20-mile hexes are divided into smaller units of area, called “six-mile hexes.” This is a convenient misnomer, as each of these smaller hexes are about 6.67 miles in diameter. These six-mile hexes are then further subdivided into “two-mile hexes,” which is again a misnomer, as these smaller hexes would be about 2.22 miles in diameter. The subdivision of each larger hex into a set of sub-hexes will, as indicated by the diagram, contain a set of seven complete hexes and parts of six shared hexes.

When speaking of a “group,” we are describing the central collection of seven 6-mile hexes that occurs inside a 20-mile hex (shown in yellow). When speaking of a “type,” we are describing the central collection of seven 2-mile hexes that occurs inside a 6-mile hex (shown in green).

__Hex Type__Within the 6-mile hex, the collection of seven 2-mile hexes are defined as being either “civilized” or “wild.” The ratio of civilized to wild among these seven hexes defines the infrastructure of the 6-mile hex. As a shorthand, we can express all seven hexes as being civilized with “7c.” Likewise, we can express all the hexes as being wild as “7w.” Including and between these two extremes, we have seven “hex types”: 7c, 6c1w, 5c2w, 4c3w, 3c4w, 2c5w, 1c6w and 7w. In nomenclature, these are defined as type-1, type-2, type-3 and so on up to type-8.

The image shows the arrangement of 2-mile hexes inside the 6-mile hex. We can see there are 26 possible 6-mile hex arrangements (with white hexes being civilized and black hexes being wild). A collection of type-7 and type-8 hexes would likely describe homesteaders on the periphery of civilization, eking out a living surrounded by constant danger. A collection of type-1 and type-2 hexes would surely describe the denser urban parts of the world, with every bit of arable land under the till or carefully preserved for hunting or access to managed sources of timber. Most provinces would consist of a core of type-5 to type-2 hexes, surrounded and intermixed with type-6 or type-7.

Taken together, a map of 6-mile hexes like these shown in the image would produce an interesting juxtaposition of both civilized and wild areas, some extensive and some isolated, depending on the larger picture created by the distribution of infrastructure.

__Creating Groups__Just as a single 6-mile hex has a specific hex type that depends upon the number of civilized and wild hexes, the 20-mile hex has a specific group of 6-mile hexes, the type being determined according to the 20-mile hex’s infrastructure. To understand how this is determined, we must begin with an understanding of the infrastructure point-cost of one type of hex vs. another.

Group distribution for 1 pt. of infrastructure. |

Naturally, this would mean that any result of 0 infrastructure would result in a group of seven type-8 hexes.

Having 2 points of infrastructure would slightly expand the possible results: a group would either contain two type-7 hexes (1 pt. of infrastructure each) or it would contain a type-6 hex, with two civilized hexes, distributed in four possible ways. Type-6 hexes cost two infrastructure points.

In turn, type-5 hexes cost four infrastructure points, which means that a hex must have a minimum of 4 infrastructure to have a chance of a type-5 hex occurring. Progressively lower hex types require double the number of points: 8 for type-4, 16 for type-3, 32 for type-2 and 64 for type-1.

For a hex group to be made entirely of type-1 hexes (with no wild 2-mile hexes at all), it must have a total infrastructure of 448 pts. or more.

In all, there are 3,131 possible groups that might occur, limited of course by the number of infrastructure points. Less infrastructure is more common, so certain groups occur far more often. Shown is a chart of the possible random distribution of hex types for infrastructures of 0 to 8. Take note there are 35 possible combinations available to a hex with 84 infrastructure.

Each possible group has an equal chance of occurring ~ so that a group of seven type-7 hexes will occur with a 1 in 9 chance in hexes that have a 7 infrastructure … and, notably, nowhere else.

Given that the selection
of hex types per group are also subject for random placement, the total
possible arrangements are considerable (sorry, I’ve forgotten the math that
would let me calculate it).

A generator for choosing the pattern and position of hex groups can be found at this link.