How would an AI divide its physical sphere of inflence into a "grid" of sectors?

Question

So, my colony mothership crawls along through sub-space at a "slow" ftl as it sends out faster probes ahead of it. Once it has located a cluster (meaning an acceptably dense grouping, not necessarily an actual star cluster) of worlds with "acceptable habitability" ratings (either habitable or can house stable enclosed colonies and have potential for possible eventual terraforming), it parks itself in the center of its selected region of space and then divides the space around it into "sectors", at least 8 of which contain at least 1 of the identified worlds. It then starts waking command crew for smaller colony ships to disperse in waves to each of these sectors.

My question is: what shape/angle should I make these "sectors"?

The outer radius of the "sectors" from the mothership is 1,000 ly (maximum 2-way distance for the ship's probes, which act as communications shuttles after colonization begins)

They need to (edited as actual shape is not required) allow the AI controlled mothership to use as a grid/array to organize, control, and monitor the colonization effort.

The sector size does not need to be large enough for the sphere to only house the 8 primary habitation sectors. It can include "dead" sectors of empty space or uninhabitable systems. However, each sector unofficially becomes the initial colony's "territory" for expansion, resources, and protection. As this is for a colony/empire control style game, they should be large enough that an ftl capable faction can establish a reasonable power-base and there still be room (at least on the outer/broader section of the sector) that most or all of the colonies are still exploring their sector, with only the ring around the mothership being very "crowded" space.

For conceptualizing: The probes and non-mothership vessels use an ftl drive that allows jumps of only a few hours between nearby (10-50 ly) systems, but can only maintain those speeds for a few jumps before needing resupply.

The mothership's support helps new colonies rapidly establish themselves to the point of being able to construct their own space craft (within about 20 years), and maintains a "carrier pigeon" transport that carries resources back and forth at regular intervals until then. Most are able to start establishing in-system mining operations and exploring neighboring systems within 30 years. First wave factions develop warships due to disputes over narrow trade lanes near the mothership and have warfleets protecting their territory by the end of the first century.

So, the goal is for "inner space" (meaning the region within 100 ly of the mothership) to be very metropolitan, highly populated and sometimes hotly disputed. The middle area (where the majority of the habitable worlds reside) is "civil space", each sector pretty much exclusively controlled by one faction. The outer edges of the sphere are still "frontier space" with mostly exploration expeditions, private prospecting efforts, and criminal havens separated by lots and lots of empty space.

The game begins as humans are starting to figure out what sort of neighborhood they landed in. Not that it has much bearing on the question, but the AI selected an area where its probes found no active interstellar civilizations out to their radius. So, at least through the establishment of its sectors, existing political boundaries were not considered.

When initially brainstorming the ship's process, the "sector" map was quickly sketched in 2d for conceptualizing purposes and we moved on to other things. I'm making a retro pass over things and hate the "orange slice" effect that putting the 2d map straight into a 3d universe would do. However, I won't have access to a decent ball of 3d playdough for at least 3 days. Help me out?

Edit: this is for a 3D video game, so the map perspective will be quite adjustable by the player.

Answer 1

Since distance is rather important, division based on Voronoi cells seems appropriate. Perhaps with modified metrics/topology based on "jump points" or whatever. This however won't give you equal volume cells without some modifications.

Answer 2

Use a set of spheres-of-influence around points of interest, rather than a single sliced sphere

This suggestion challenges the OP concept of dividing the entire sphere into sectors, offering an alternative which can be explained using in-game logic and is comparable to the way real life international law treats territories, territorial waters and international waters.

First, define one large sphere centered on the mothership - that's the "inner space" area and it relies on the mothership for provisions and possibly government (or it uses a "colonial senate" as a centralized government etc.).

Next, define another sphere around each player's initial ("capital"?) colony. Make them sized so that a single/few FTL jumps are enough to reach the capital - those spheres each depend on that capital for provisions and government, and is treated as that player's territory. Another player taking unsolicited actions in that region is basically invading the first player's territory (likely a clear act of war).

Finally, define another, larger sphere around each player's capital colony, designating that player's outer-space equivalent to "territorial waters", we'll call that "territorial space". While territorial space is still under the jurisdiction of a player, it marks that player immediate vicinity rather than actual territory. Additionally, while the inner space and territorial spheres should be exclusive (no point belongs to more than one sphere of influence), territorial space spheres may overlap. In such a case, divide the overlapping volume in two, assigning each to its closest player.

Areas so remote that they are outside any of the spheres don't really need to be allocated - it makes little sense to allot them to a specific colony, as that colony won't necessarily be able to claim that area, while another, more developed one might. Those areas will be considered "international space", where it may still be an act of war to attack or detain another player's ships, but anyone may travel through them and execute any mining operations they can defend etc.

As the game progresses, players will create new colonies - each with their own sphere of influence (possibly make these smaller as the are dependent on secondary colonies with more limited resources and no direct assistance from the mothership) and more territorial space. Depending on the exact game-mechanics, density of habitable planets and distances involved, it might make sense to have special handling for new colonies outside a player's current territory/territorial space - e.g. to define a "tunnel" of territory/territorial space between the new colony and the existing territory of that player (I'm happy to discuss some mathematical solutions that will be practical/aesthetic, not going into this as it's a bit tangential).