|
Click here for a really neat tesseract dungeon template I came up with today while bored. Throw your PCs into it and watch them become increasingly puzzled as the non-Euclidean geometry destroys all sense of direction. Hope someone out there enjoys it.
|
I think this reminds me of Cube- the good one, not the weird sequels. =p
DM: You are in a 30 foot cube, painted entirely in green. There are six doors- one on each face. What do you do?
Sorcerer: I go to the one on my left!
DM: Okay. The hatch closes behind you as you enter a yellow cube, 30' on a side. The rest of the party hears something sharp happen, followed by the sorcerer's agonized death scream.
|
|
I think this reminds me of Cube- the good one, not the weird sequels. =p
Cube was in fact one of my inspirations, why I structured the rooms the way I did, and why I decided to give them a color theme.
I'm not entirely happy with it at the moment, I need to change a few things to make them more clear. Like the fact that no matter what door you exit room 1 from, you end up coming out of the ceiling hatch of the room you enter. And from room 2, you end up coming out of the floor hatch of the room you enter. I should have made that clear in the notes to the right of the map.
When I'm fully happy with it, I'll provide the source Excel file, and maybe try to make an Acrobat form version.
Although I think you have the relative positions of the rooms correct, the orientations are a bit off. A 4D cube is symmetric (much like its 3D or 2D versions) so any one of it's volumes can be thought of as being the "centre" and having the same relative positions to the volumes surrounding it.
So, you shouldn't have a room that exits into the ceiling hatch of every other room unless every room has that property.
The easiest way to visualize it is by examining its "shadow" in 3d which looks like two nested cubes with corners connected. The hardest part is that the outside volume is infinite and going "up" from it goes into the bottom of the finite volumes whereas going "down" from it goes into the top of the finite volumes.
Non-Euclidean geometries are one of my favourite topics and I try to fit it into classes I teach whenever possible.
|
I really dont see there is any understanding of a tesseract by those who keep mapping these things out...
Get yourself a Glass cube and look at it from a corner so that there appears to be a second cube further in: Despite the fact that you are looking at the same 'room' through three different 'faces', you are in fact looking at three different rooms that are 'superpositional'. This means the rooms are the same room at superposition, but seperate rooms when they are not.
|
|
I realize that it's not a perfect representation of a tesseract, but I wanted to make something that is at least somewhat accurate to the concept while still being usable by someone who knows almost nothing about higher-dimensional physics (ie, the vast majority of people who might ever look at it).
I've seen them used in dungeons before (and even a few old issues of Dragon), but those always ignored any other entrances/exits from rooms 1 and 2 other than the connections to room 5. So mine does gain a layer of complexity that those lacked.
Tem, I think I know what you are saying when you state "So, you shouldn't have a room that exits into the ceiling hatch of every other room unless every room has that property." I think it's really more a matter of me clarifying the existing connections than making any changes. I'll give it a go tomorrow and throw up a revised version...I'd love to get any further input that you have.
|
|
I realize that it's not a perfect representation of a tesseract, but I wanted to make something that is at least somewhat accurate to the concept while still being usable by someone who knows almost nothing about higher-dimensional physics (ie, the vast majority of people who might ever look at it).
I've seen them used in dungeons before (and even a few old issues of Dragon), but those always ignored any other entrances/exits from rooms 1 and 2 other than the connections to room 5. So mine does gain a layer of complexity that those lacked.
Tem, I think I know what you are saying when you state "So, you shouldn't have a room that exits into the ceiling hatch of every other room unless every room has that property." I think it's really more a matter of me clarifying the existing connections than making any changes. I'll give it a go tomorrow and throw up a revised version...I'd love to get any further input that you have.
I know...Gary and Co. had one in a 1978 issue of Dragon (Check Best of Dragon Magazine 1-2). You would likely enjoy the read of the two page article.
Since a 2 dimensional square has 4 sides, and a cube has 6 square sides, a hypercube has 8 3D cubes. It is often represented by the cubes within a cube because it is easier to visualize. Actually, if you visualize a hypercube by thinking of a cube with a cube stuck to all sides, then a final cube attached to the far side of the cubes, that's more representative. If you go through the north door 3 times, you come back into the starting room. If you go through the trap door in the floor, you come up out of the floor in the next room.
|
|
Since a 2 dimensional square has 4 sides, and a cube has 6 square sides, a hypercube has 8 3D cubes. It is often represented by the cubes within a cube because it is easier to visualize. Actually, if you visualize a hypercube by thinking of a cube with a cube stuck to all sides, then a final cube attached to the far side of the cubes, that's more representative. If you go through the north door 3 times, you come back into the starting room. If you go through the trap door in the floor, you come up out of the floor in the next room.
And you will note that my map works exactly like this. :)
non-Euclidean geometry
Psst Tesseracts do use Euclidean geometry locally. If you want non-Euclidean geometry you'll need to use something like a sphere or torus as your foundation. Any hyperbolic space is just plain cruel against anything that uses range.
This makes me want to go back to an idea i had for using various groups and structures that I encountered in an Abstract Algebra course as well as some different topological spaces as inspiration for locations. Might be time to dust off some old text books.
