Difference between revisions of "Hex Group"

From The Authentic D&D Wiki
Jump to navigationJump to search
 
(23 intermediate revisions by the same user not shown)
Line 1: Line 1:
−
'''Hex groups''' are used in mapmaking to provide cohesion to the random distribution of [[Infrastructure|infrastructure]]. The [[World (Alexis' game setting)|game world]] is mapped in [[20-mile Hex Map|20-mile hexes]], this being the best size for estimating [[Travel|travel]] times for [[Player Characters|player characters]] and determining the [[Transport (trade)|movement of goods and services]].  As a means of expanding details of the game world, these hexes are progressively subdivided into smaller and smaller hexes, reaching all the way down to the [[Combat Hex|combat hex]], which is 5 ft. across.
+
[[File:Hex Groups.jpg|right|490px|thumb]]
 +
'''Hex groups''' designate a constituency of 9 hexes that fit conveniently inside a larger hex: seven '''prime hexes''' and six diamonds, each representing ⅓ of a hex. This allows a hex to be subdivided for the purpose of randomly assigning portions of a [[20-mile Hex Map|20-mile hex's]] [[Infrastructure|infrastructure]] number, producing a range of [[Hex Types|hex types]] from type-1 to type-8. While the [[World (Alexis' game setting)|game world]] is mapped in 20-mile hexes for estimating [[Travel|travel]] times for [[Player Characters|player characters]] and the [[Transport (trade)|movement of goods and services]], [[6-mile Hex Map|6-mile hexes]], as determined through hex groups, are used to provide more detailed information for the purpose of running the game setting.
  
−
[[File:Divided 20-mile hex.jpg|right|245px|thumb]]
+
[[File:Divided 20-mile hex.jpg|left|280px|thumb|'''Showing the 7 prime hexes within the 20-mile hex'''.]]
−
== Scale ==
+
This method of subdividing hexes can be used to expand the details of the game world as desired, since 6-mile hexes can likewise be subdivided into [[2-mile Hex Map|2-mile hexes]], which can then be reduced progressively into [[Land Hex|land hexes]] (1,304 yards), [[Village Hex|village hexes]] (434 yards), [[Block Hex|blocks]] (145 yards), [[Sub-block Hex|sub-blocks]] (48 yards) and [[Lot Hex|lots]]. This makes it possible to map virtually anything.
−
20-mile hexes are subdivided into '''nine''' hexes that are 6.67 miles across, called "[[6-mile Hex Map|six-mile hexes]]" as a simplified misnomer.  Two of these nine hexes are shared with adjacent 20-mile hexes, as shown in the sketch provided.  Six-mile hex maps are used for local regions and to calculate general productivity and wealth.  A '''Hex Group''' describes the infrastructure distribution inside the 20-mile hex, among the six-mile hexes, as determined by the method described below.  Each individual hex is defined by its '''Hex Type''', from 1 to 8, by how much infrastructure exists inside that one six-mile hex.
 
−
 
 
−
Six-mile hex maps are subdivided into nine hexes that are 2.22 miles across, called "[[2-mile Hex Map|two-mile hexes]]."  These are used for closely mapping areas where the party has settled, where great detail is needed for clarification.  The "Hex Type" defines how many of these two-mile hexes are domesticated rather than wild.
 
  
 
== Distributing Groups ==
 
== Distributing Groups ==
−
This describes the means by which the infrastructure of the 20-mile hex is distributed among the seven '''prime''', or whole six-mile hexes forming the hex group. Infrastructure numbers range from zero (no habitation or infrastructure at all) into the thousands — though for distributing groups, an infrastructure of 448 or more means the hex group is fully civilised.
+
Beginning with the infrastructure number for a 20-mile hex, the seven prime hexes, or "group," are randomly assigned an order from 1 to 7. They are then allotted infrastructure according to that order. The hexes are designated beginning at the top right and proceeding in a circle, with the final hex in the centre, as Hex-A, Hex-B, Hex-C and so on. A new random order is assigned to the seven hexes each time infrastructure is distributed, ensuring a unique pattern for every group.
  
