A lot of material has accumulated, it is time to start assembling the puzzle.
Let’s look first what we have:
- an artificial chemistry – chemlambda or chemical concrete machine, which is a purely local graph rewrite system, Turing universal
- a model of distributed, decentralized computation based on chemlambda – Distributed GLC
- another purely local graph rewrite system, described in the post The graphical moves of projective conical spaces (II), which makes the link with emergent algebras as described in the triple of posts
- there is also this maybe mysterious pair of posts: Parallel transport in spaces with dilations, I and What group is this? (Parallel transport in spaces with dilations, II)
- finally, recall the extended beta move, which is equivalent with the pair of moves :
These are the pieces of the puzzle.
Today I want to show you that the extended beta move can be done in a formalism which is made by chemlambda with dilation nodes added, and with the local emergent algebra moves added.