Playing a bit with chemlambda, let’s define:
- two types of distributors
described in the first figure.
The blue arrows are compositions of moves from chemlambda. For instance, referring to the picture from above, a graph (or molecule) A is a multiplier if there is a definite finite sequence of moves in chemlambda which transforms the LHS of the first row into the RHS of the first row, and so on.
- any combinator (molecule from chemlambda) is a multiplier; I proved this for the BCKW system in this post,
- the bit is a propagator
- the application node is a distributor of the first kind, because of the first DIST move in chemlambda
- the abstraction node is a distributor of the second kind, because of the second DIST move in chemlambda.
Starting from those, we can build a lot of others.
If is a multiplier and is a propagator then is a multiplier. That’s easy.
From a multiplier and a distributor of the first kind we can make a propagator, look:
From a distributor of the second kind we can make a multiplier.
We can make as well guns, which shoot graphs, like the guns from the Game of Life. Here are two examples:
We can make clocks (which are also shooting like guns):
Funny! Possibilities are endless.