−
A hex group with zero infrastructure has seven '''type-8''' hexes; "type-8" being the least civilised type.  Every six-mile hex in this group is wild, without any human structures or facilities.  If adjacent to human culture, a hex like this would be considered "[[Hinterland|hinterland]]" — visited regularly by hunters and gatherers, but with nothing more developed than an [[Roads & Routes|animal-made trail]].
+
When assigning infrastructure, the original number is divided according to powers of 2: 2<sup>0</sup>, 2<sup>1</sup>, 2<sup>2</sup>, 2<sup>3</sup> and so on, while empty hexes are assigned zero infrastructure. That is,
  
−
[[File:Hex Group Patterns.jpg|left|420px|thumb|Distribution of possible hex group patterns<br>white = civilised, black = wild]]
+
:* 0 = 0 infrastructure (0-IN) — [[Type-8 Hex|Type-8]] (see "[[Hex Group#Hex Types|Hex Types]]" below)
−
1 point of infrastructure would mean the hex group has ''six'' type-8 hexes and '''one type-7''' hex.  This type-seven hex, 6.67 miles across, has ''one'' two-mile hex within it that's civilised.  The remainder of the 2 mile hexes, and most of the six-mile hex, is counted as hinterland.  A single point of infrastructure is very little.  It's understood, then, that the "hex type" is determined by how many two-mile hexes within that six-mile hex are civilised.  None equals a type-8 hex; one equals a type-7; two equals a type-6 and so on, until if every two-mile hex is civilized, the six-mile hex is a type-1.  Conversely, if there are no wild hexes, that's a type-1; and for each wild hex that's added, the hex becomes type-2 (one wild hex), type-3 (two wild), type-4 (three wild) and so on.  While this counting systems seems confusing at first, it quickly becomes second-nature.
+
:* 2<sup>0</sup> = 1-IN — [[Type-7 Hex|Type-7]]
 +
:* 2<sup>1</sup> = 2-IN — [[Type-6 Hex|Type-6]]
 +
:* 2<sup>2</sup> = 4-IN — [[Type-5 Hex|Type-5]]
 +
:* 2<sup>3</sup> = 8-IN — [[Type-4 Hex|Type-4]]
 +
:* 2<sup>4</sup> = 16-IN — [[Type-3 Hex|Type-3]]
 +
:* 2<sup>5</sup> = 32-IN — [[Type-2 Hex|Type-2]]
 +
:* 2<sup>6</sup> = 64-IN — [[Type-1 Hex|Type-1]]
  
−
=== Patterns ===
+
The total infrastructure must be divided among these seven options, plus zero, when distributing that infrastructure into the subordinate hex group of seven prime hexes, recognising that multiple combinations are possible for most infrastructure totals above 1. '''For example''', 3 infrastructure divided into seven hexes may, according to the assigned order of the hexes, produce either 2-1-0-0-0-0-0 or 1-1-1-0-0-0-0. For a total infrastructure of 8-IN, there are nine possible combinations; for 42-IN, there are twenty-nine. The chance of any specific combination occurring, regardless of the total, is always equal. Thus, for a total of 42-IN, each of the 29 possible distributions has an equal probability of being selected.
−
The image shown indicates the possible hex distributions for each type of hex, with '''black''' indicating a wild hex and '''white''' indicating a hex that's civilised.  Type-1 and type-8 hexes can only have one possible pattern, or distribution: every 2-mile hex is of one type or the other.
 
  
−
Type-2 and type-7 hexes may have the single civilised/wild hex in the center of the group, or as one of the six outer hexes. There are seven permutations for where the exact distribution may be, but there are only 2 patterns: in the middle or on the outside.
+
[[File:Hex Generator.jpg|right|490px|thumb|Hex generator]]
 +
A [https://docs.google.com/spreadsheets/d/1OD6XRL4yDHfS5N0F7SFIspfWpy72bYB2/edit#gid=1269951915 generator] in Excel has been created to perform both tasks automatically: assigning the order of the prime hexes and randomly distributing infrastructure among them. The result is expressed as '''types''', ranging from type-8 to type-1. The file also includes various flotsam and jetsam that can be ignored.
  
