Four-Dimensional Hexcrawling Through Abyss and Space

I’m planning on making this a blog post, but I actually wanted to share it here first and get peoples thoughts before posting. I think I’m on to something cool here, but I haven’t had a chance to test it yet so maybe it’s bunk. Do these ideas make sense? Are there good visual aids I can include?

I may also try to include a small example hexcrawl using these mechanics as well, although I currently have not done so. Maybe that’ll be a separate post later.

Below is the current draft of the idea:

Space and Underwater settings and campaigns are hardly novel, but anecdotally, it seems like nobody is really satisfied with the mechanics. Many games with mechanics for this kind of movement are super crunchy attempts at simulation which don’t appeal to me, personally, or they’re handwave-y and basically just treat movement through those spaces as regular land travel. The latter is generally fine for me, but it would be cool to have some kind of middle ground; an attempt to model this kind of movement in a way that doesn’t just exist for the sake of simulation, and isn’t super crunchy, and also adds something to the game experience.

Here I outline an idea for how to design a hexcrawl in four dimensions; not just two axes (left/right, forward/backward), but also up/down and moment, or baseline movement (e.g. a school of fish, a massive space fleet, etc.). These ideas have not been tested yet, and there are edge cases I can think of, but hopefully, people will find this idea intriguing.

In addition to managing a hexcrawl, these same mechanics should theoretically be applicable to grid-based combat, or even just as fictional positioning helpers for theater of mind play, but I am primarily describing these mechanics in terms of a hexcrawl.

Finally, I’ll also say that this was also somewhat inspired by three-dimensional movement in Veins of the Earth. While I model three-dimensional space in a very different way here, that may have been the first game I had read that really made me think about how to model space in a game that seemed fun and not overly cumbersome or simulation for the sake of simulation.

A brief statement on the Moment dimension

I’m open to suggestions, but I’m thinking of calling the fourth-dimension “Moment”. Taken from the wikipedia article on Moment:

In physics, a moment is an expression involving the product of a distance and physical quantity, and in this way it accounts for how the physical quantity is located or arranged.

I think it would be perfectly reasonable to stop at three-dimensions; that’s already novel and potentially complicated enough. However, I was inspired quite a while ago by nature documentaries, specifically seeing aquatic ecosystems, and how these three-dimensional ecosystems work. A school of fish can be attacked from all sides; birds diving from the sky, other fish and aquatic mammals swooping in from below and all sides, so as a necessary survival mechanism to defend from so many vulnerable positions, they are more or less constantly in motion. This was a major inspiration for my Vortekka campaign setting (setting, play report), and also The Jellyfleet and The Choir from Phantasmos (included in my post on Weird & Wonderful Places; even then I was thinking of these moving groups as an alternative to geopolitics per se).

In this case, the fourth-dimension is like the relationship between different objects over time as a function of their baseline movement. This will be elaborated upon further when I get into the mechanics of this system, but it will hopefully be not as complicated as that may make it sound. The point of a good model is to be parsimonious- to condense more information into fewer arguments, and I think Moment is potentially a good way to do that here.

Extrapolating this idea to intelligent species, you’d have a fundamentally different kind of “geo”-politics, really more of a “moment”-politics, defined less so by static geographical locations (or statically-keyed hexes on your hex map), and instead by nomadic groups and their Moment-level relationship to other nomadic groups or geographical features. I suppose this is also true with nomadic land-dwelling species, in which case I could see this being useful for a land-dwelling campaign with nomadic cultures, or for a pre-civilization or post-apocalyptic setting, independent of the mechanics for a three-dimensional hexcrawl, and in fact, the mechanics described below, despite the labels, can be used independently.

For reasons which should also be more clear when I describe the mechanics, this Moment mechanic could also be a fun way to do chases and races.

Three-dimensional Hexcrawl

Let’s start with how to model the third dimension in a hexcrawl; up/down. First, you need to decide on how many “levels” of up and down there are, in the same way that you need to decide on the dimensions of your hexcrawl in two-dimensions. I don’t love the idea of treating three-dimensional space as planar, but I don’t see a better way around it that isn’t mechanically or logistically much more complicated (i.e. requiring some kind of physical diorama or digital tool). The volume of each hexagonal prism can be arbitrary in the same way that the area of a hexagon in a hexcrawl can be arbitrary, as long as it’s internally consistent (I guess that’s just common sense…). That being said, I’ll still be referring to these prisms as hexes, since we’re treating the third-dimension as planar, and therefore in effect, it will still be represented as hexes across multiple planes.

