeba_5: compete Amoeba_4->Amoeba_2: compete Amoeba_4->Amoeba_5: compete destroy Amoeba_5 Amoeba_2->Amoeba_4: compete Amoeba_4->Amoeba_2: compete
The diagram generated by the online tool looks like this: