Infrastructure I

In my discussion on desirability (for population centers), I realized that existing infrastructure is extremely important. Communities can exist in isolation but will inevitably spread themselves out, creating new communities and so on.

Eventually, I'll split infrastructure out into separate races (at least for the desirability index). Infrastructure, of course, determines what sorts of services and industries could be available in a given hex, so I only need a single (non-racial) number eventually. But as far as settlement placement goes, it would make more sense that an elven village would prefer other elves rather than humans or dwarfs, given the chance. I can also define rough guidelines to racial relations - humans and elves might get along better than humans and dwarfs, and who likes the poor, stereotypically brutal orc?

However, making this switch is pretty easy, so for now I'll work with a single value. This will make settlements more heterogeneous during these tests.

To really get an accurate base number for infrastructure, I need a value for the total population in a region (or the whole world, as it may be). This part is tricky when starting from scratch and looking at the entire planet - I don't know how many people there are, and where they live. After all, that's the point of this system in the first place.

The equation in question is as follows, where $I_{i,0}$ is the base infrastructure index of the $i$th city, $p_i$ is the population of the $i$th city, $p_t$ is the total population (urban and rural), and 346 is the number of square miles in a 20-hex:
\[I_{i,0} = {p_i \over 346} {\sum_i p_i \over p_t}\]
Essentially, I am ignoring the ${\sum_i p_i \over p_t}$ term, because I don't (yet) have access to $p_t$. Or I could make up a number. Ignoring it is the more palatable option, but adding a multiplicative factor will make the influence of a settlement "reach" farther.

Placing a bunch of random cities and applying those rules:

I'm excited to lay down some roads on this bad boy (and to feed it back into the desirability map).