So for the sake of simplicity, let’s say we’ve decided there are three levels. In that case, key each hex on your hex map three times, or alternatively take your hex map, and triplicate it. When you key your dungeon, you’ll have the normal two-dimensions and level. If one unit of movement is moving from one hex to an adjacent hex, movement between levels can also be treated as one unit. So objects can move either to any adjacent hex as normal, or move one level up or down. Diagonal movements, like going up or down a level and also moving planarly adjacent, should probably be two units of movement, which is about as close as I can think of to model this in actual three-dimensions off-hand without making it massively more complicated.

If you are keying the hexcrawl arbitrarily, there’s really nothing more to it than that. However, if there is supposed to be some internal consistency, such as geography, environment, celestial bodies, etc., then you’ll want to keep in mind not just these relationships from hex to hex on each plane, but also between planes.

So when prepping a three-dimensional hexcrawl, as already stated, you can decide whether you want to design a separate hex map for each level and lay them all out, or have a single map with multiple keys depending on level (*I also describe another approach further below). I think the latter is probably more practical, but you could potentially have your cake and eat it too by having a separate hex map for each level on a semi-translucent sheet and physically layering them or splitting them as needed (or digitally using layers in some design tool).

If you are using a single map with multiple keys, then next to any object/group token, you should have a die alongside them, with the number on the die representing their level. I would worry that this might get overly complicated in hex or grid combat, although still doable, but for a hexcrawl, my hope is that this will not be too complicated, especially if the only token is the party.

I hesitate to suggest this because I think it would probably just overcomplicate things, but you could also imagine pivoting the hexcrawl, so that for instance moving forward/backward or left/right on a given hex map is actually up/down, and the planes represent whichever directionality is being superseded. This could work particularly well if e.g. your hexcrawl is intended to relatively linearly model rising from the depths of the abyss back up to the surface, or being pulled by a gravitational force.

This kind of pivot could also be a useful way to visually/physically model the hexcrawl in multiple dimensions without needing a separate hex map for each level; where you have three hex maps representing the intersections of all axes (e.g. left/right, forward/backward; up/down, forward/backward; left/right, up/down). So even if you had ten levels, you should only need three hex maps, if I have thought this through correctly. Talk about parsimony! Even so, personally, I think this would be more complicated than just one hex map with multiple keys, but for another group, it might be preferable, or after testing it might be that this is a better approach.

Four-dimensional Hexcrawl

Despite the label, one could choose to use this Moment dimension independent of up/down, but for the sake of continuity, I will describe this as the fourth-dimension.

In an abyssal, aquatic, or maybe even an outer space hexcrawl, as discussed at the beginning, objects are generally not remaining in place, and so you need to represent their “moment”. As with the spatial dimensions, we can measure moment in arbitrary but internally consistent units, like 5 ft for general movement on a grid. As with three-dimensional level, we can use a die next to a token on a hex map to represent its moment (presumably in a different color or size than the one used for three-dimensional level), or as a feature on a key in addition to whatever text is associated with that key. In other words, this is the baseline movement for the token, or key, before any groups have made any active movements.

So if the party have a moment of 1, and the hex in front of the party is of a school of fish people also with a moment of 1, there is no difference between their baseline movements, so if the party move one hex forward on their next turn, they’ll reach the hex with the school of fish. On the other hand, if the school of fish has a moment of 2, then the GM would move the key for that school of fish people at the beginning of the turn before the party has made their active movement.

Admittedly, it could get complicated having to move all of these keys around on your hex map, especially if you’re doing it behind the scenes (the players are unaware of what is in any given hex far enough afield), but intuitively I think this moment dimension, or relative distance or baseline movement, is both easier than manually accounting for the active movements of all keys containing nomadic groups, and also just a fun way to mechanically reinforce that this hexcrawl is not static. And also, I think it’s ok if certain keys “slip off” the hex map. There’s plenty of fish in the sea ;), maybe this is how you treat wandering monsters / random encounters.

You could potentially imagine the keys as being placed on hex chips, like settlers of catan, and that would make it easier to move and keep track of the keys with moments greater or lesser than the party, although that has some shortcomings as well (such as the players being able to see you moving keys tells them that such keys exist…). I think this key shuffling would be the hardest part, unless it were automated digitally, but not necessarily impossible.


I would still welcome comments here or on the blog, but I decided to just go ahead and post it more or less as-is, but I may build on this idea in a future post.

Don’t know if this would help for combat. I’d need to think how it might be useful for navigation …

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Ya I could see hexflower being useful here, would have to think about it more but that’s a good idea. I’ve seen this particular thing of yours before but now I need to take a closer look and see if I didn’t just reinvent the wheel except as a square 0.o…

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The idea has me interested.
May need to give it some more thought.
I recall on G+ I considered something like this, maping in 3D but using a 2D map.
It was for a cave system with three layers.

