Non-Euclidean maps

[ShadowSandbag]

I'm currently running a Call of Cthulhu game and could use some advice. A decently big thing in Lovecraft's stories is the wrongness of the buildings , having unnatural angles and the like. I was wondering if anyone had any tips on making maps that incorporate this idea. Most of my maps are digital if that helps at all.

Thanks!

[Arcane_Snowman]

I'm currently running a Call of Cthulhu game and could use some advice. A decently big thing in Lovecraft's stories is the wrongness of the buildings , having unnatural angles and the like. I was wondering if anyone had any tips on making maps that incorporate this idea. Most of my maps are digital if that helps at all.

Thanks!

Well, from a purely mathematical standpoint non-euclidean in essence means that the the surface upon which the drawing is being made is not a flat piece of paper. As such the only real way to make a true non-euclidean map you'd probably need to use a 3d render program to draw the map upon some other object. However given that that is a horrible way to go about I would suggest you don't do that. If however you know how to use such a program I suppose you could make the map on the 3d surface and somehow then transpose it onto a flat plane, ala. a bitmap? (don't know the correct term, but it's the flat plane equivalent of whatever gets painted on top of a 3d sculpture).

From a person standpoint the biggest feature of non-euclidean areas is the fact that they don't follow the intuitive laws of transportation, walking in a straight line on a sphere does not produce a straight line if the sphere is squashed into a flat surface.

Unless you have some of the aforementioned skills, it'd probably be better to avoid drawing a real map as walking in a straight can make the road double back on itself or perhaps lead you to be walking on the ceiling, and making a map for something like that just constrains your creativity needlessly. Looking at stuff like MC Escher, Fractals, Mobius Strips and 4D Objects (or any object more complicated for that matter) could provide significantly more inspiration. And having the maps suddenly disappear will also help give the impression to the players that where they are can't be properly understood by mortal minds.

[jayem]

You can do map segments (where each is almost Eucalidean*) and then mark where they join.
The good thing is that where when you do that in most spaces you have to transform and add upp. (Euc space you have to make sure that it adds up) in Cuthulu space if you get it wrong it's just another feature.

*so you could have a straight corridor that runs north-south at the beginning and east west at the end just by labelling it as such (perhaps draw it half way between the two so you remember (in general from the point of view of one corridor and it's rooms things are more or less going to be drawable - and if most pages have say 20 internal jumps and 6 external) that's probably more trackable than defaultly bigger or smaller segments)
Or a grid of rooms where one room is a broom cupboard and the other a great hall

[Satinavian]

You can't really. Because the geometry of your map does not match the geometry of what to depict.

There are two workarounds :

- Going to higher dimenssion and build a 2D map as a 3D object

- Using topological maps only that only tell what is connected to what else, but don't include informations about angles or distances

[Cluedrew]

Go with the Zork solution, describe things in terms of locations and connections without actually making a map. Or at least start there, because that gives you the end results you are probably looking for anyways.

Now the 3d map things sound really cool as well, but I don't know how one would do that.

[Florian]

Create two maps for the same area with more or less pronounced differences. Use cardboard tiles to recreate the first map and start rebuilding those differences when the characters move around the area, switching the layout ever so slightly back and forth between the two maps.

[SimonMoon6]

Some people have already made good points. But here is something else to consider: do you want the geometry to be literally non-Euclidean or just freaky weird? Freaky weird is easy. You can have places where you run and you run just to stay where you are (like in Through the Looking Glass). Perspectives can be weird, like living in a Picasso painting and traveling in a straight line causes you to turn a corner. Or if you travel far enough in one direction, you end up back where you started (like scrolling across the screen in a computer game); that might sound ridiculous because on a flat plane (using Euclidean geometry), if you travel along a straight line, you will never return to your starting point. However, if you live on a planet (like most of us do), then you do not live on a flat plane and instead, if you were to travel far enough along what we might consider to be a straight line (which might actually be a circle whose center is the same as the center of the planet), then you will inevitably return to your starting point. By living on a spheroid shape, we automatically are part of a non-Euclidean geometry.

But if you want things to be literally non-Euclidean, you have to understand what that means. Euclidean geometry is the geometry of a plane and there are a few basic axioms that have to apply to geometry in a plane, from which all the rest of plane geometry can be deduced. For example, in Euclidean geometry, given one line, it is always possible to find a line which is parallel to that first line (meaning that it does not intersect). However in "projective geometry" (which is one of many kinds of non-Euclidean geometry), there is no such thing as parallel lines. For more on projective geometry, go here: https://en.wikipedia.org/wiki/Projective_geometry

But then we have to consider which kind of non-Euclidean geometry do you want to have? Which of the rules of Euclidean geometry do you wish to break?

Also, for a modern person wishing to play with Euclid's axioms, it may be easier to consider Hilbert's axioms which make things more rigorous for a modern mathematician to understand.

[Bohandas]

Take a square piece of graph paper. Remove one quadrant. Draw the map as if the remaining 3 quadrants were joined (if necessary you can actually tape them together into a cone but this will make the map nearly impossible to draw on or read). You now have a map with a 90 degree angular defect

[Inevitability]

Make a map that incorporates any number of spatial distortions, then overlay a 'grid' that makes clear what spaces are next to what other spaces. By altering the size/shape of some of the spaces on the grid you can create maps that allow for movement in non-intuitive ways.

[Bohandas]

You could also draw the map on a hyperbolic grid of squares, although this has the disadvantage that to draw it such a thing in euclidean space you need to either draw the grid on a saddle shaped surface, use specialized software, or use a projection like the one shown below that rapidly becomes smooshed up around the edges



EDIT:
You also, if you do this, might need to rework the rules for moving on diagonals. I'm not sure whether or not a diagonal step from the large square on the center right to the large square on the center left should or shouldn't cost the same as a diagonal step from the large square on the center right to the large square on the upper left

[Eldan]

I'd say the simplest way is to have a series of squares, tiles, rooms, whatever, and then number the edges of each square, then write down which number connects where, in illogical ways.

[ExLibrisMortis]

Take multiple sheets of paper. Draw a map on each. Add some ways to get from one map to the other (not at the edges). Declare that all maps share the same edges in one direction (in to out). For each map, designate one edge to be an out-to-in edge.

For example:

Map 1 1 1 1 1 D	Map 2 D 2 2 2 2
Map 3 D 3 3 3 3	Map 4 4 D 4 4 4

Matching faces indicate map transitions (doors, for example--it doesn't have to be complicated). Each map leads to each other map.

If you approach from the north, you enter Map 1 at Edge 1.
If you approach from the east, you enter Map 2 at Edge 2.
If you approach from the south, you enter Map 3 at Edge 3.
If you approach from the west, you enter Map 4 at Edge 4.

Exiting either map to the north, south, west, or east, will simply put you north, south, west, or east of the four maps. They all share one outside.


You are on layer 3. You wake up and leave the house. You exit the area walking north. Later, you return and walk in from the east.
You are now on layer 2. You find yourself looking at a different building in the same spot. You run back and retrace your step, approaching from the north.
You are now on layer 1. The same building is there, but fifty feet to the left. You enter through the side door, with an orc face sticker on the doorbell.
You are now on layer 4. The interior does not match the house you woke up in. You run out through the side door, with a grinning skull doorknob.
You are now on layer 2. You are in your bedroom. You bar the door, and sit by the fire, worried and afraid. A few hours later, you hear noise in the hallway. The man entering your house is surprised and angry to find you in his house. At this point, you have a nervous breakdown. After watching the ambulance leave, the man enters through the side door...


For extra mayhem, map transitions (doors and edges) change over time, with the phases of the moon, knowledge of the subject, presence or absence of certain people in the buildings, or randomly. I don't recommend randomly. It's fun to try to get players to figure out the system. When they do, it's very satisfying to 'game the system' and walk around like it's all normal. I suppose that, in typical Lovecraftian fashion, this is the point you a) never reach, because you are dead/insane, or b) only reach when already insane and an NPC, or c) reach quite easily, only to get eaten by the 4D equivalent of an antlion.

[Bohandas]

Here's another hyperbolic grid

[Beleriphon]

Do you want Non-Euclidian, or do you want MC Escher? Because MC Escher fall much more into the world of things that look possible, but aren't.

Otherwise just go with maps labeled weird that your start sticking together but don't necessarily have rules that make sense. For example point A connects to points B when traveling to it from one direction the first time, but passing Point A connects to Point C on the second pass through. While travel from Point B back to Point A actually goes to Point X every time.

Add to that fractured strangeness Kirby Krackle filled worlds and you should be all set.

[Crake]

You can do map segments (where each is almost Eucalidean*) and then mark where they join.
The good thing is that where when you do that in most spaces you have to transform and add upp. (Euc space you have to make sure that it adds up) in Cuthulu space if you get it wrong it's just another feature.

*so you could have a straight corridor that runs north-south at the beginning and east west at the end just by labelling it as such (perhaps draw it half way between the two so you remember (in general from the point of view of one corridor and it's rooms things are more or less going to be drawable - and if most pages have say 20 internal jumps and 6 external) that's probably more trackable than defaultly bigger or smaller segments)
Or a grid of rooms where one room is a broom cupboard and the other a great hall

I support the use of this method. I implemented a hypercube by having each individual room connect to other rooms, and of course, each individual room had euclidian geometry, but they were connected in non euclidian geometry. This link is what I used it as a basis for, but people have gone one step further, upping the ante to 5 dimensions like this.

[Glorthindel]

Another way is to draw the map on hex paper, but describe it as if it was square. By this I mean, if you imagine the party entering from the bottom of a hex, the map has 5 other "sides", but you just describe it as if there were three. Straight on is still straight on, but there are now two "right walls" and two "left walls". Say that on your map there is an exit in the south-east wall, and another in the south-west wall, you would just describe these as exits in the east and west - to the players mind, this is basically a T-junction, when in reality these passages are angled away from each other by quite a significant amount. Very quickly these angles will scramble up the players perception of the layout.

[Lvl 2 Expert]

An extra complication in a hypercube scenario is that the 3D rooms you're in are the "sides" of the 4D hypercube. Imagine a square in a flat environment, every side (line) is connected to one other square. Imagine a square in a 3D environment of stacked cubes, each side is now connected to 3 different squares. One straight ahead and 2 under 90 degree angles in the 3rd dimension. When a flatworm opens a door in that side, to which square does it connect? That's the situation you're in if you're in a 3D room inside of a 4D environment. (The number stays 3 because that's also the number of other lines every dot at the end/edge of a line connects to when placed in a 2D environment of squares. Extrapolating can give some cool insights into these things.)

You can ignore that if you're in one isolated hypercube (say a dancing hut containing 8 3D rooms connected weirdly), but it's something else to add to make things just that much weirder.

[Cluedrew]

This link is what I used it as a basis for, but people have gone one step further, upping the ante to 5 dimensions like this.

If I ever run another classic dungeon, this might just be how I do it. And the final treasure of the dungeon will be a box, and inside that box will be the dungeon. And if you take the box out of the dungeon you can move it around and set up the dungeon elsewhere. Or maybe it will just recursive.

Still there is still work to do to get these dungeons up and running. Like filling each one in an interesting way that allows for the 6 different forms of navigation (six different directions) to work. Plus as confusing as it is to navigate, nothing is ever far away so it is pretty easy stumble on the end, well there really isn't and end. Still it would be a very interesting place to explore and navigating around it when you got the feel of it would probably be awesome.

[Bohandas]

Do you want Non-Euclidian, or do you want MC Escher? Because MC Escher fall much more into the world of things that look possible, but aren't.

