Detail III: Infrastructure

I have been thinking more about how to generate infrastructure for the detailed hexes. I've floated a few ideas here and there which seem to work well, but I thought of an interesting situation where the current system might give odd results.

To sum up, the infrastructure number of a 20-mile hex will indicate how many of the 400 1-mile hexes will be settled. For ease of experiment, let's assume that the 20-hex is forested, and that the settled 1-hexes are cleared land (whether for grazing animals or for houses, doesn't matter yet).

Previously, I was just using the infrastructure number as the number of settled 1-hexes, up to a maximum of 400, at which point the hex would be totally settled. But after reading this post several more times, I believe I can come up with a more robust system.

The problem is that infrastructure spread stops at the boundaries of a hegemony. This means there is a possibility of a hard edge where there is a totally settled 20-hex ($I\geq 400$) next to a relatively unsettled 20-hex (say, $I=10$). The whole point of the detailed 1-hex view is to give a smooth interpolation between discrete 20-hexes.

So what's the point?

The Tao (Alexis) uses 2-mile or 6-mile hexes, allowing a smoother interpolation because the detail is not as fine. With the 1-hex, there are 400 hexes that must be made to play nice. He gives a chart, however, detailing the behavior of each hex type and group depending on the number of wilderness hexes that surround it. 2-hexes which are completely settled (Type I) contribute 64 points of infrastructure to the total, and so on down the line. Read the links for more info, I won't rehash it here.

Since I'm not dealing with hex groups directly, I need a way to translate or spring-board off this existing system of ideas into my own map. I will define groups of 1-hexes in the following way: counting the 1-hex itself and the surrounding 6 hexes, how many are wild (of the 7 total)? This gives us 8 total types. Furthermore (and here's the distinctive key): these groups are not discrete. Each hex contributes not only to its own group type, but also those of its neighbors. In this way, the combinations are made even more unique...if it works.

Type	Adjacent Settled	Infrastructure
I	7	7
II	6	6
III	5	5
IV	4	4
V	3	3
VI	2	2
VII	1	1
VIII	0	0

This has some interesting implications. Observe the minimum situation for a Type I hex:

The very presence of the Type I implies a further 6 Type IVs. That's a total of 31, if the above values are used.

Type II (total 24):

Type III (from here on out, I've tried to show the lowest configuration, there are others that could be higher, total 17):

Type IV (total 12):

Type V (total 7):

Type VI (total 4):

Type VII (total 1):

So how do I make this work? I'll start with a brute force approach.

It's very quick to run an algorithm over the 20-hex and get the total infrastructure number based on the 1-hexes. So what I'll do is gradually increase the number of settled 1-hexes and check the number. When I reach the target number, I'm done.

So far, this works pretty well.

$I=113$

Let's try it out for a stark difference. The top hex has $I=1000$, and the bottom two, $I=10$.

Not bad! The edge is still pretty hard...but not as hard. Furthermore, the individual hex groups could be identified for feature placement.

An issue with the infrastructure values for each hex type: The higher the numbers go, the fewer 1-hexes will end up on the final map. Earlier, I had defined 400 as the value of a filled 20-hex: but with the new system, a 20-hex must have $I=2268$. That's pretty high. But it does imply 346 sq. mi. of continuously occupied land (including farmland).

Finally, each iteration is totally random. I want a way to save them so if I come back later, or make a map for a game, I can reproduce it. Each configuration is extremely unique, and so I need a fingerprint. There are a couple of ways I can do it, but here's a very simple one.

First, I sort the hexes by their address, then assign 1 for settled and 0 for wilderness. Then I join all those numbers into a long binary string, padded to 400 zeros. For $I=1000$, that looks like this:

0b0000010000000000000010010011000100000000000000001000000000000000000001000000001001110000000000000101000000010000010000000000100000000010101010000100000010010000010001001000000000001000000011100000000000100000000001000100010010100000001101010000110010000000001000000010000000000000000010000100000000001000000000010000000000000000000010000000000100001000001001000100000000101000001011000100110000010000

But that's super long! So instead, I'll convert that number into hexadecimal. It's still long, but manageable.

0x400093100008000040270005010400802a840904480080e00200444a0350c802020000840080100000801082440282c4c10

I can save this fingerprint for use with this specific hex. When I'm recreating it, I can just pass the seed back to the generator. It's very simple. I think I should try and implement it for the height and river data, but that will require some extra thinking.