This is where it started (never finished this; purple the deepest layer, pink the next and brown the highest layer) …

… but I beleive it ended up with an idea based on colour mixing.

I think each layer had a colour like red, green and blue. So when ‘seen’ from above the mix of colours would tell you which layers had areas of overlap. So if all three layers lined up in that spot, then the cell would be white. If only the red and green layers overlapped then the cell would be yellow etc.

Of course, in places like the sea all layers are not ‘patchy’ - if in the middle layer you can go up and down etc …

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The work is only my old laptop. I think there may have been edge colours too … need to power the thing up, and I’m not sure I’d find the stuff I did anyway !!!

I have long advocated for 3D space combat in things like Starfleet Battles, but have generally been met with statements as to how so little is gained for the labour involved. A 3D game from the late 70s or early 80s seemed (IMO) rather more concerned with making it feel like it was different, rather than the system making it significant tactically. WarpWar has an interesting system of diceless plotting which emulates the effect of lots of chances to miss, while preserving the thrill of hitting, and all of this with only a 2D hex-map. My experience in an unreleased Sci-Fi rules set is that relative speed has so much greater effect on hit/miss than 3D positioning that I too found only occasional reason for making the effort.

These instances are more significant in atmospheric or interface combat/dogfights. Positioning oneself in a dive perpendicular to the dorsal plane of the enemy increases your target size, while making your approach much harder to scope; the effect is that even longer range strafing and then pulling away makes it much likelier of inflicting drive-off or destroy hits. Since the attacker is always attempting to achieve this positioning, it makes the job of an incurring bomber much harder (as evinced in WWII).

However, in space, where distances are measured in Light-Seconds or greater, the real difficulty becomes one of detection of threat in short enough time for both accurate estimation of target trajectory and travel time of the strike before the target has moved out of range; yes, distances can be so great that the speed of the laser cannot ever hope to engage the target, much less the targeting systems be able to predict where far ahead to shoot with any hope of striking. That is the real reason why computers in Traveller still take up a room, as they do on modern Destroyers or Littoral craft: plotting a strike on a moving target while moving, etc. is difficult, far more difficult than the much touted ‘cell-phone computing power’ argument.

So, if none of what I have presented dissuades you for whatever reason (genre, feel, etc.), then the next question becomes, from which axis are your representations being plotted? Top-down, side-view, bottom-up? The reason why I ask is because of the fact that a different shading system would register a different map from every angle unless the space was entirely uniform (a 3D grid of cubes in rows and columns and fields, for instance). in this example, no map would be different from any other, and therefore still reduces this exercise to a 2D engagement. If a scene is one of submarines plotting courses through holes in the sea floor, then each axis would require its own shading map (cubic should suffice, six maps like a d6) – seems like a lot of effort. Mechanically, it is a lot like D&D’s 1/4, 1/2, 3/4 Cover rules, where any given target may be partially shielded by hard cover making an actual strike to the target that much less likely: success is hitting the part left exposed. This may be less appealing, but statistically, is essentially what the outcome of a more extensive system would be.

I hope you are able to find the solution which has eluded me, and, regardless, that your games are rad.


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I address both of these ideas in the post ;).

In regards to relative speed, that’s what I’m calling the “Moment” Dimension in that post, hence 4D rather than 3D. That being said, it can be used independently from 3D.

I also addressed a couple of different ways for representing axis. One was to just use the same axes as on a 2D hex/grid, with the third dimension being represented by a separate plane for each level on that dimension (obviously a bit unwieldy). I also suggested switching the axes for different purposes, or using a separate hex/grid for each orientation, and use that to basically triangulate, rather than treating it planarly with a separate grid for each level of the 3rd dimension.

I’m inclined to agree that even this all would still likely be trickier than it’s worth for combat, as I said in the post I see this as being more for multidimensional hexcrawling rather than for combat per se, although in theory it could be used that way.

Also, I like your thoughts on aerial/spatial dogfighting and targeting, but that’s definitely at a deeper level of simulation than I’m concerned with, especially for this- although if there were a way to model those ideas in a simple, less simulation-y way, that would be interesting.

There’s a boardgame (or I guess really pen and paper game), can’t remember the name of it for the life of me, but it’s all about trying to model trajectories and orbits, and gets at some of what you’re saying I think. It’s a pretty cool game, and one could imagine embedding that into a space campaign. In fact, a friend of mine was interested in trying that. But again, personally, that’s a deeper level of simulation than I’m interested in and I think would bog things down as you’re saying. I generally would prefer to find a way to model things that is less about simulation per se and more about evoking that “feeling” in a simpler way. To some extent, my “Moment” Dimension was an attempt to do that, but the general census seems to be that either I failed to simplify it sufficiently, or failed to explain it coherently…

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I need to take a closer look at this at some point, but was this the thing where you were basically taking a graph database approach (nodes / edges), or was that something else?