−
The remaining hex types continue become more elaborate, with type-3 mirroring type-6 and type-4 mirroring type-5.  Altogether, there are no more than 26 patterns, but as these patterns are turned clockwise and interface with the permutations created by adjacent hexes, they form an interesting and functional mosaic of civilized hexes.
+
By entering the infrastructure number into the yellow box and pressing return, the resulting hex types are generated, showing how many of each type are present. Seven boxes then show how these hexes are randomly arranged. In the example shown, the single type-4 hex is placed in "Hex D," with the corresponding box below marked "1st." The single type-5 hex is placed in the "2nd" hex, which is "Hex G," the central hex. The remaining hexes are all type-8 and are distributed among the other five hexes.
  
−
=== Random Distribution ===
+
The resulting hex types are then assigned, in order, to the hexes labelled 1st, 2nd, 3rd and so on. Thus, with a total of 12 infrastructure, the type-4 hex is placed in Hex D, the type-5 hex in Hex G, and the remaining five type-8 hexes are distributed among the other hexes.
−
While 1 point of infrastructure creates a type-7 hex, it requires 2 points of infrastructure to create hex that is type-6.  Therefore, distributing 2 infrastructure among a hex group might create either TWO type-7 hexes or ONE type-6. Which is rolled randomly, with an equal chance for each.  More civilised types progressively require more infrastructure to generate: at least 4 pts to make a type-5, 8 pts to make a type-4 and so on.  A type-1 hex cannot occur with less than a minimum of 64 infrastructure pts, and seven type-1 hexes would cost 448 total.  This explains the number needed to obtain a fully civilised 20-mile hex.
 
  
−
A complete list of possible group combinations occuring at specific infrastructure totals for a hex, can be found [[Possible Hex Group Combinations by Infrastructure|here]].  Because the number of possible combinations is considerable, manually interpreting the die roll for each level of infrastructure quickly, and as often as it needs doing, is impractical. Therefore, a [https://docs.google.com/spreadsheets/d/1OD6XRL4yDHfS5N0F7SFIspfWpy72bYB2/edit#gid=1269951915 generator] has been created that can be used on google sheets or downloaded. The file includes various flotsam and jetsam that can be ignored.
+
If an infrastructure result is impossible to produce, such as when the powers of 2 cannot sum to 191, the hex is treated as the next lowest possible number, in this case 190. The highest possible number, 448, also accounts for all infrastructure values above that, resulting in a group of seven type-1 hexes. These cases are handled automatically by the generator. Hex groups of this size and larger are considered fully civilised.
  
−
[[File:Hex Generator.jpg|right|420px|thumb|Hex generator]]
+
== Coastal Areas ==
−
By inserting the infrastructure number in the yellow box and hitting return, the hex types resulting will be generated, explaining how many of each type.  Seven boxes then show how these hexes can be arranged randomly.  In the example shown, the single type-4 hex would be located in "Hex D," which has the box below reading, "1st."  Thereafter, the single type-5 shown is placed in the "2nd" hex, which is "Hex G," the center hex. The remaining hexes are all type-8, which are placed in the other five hexes.
+
If the hex is partly water, so that Hex D contains no land or only an inconsequential sliver of it, then the type-4 hex is placed in the next suitable hex in order, moving from 2nd to 3rd to 4th and so on. This provides a quick adjustment for unusual circumstances that arise in mapping, without requiring a complicated program to account for them.
  
−
If the hex were partly water, so that Hex D had no land or perhaps an inconsequential sliver of land, then the type-4 hex would be placed in the next suitable hex in order, from 2nd to 3rd to 4th and so on.  This allows a quick adjustment for odd circumstances that arise in mapping, without needing to create a complicated program to account for such things.
 
