I${}^{*}$ have randomly come across a couple of websites (Chemlambda project, chorasimilarity) that seem to be about a certain "thing" (a computer program, I think) called Chemlambda that does "stuff" with some kind of decorated graphs called *molecules* according to some "rules".

${}^*$ Disclaimer: I don't know anything about computer science, computability theory, rewriting systems, distributed computing, or the like.

Chemlambda molecules look more or less like this:

and can make up much more complicated shapes:

*Looks* cool, doesn't it?

Also, there are links to very cool looking youtube videos which show such decorated graphs in action, such as this one or this one, and a gallery of videos perhaps trying to explain some elementary Chemlambda "operations". Notice that the title of one of the youtube videos contains "factorial of $4$", so it seems to suggest that some kind of computation is being performed...

Question 0.Does all this contain some legitimate and/or interesting maths ̶o̶r̶ ̶i̶s̶ ̶i̶t̶ ̶b̶u̶l̶l̶s̶h̶i̶t̶ ?

There are some articles on the arXiv authored by M. Buliga, such as this one or this one, that are relevant to the topic. Notice that the second linked article is coauthored with L.H. Kauffman, who is a well known mathematician (for reasons unrelated to this project).

Question 1.What is Chemlambda?

Provided the definitions on which it is based are mathematically sound/rigorous, I would like to roughly understand *what* this program does with such decorated graphs and *why* it would be interesting (from the point of view of mathematical logic, or more generally of mathematics) to consider such kind of operations with decorated graphs. Skimming through the websites and the articles, I wasn't able to *precisely* understand what the point of Chemlambda is, besides providing cute animations:

Question(s) 2.As far as I -kind of- understand, Chemlambda graphically models $\lambda$-calculus, so it's suitable for computation. Why would one want to encode computations graphically? Does it provide any conceptual insights or practical advantages? How are, roughly, inputs encoded and the output read off the resulting molecules? Are the operations on molecules performed deterministically or randomly? If randomly,how?