I think I need to better understand what the Moment will add to game play.
How does one use it in, for example, combat, or, a search sequence?

As far as 3D exploration, an early D&D map is a side-view of the various levels of the ‘dungeon’, which style was not used for a long while until it became necessary to to show the interrelationship of levels that independent would not properly convey how they lined-up. Isometric dungeon maps help to illustrate the 3D aspect of spaces. Are you looking to avoid using this sort of ‘2.5D’ projection method for a practical production reason, or are you more interested in developing the shading map method because you find that it has merits which Isometric does not possess?

I may be wrong, but it seems like you are pursuing this for more theoretical purposes.
Many an hour has been invested in some of my more abstract design pursuits, but even if I was fully satisfied with them, few seemed to make enough practical sense to my players or play-testers for them to engage with ‘the new thing’; I hope that I am able to understand the advantages of your proposal so that it can be brought to light for the hobby’s benefit; it sounds intriguing.

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The idea of “Moment” is to add that relative speed effect. In the case of a hexcrawl, this could mean that, as you move one hex, the school of space fish you’re tracking move two hexes. It allows the GM to adjust the board state in tandem with the actions of the party. You could imagine it existing even in a regular 2D hexcrawl, such as if it’s a nomadic tribe of centaurs, but I originally thought of it in terms of 3D because I was thinking about oceanic ecosystems.

You could in theory use this for combat as well, but it’s already more parsimoniously modeled with regular movement mechanics such as typically found in D&D.

In retrospect, maybe the “Moment” dimension could also be better modeled as just a movement stat for the nomadic groups/objects on the hexes…

As far as the 3D map approach and why to use this vs. an isometric/2.5D map, personally I just find isometric maps really difficult to understand. I’d rather just have multiple views of different 2D slices, whether that be planar (one 2D view for each level on the 3rd dimension), or triangulation. The planar approach is the most intuitive to me, but also the most work, and with enough levels would be really difficult to keep track of. The triangulation approach requires less work if there are more than a few levels, but is going to be harder to mentally track, at least for someone like me with poor visuospatial aptitudes.

It would be basically impossible for me to design an isometric dungeon, I just don’t have the visuospatial capacity for that, but the triangulation approach, I think I could at least design it, although I imagine I’d struggle to actually be able to use it in play and would probably default to the planar approach, which to me, for just a few levels, I think would be perfectly fine, but I still need to test it.

Also, I did suggest in the post how you could just have a literal 3D model of a hexcrawl (presumably digitally), which would probably be the best approach if you’re comfortable doing that.

I don’t disagree that this is more so a theoretical pursuit, but I do think some version of the Moment dimension (I’m increasingly liking the idea of just treating it as a regular movement mechanic…), and maybe a very restricted version of the planar slices of the 3D hexcrawl (~3 planes), should be doable and not too much extra effort, but I haven’t had a chance to test it yet.

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Thanks; I better understand now.
I’m interested to see how it works out.
Please keep us posted on your progress.

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Hrmmmm … perhaps you are referring to my procedural “Battleships Dungeon”?

The idea mentioned in my last post was not finished (just a test Excel widget), so not really in the public domain (but I can share the link?). The idea was an offshoot from an Excel widget I made for generating random and editable hex crawls in Excel:

In this case, the idea was to cover spaces (i.e. caves) in interconnect layers in a cave system. Looking at your post, made me think that this could also apply to interconnect layers in “Space” etc.

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The more I think about the color idea, the more I like it. That’s a really cool way to track multiple levels of a third dimension onto a two-dimensional plane. It wouldn’t work for more than three levels (or at least, can only map relatively- so if things are above or below overlap), but it could be used to map scale (the overlap of colors suggesting an object exists on multiple levels) in addition to mapping three-dimensional space on two-dimensions. I think I would prefer this method on the whole (with the caveat that you can only have three levels, as opposed to the triangulation method).

Having thought more about the hex flower, the “it came from above/below” thing in particular, it seems like it would be useful in tandem to these other ideas.

This is really cool, between the two of you, I think I’ve got some good ideas for improvements for all this.

EDIT: You may be right about the battleship thing, need to reread that…

EDIT: Also, need to give the interconnected caves thing a closer look…


@GoblinsHenchman The most recent episode of your podcast was interesting :wink:

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Updated the episode show notes to mention this thread.

Before I start talking, I’m not always certain what I’m going to talk about!


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