See also
This is vague. It would need to be made precise to be interesting. I’m thinking of hyperbolic and other non-euclidean geometries and wondering about them.
To consider- a continuous L-System Model, where you attach nodes to other nodes at a given rate. What mean density does that produce? What kind of attachment mechanisms are plausible? Could you mine patent networks or theorem networks to parameterise a stochastic process for this model which made it a plausible model for theorem growth? If not, what quality does knowledge posses which this could not encapsulate? (See also Design grammars)
Can we revert to technology as being an environment, albeit, maybe one that is constructed by the agents? Say, a landscape that they deposit, and upon which accreted manifold they interact? links could be deposited incrementally by some kind of growth process. Dimensions could be high or unspecified. (keywords: “models of growth aggregation”, “rough interfaces”, “growth with surface diffusion”, “nucleation”, “morphogenesis”) Is this a constrained growth problem like the one that governs coral drills?
To consider - conductances, network topology
Investigate configuration spaces of technologies. (see Configuration space of the economy) Maybe use genes as a model? What is a gene but a body plan? How do different characteristics of body plans intervene with other body plans? With the environment? Is there a stochastic process that would serve as a statistically equivalent model of this?
Model of strategic research. How to researchers progress? What is the human knowledge landscape shaped like? How much area must a new thesis carve out from the unmade world?
The class of things I think of as string dynamical - artificial chemistry and the like.
Think of the pattern matching that goes on in theorem proofs - the pattern against which things is matched gets more subtle and interlocking. Not a simple tagging system, nor a regex, but a detection of new regularities in structure. (When can you integrate under the sign? How does one collapse infinite series out of power sums?). I’m sure the Automated REasoning folks have a few models of this. In those rewriting systems, lower order properties and generalisations are extracted from an increasingly entropic structure, but those regularities might reflect a simplicity that was already there but not accessible from the earlier theorem configuration space. (or not apparently “useful”)