Quote:
Originally Posted by RustedKitsune
As an example, consider a map of 36x36 hexes, for an area of 1,296 hexes. Average stellar density is 50%, for 648 systems. We’re interested in the habitable ones, which average 14.8% of all systems (these worlds are far more common in Traveller than GURPS), for 95.9 worlds. Eh, 96 worlds.
For all three formula, average distance between them is:
Thrash: 3.93 hexes. (4 hexes)
Rupert: 2.94 hexes (3 hexes)
Agemegos: 0.55 hexes
Umm... Age? I think this needs to be checked. It is 0.5/(sqrt(N/A)), right?
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0.5/sqrt(96/1,296) = 0.5/sqrt(0.0741) = 0.5/0.2722 = 1.83
Three things to note.
1. The formula is for the case of a uniform distribution where any point can have a star at it, not for the queer case in which stars are constrained to be at the centres of hexes.
2. You are using "hex" as both a unit of distance and a unit of area, where your hex-area is not the square of your hex-distance. That is an error. The formula I gave you is for distance and area in consistent units: used the way you used it it gives distances in terms of the square root of the area of a hex.
3. The formula I gave is for actual Euclidean distance, not for the measure produced by counting hexes.