  
 +
See also,<br>
 +
[[Hex Types]]<br>
 +
[[Mapmaking]]<br>
 +
[[Talk:Hex Group|Visual breakdown of distributed infrastructure]]
  
−
See [[Mapmaking]]
+
[[Category: Reviewed]]

Latest revision as of 19:59, 31 March 2026

Hex Groups.jpg

Hex groups designate a constituency of 9 hexes that fit conveniently inside a larger hex: seven prime hexes and six diamonds, each representing ⅓ of a hex. This allows a hex to be subdivided for the purpose of randomly assigning portions of a 20-mile hex's infrastructure number, producing a range of hex types from type-1 to type-8. While the game world is mapped in 20-mile hexes for estimating travel times for player characters and the movement of goods and services, 6-mile hexes, as determined through hex groups, are used to provide more detailed information for the purpose of running the game setting.

Showing the 7 prime hexes within the 20-mile hex.

This method of subdividing hexes can be used to expand the details of the game world as desired, since 6-mile hexes can likewise be subdivided into 2-mile hexes, which can then be reduced progressively into land hexes (1,304 yards), village hexes (434 yards), blocks (145 yards), sub-blocks (48 yards) and lots. This makes it possible to map virtually anything.

Distributing Groups

Beginning with the infrastructure number for a 20-mile hex, the seven prime hexes, or "group," are randomly assigned an order from 1 to 7. They are then allotted infrastructure according to that order. The hexes are designated beginning at the top right and proceeding in a circle, with the final hex in the centre, as Hex-A, Hex-B, Hex-C and so on. A new random order is assigned to the seven hexes each time infrastructure is distributed, ensuring a unique pattern for every group.

When assigning infrastructure, the original number is divided according to powers of 2: 20, 21, 22, 23 and so on, while empty hexes are assigned zero infrastructure. That is,

The total infrastructure must be divided among these seven options, plus zero, when distributing that infrastructure into the subordinate hex group of seven prime hexes, recognising that multiple combinations are possible for most infrastructure totals above 1. For example, 3 infrastructure divided into seven hexes may, according to the assigned order of the hexes, produce either 2-1-0-0-0-0-0 or 1-1-1-0-0-0-0. For a total infrastructure of 8-IN, there are nine possible combinations; for 42-IN, there are twenty-nine. The chance of any specific combination occurring, regardless of the total, is always equal. Thus, for a total of 42-IN, each of the 29 possible distributions has an equal probability of being selected.

Hex generator

A generator in Excel has been created to perform both tasks automatically: assigning the order of the prime hexes and randomly distributing infrastructure among them. The result is expressed as types, ranging from type-8 to type-1. The file also includes various flotsam and jetsam that can be ignored.

By entering the infrastructure number into the yellow box and pressing return, the resulting hex types are generated, showing how many of each type are present. Seven boxes then show how these hexes are randomly arranged. In the example shown, the single type-4 hex is placed in "Hex D," with the corresponding box below marked "1st." The single type-5 hex is placed in the "2nd" hex, which is "Hex G," the central hex. The remaining hexes are all type-8 and are distributed among the other five hexes.

The resulting hex types are then assigned, in order, to the hexes labelled 1st, 2nd, 3rd and so on. Thus, with a total of 12 infrastructure, the type-4 hex is placed in Hex D, the type-5 hex in Hex G, and the remaining five type-8 hexes are distributed among the other hexes.

If an infrastructure result is impossible to produce, such as when the powers of 2 cannot sum to 191, the hex is treated as the next lowest possible number, in this case 190. The highest possible number, 448, also accounts for all infrastructure values above that, resulting in a group of seven type-1 hexes. These cases are handled automatically by the generator. Hex groups of this size and larger are considered fully civilised.

Coastal Areas

If the hex is partly water, so that Hex D contains no land or only an inconsequential sliver of it, then the type-4 hex is placed in the next suitable hex in order, moving from 2nd to 3rd to 4th and so on. This provides a quick adjustment for unusual circumstances that arise in mapping, without requiring a complicated program to account for them.


See also,
Hex Types
Mapmaking
Visual breakdown of distributed infrastructure

Retrieved from "http://wiki.alexissmolensk.com/index.php?title=Hex_Group&oldid=30831"