An extra-dimensional dungeon

I’ve been listening to the Wheel of Time audiobooks, and thinking of the extra-dimensional dungeon that Mat enters to face the Snakes and the Foxes, this worlds’ version of fae. This dungeon’s layout is asserted to follow rules alien to the human heroes that enter it.

One example is following a hall that turns to the left, until it seems as if you must be walking in a circle, the inside windows displaying the outdoors, despite that. Another is having to return back through the same door as you came through a number of times back and forth, before reaching your destination.

I’m calling. this extra-dimensional because I’m sure a mathematician somewhere will be frustrated with my calling it non-euclidean, but that honestly feels like a better term because architecture and geometry is what is alien in this dungeon, not all of physics.

A friend on discord gave some interesting suggestions when I remarked on being unable to figure out how to do this in a way that was 1. Systematic; 2. Reasonably Solvable; and 3. Fun to Figure Out.

We draw dungeon maps with six directions, so the easiest solution is that I map each real life direction to a non-euclidian version, with the number of repetitions of the new direction being equivalent to distance, one square being equal to one repetition.

We need to set some rules for description:

  • The PCs know the world is not like ours, and that they need to figure it out; give them a guide to start, or a riddle or something.
  • Windows are in all hallways, except that does replace hallways when they are present.
  • Windows are sealed and unbreakable, in order to cue PCs into the uncanniness of the geometry.
  • Keyed rooms always have doors that are marked in some way, to provide clear cues to identifying the six rules.
  • Keyed rooms may have multiple entrances, but the direction you exit in is irrelevant to the direction you go.
  • If a hallway requires doors, they are unmarked doors alternating on both left and right, for each cycle of hallway.
  • Failure to complete a direction correctly results in re-entering an identical room to the one you started in.
  • Describe how the outdoors doesn’t respond to the movement inside the way you’d expect from the geometry the PCs can see.
  • Both indoor and outdoors should be described as strange or wrong. Dr Seuss feels like a good reference here, perhaps Paul Nash, Hernán Bas, or the World of Edena by Moebius.

I need to think about what it might mean for a hallway to change direction, in terms of description, when I choose my six directions. If I turned west from south, for example, the PCs may not be able to tell, rendering the puzzle unsolvable; as would up a level from east. This suggests that different directions might need alternative descriptions.

Time is also important. It’s typical that these extra-dimensional dungeons warp time in certain ways. Potentially we add a speed multiplier affecting parties travelling in a certain direction.

  1. North: Follow the hallway a full circle to the left. Sinuous. 150% speed.
  2. East: Do not follow the hallway, rather pass back through the entryway you just came through. Sinuous. 100% speed.
  3. South: Follow the hallway until it disappears behind you. Angular. 50% speed.
  4. West: Go through every second door you find in the hallway. Sinuous. 50% speed.
  5. Up: Go through every first door you find in the hallway. Angular. 100% speed.
  6. Down: Follow the hallway a full circle to the right. Angular. 150% speed.

I feel like this won’t make total sense until I build a small dungeon, so here’s one. We’ll describe the path taken while traversing the pink arrow, assuming all rooms are keyed.

You arrive through the twisted red doorway into a room with five walls and an oddly high roof. You walk out the strange, trapezoidal archway ahead of you, seeing a long hallway with marked with strange, sinuous patterns, that curves out of sight to the right, lit by strange yellow lights that span the width of the hallway. You return through that doorway and return to the room you came from. When you return to the doorway a third time, it is no longer trapezoidal, but pentagonal, and you teach a new room. You pass through the same doorway twice this time, and then the patterns on the walls change to an angular, regular pattern. You follow this hall until it disappears behind you, coming to a room with three exits. You choose one, and follow the hall until it disappears behind you before finding a pentagonal door to a new room. You leave and find the sinuous patterns have returned. You re-enter this door five times, enter a new room when the trapezoidal door becomes pentagonal, and exit through the first door you see, finding angular patterns on the walls of the hall. You exit the first door in the hall that follows, and leave the new room you find to enter another hall. This hall is sinuous, so you enter the second door, which leads to another sinuous hall. You enter the second door here, and there is yet another hall. You enter the third hall again, this one also on the right, and find a pentagonal door, and a new room. You follow the hall, now patterned in an angular fashion, in front of you until it disappears behind you and the patterns turn sinuous, pass through the door you find twice, and find a room with one exit. You take it, curving to the left; you turn around until you are back at the beginning again, and repeat it again, and then the hall straightens and doors appear. You take every second door, three times, and find yourself at the Courtroom, your destination.

Phew, that was alot. But it works. This might be too hard a puzzle, or too punishing a fail state, but pepper the dungeon with treasure and battle and the bloody scrawl of those who’ve come before, and we have a compelling life or die puzzle. And in the Courtroom you get to bargain for three wishes with wicked devious entities.

I’d love to see other takes on mapping and running extra-dimensional or non-euclidian dungeons, if anyone has thought about it. This is but one way, the only one I could come up wjth

13th December, 2022

Idle Cartulary


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