This is largely based on the process here. I recommend reading through that first, to get a grasp on the basic concept.
The total number of people in the towns (all less than 1,500, seems inappropriate to call them cities) is 3,539. The total number of people is 52,044. Therefore, each urban dweller influences about 14.7 people (or the inverse of 6.8%, the urbanization rate). Taking Andox as the first example: it has a base infrastructure of $1208 \times 14.7 / 347 = 51$.
Here I've given 1 extra point of division per 2000 ft of elevation. This is less than I will probably use in the future, but I wanted things to spread out a bit here. I've changed all the terrain to initial woodland, which is 3 points of division. Those numbers can change, and once I get this system working in the code I'll play around with them a bit more. I did this one by hand to get the system in my fingers, and that's too much work to play around with.
The woods here really constrain the spread of the people. Fascinating. The elevation penalty tends to push the infrastructure down the same paths as the river, which makes sense.
Interestingly, there are two hexes with no infrastructure at all, between Betryn and Ffith. I want them to still count towards the whole population density, so I gave them 0.1 points of infrastructure each (all other numbers are integers).
To figure out how the rural population shifts (discussed here), I considered where the infrastructure points were concentrated. For example, the main Andox hex has 56 points. The total is 486.2, and hence that hex contains ${56 \over 486.2} = 11.52\%$ of the total infrastructure, and thus the total population. This works out to $(52044 - 3539) \times 11.52\% = 5587$. If we look at the local urbanization rates, Andox has about 21%. All the numbers work out and I'm happy.
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