A lot of the things are consistent but wouldn't actually look like that. A lot of his stuff is based on the Penrose Triangle for example, which is theoretically possible in multiply connected space but in real life would just look like a square with one corner cut off

 —— ->wormhole
|
|    (wormhole)
|    |
|    |
 ————

[Knaight]

Non-Euclidean geometry is really easy to achieve, with simple things like being on a sphere doing it - which in this case can be represented with a simple wrap-around map. To make that a bit weirder, add wrap around in all directions, including top to bottom. This also has the advantage of being easy to graph, and easily combined with other techniques (such as the hex grid described upthread, which is extremely clever).

Another easy option involves mapping discrete rooms, and leaving gaps between them. Then, color code each exit (preferably with about eight colors), and number the rooms. Leaving from an exit of a given color puts you in the entrance of the room with the lowest number above the current numbered room with an entrance of a given color. Then there's additional fun - you can also use the colored pencils/markers/whatever you used for exits to draw room features that only exist in a room if you entered it with the same color entrance. Otherwise it can either simply not be there or exist in some sort of phantom state. The entrances to the building can easily be among the color dependent features.

[Aliquid]

I like the concept of multiple maps.

multiple smaller maps that join together. But when you line the maps up, the landscapes or floor plans on each map don't quite line up properly.

[CarpeGuitarrem]

I'd say the simplest way is to have a series of squares, tiles, rooms, whatever, and then number the edges of each square, then write down which number connects where, in illogical ways.

I did exactly this for a scenario where the PCs were trapped in a Fae Lord's castle. Most of the doorways between rooms were not bidirectional. And none of the doorways made sense, really.

I actually had a player who tried to map it. They were very befuddled.

[SirBellias]

I don't know much about the science of such, but here's what I'd do to mess with people.

Take a grid.

Erase some of the lines/line segments. Any now connecting squares now count as the same square.

Number some of them. They count as the same square. Don't do this with too many though, as it may lead to stupendous opportunity attacks.

Draw half the map in one place.

Draw the other half somewhere else facing a different direction.

Screwing with the player's perceptions in a simple way often gets a good enough effect.

[Bohandas]

I did exactly this for a scenario where the PCs were trapped in a Fae Lord's castle. Most of the doorways between rooms were not bidirectional.

The problem with that is that it always seemed to me like that sort of thing ought to bisect (or even disintegrate) anything that passes through it

[ahyangyi]

Well, an euclidean space with a pair of portals is also non-euclidean... And the multiverse is probably non-euclidean, since it is not homeomorphic to R³. That basically means we pretty much all play in non-euclidean spaces.

[Psyren]

The Mythos is a popular setting - there's got to be all kinds of online resources out there. I say, why reinvent the wheel?

[Beelzebubba]

If you can track down a copy of Dragon Magazine #83, it had an excellent article about making Tesseract maps.

Or, watch this gif until you have the 'head explodes' moment when you realize what it means:


I'd go with what other players say, though: just draw some sketches that imply the weird stuff you want, and attach it to regions of a given room, or have it happen when they move from place to place.

Like, I'd love the idea of seeing what looks like a toy building, and when you reach out your hand, it becomes really small and far away - and when it touches the toy, it's so tiny that it looks like your arm is a mile long. When you lean in your head to look closer, it's as if your face stretches and zooms in like a telephoto lens, so you are now looking at it like you are right next to a skyscraper. Then, you climb into the window. To everyone in the other place, you looked like you got sucked down a drain and disappeared.

Stuff like that maybe?

[Bohandas]

how attached are you to using a grid? Because if you're fine with working ot scale distances using a tape measure or string you could attach double sided tape to the bottoms of your miniatures and draw a combat map on a beachball

[Lacco]

how attached are you to using a grid? Because if you're fine with working ot scale distances using a tape measure or string you could attach double sided tape to the bottoms of your miniatures and draw a combat map on a beachball

For maximum confusion, but not really non-Euclidian:

Or make a rubic cube your grid/map. Rotate after every step.

Or, you know the heaven & hell paper thingie. Which door did you choose? And which brick did you push? The red one... you enter the same room where you were before, just from the opposite side. You see the same room when you turn around, with your characters standing in the doorway on the opposite side, smirking, as they close the door...

[Bohandas]

Or, you know the heaven & hell paper thingie.

What? Link please.