Piratecat's dungeon design: fun with tesseracts!

[MerakSpielman]

It must be a disconcerting feeling if you jump into the trapdoor on the floor. As your feet enter, they start trying to "fall" up towards your head, but of course the rest of your body out masses them, so your legs would go through and start trying to "fall up," eventually you'd be floating in mid-air with your center of gravity poised on the border between the two opposing gravity areas. But it wouldn't feel weightless... since gravity is affecting each half of your body, just in different directions.

 

[drnuncheon]

The changing of subjective gravity by making every trapdoor be in the floor when it's exited isn't a twist I've run into before. At the time when I was using it, I left their subjective gravity the same (two people from different sides could climb through the door at the same time, and their gravity would still be different.)

In a way, that was even more evil, because a person's subjective gravity never changes - down was always down to them. But their relative gravity can and did change - walk through the right sequence of doors and you're suddenly at right angles to the rest of your party. In the Pcat way, it's a lot easier to get back together (everyone use the same door)...

Since I don't have the Cat's Excel skills (or Excel for that matter) we're going to have to do this without pictures, but you can get some six-siders to help visualize. Arrange six of them in a cross shape, one on top of the cross, and one other off to the side to be the 'bottom' room. If each die is a room, it's easy to see how they interconnect.

Now realize that since this is a tesseract, you can move those dice on the 'cross'. Just keep one of the edges in place, and 'flop' the die over. All those connections work, too. You can flop all the way up and down the center 'post', and you can flop side to side on the cross as well.

So, imagine the PCs are at the top of the cross. They go down a level - now they're in the center of the crossbars. The rogue, scouting ahead, heads into one of the crossbars (still with the same gravity as the party), and then goes up. Since there's no die there, you 'flop' the room she was in up, to see where she winds up - and she undergoes a change of gravity relative to her teammates. Now she's back in the starting room - but she's on the "wall". It seemed to her like she climbed through a trapdoor in the ceiling. If she goes through the correct door, she'll be in the same room as her companions...just on a different wall.
A full tesseract has 48 rooms and 288 doors, enough to drive most party catrographers mad.

 

[Piratecat]

Embarrassing confession: Dr Nuncheon, I think that's how it worked in the original Dragon articles. When I was trying to figure this out myself I didn't have access to the original articles, so I took the cheap way out and just decided to make gravity keep shifting when you went through a door. It allowed me to have a relatively easy way of having bad guys on walls and ceilings, but it was simple to keep track of. Anything that slowed down the game as I tried to keep gravity straight was more trouble than it was worth at the time.

 

[Psion]

Geometrically, it's merely the answer to the question "what is the analogue of a cube in 4-space", which was considered in ancient times. I don't know if it can be credited to any particular person.

IIRC reading various books on polygotes, the book Flatlander (late 1800s IIRC) is credited with being the impetus for a lot of thought on extra-dimensions.

 

[GuardianLurker]

Let me get this straight... if you mixed a 50-50 specific gravity-ratio chunk of metal to make it weightless, it would weigh nothing but still have mass. So it would float on its own in midair, but you have to work against its mass in order to move it? If it's truly weightless, does that mean you can pick it up, toss it in the air, and it would float upwards forever? I'm trying to understand this...

Nit-pick: the "specific gravity" of an object has a meaning (density related I believe) in chemisty. Its confusing to me to see it used for "subjective gravity", which is really what we're talking about here.

The mixed subjective gravity alloy he's talking isn't really weightless. Remember, weight is really a function of mass in an acceleration field. I.e. weight is the Force part of good ol' F=M*A from high school physics. What he's done is ensure that he has two opposing accelerations operating on the same object. You can think of these accelerations as great big huge springs.

When the item is in the exact middle of the room, and the forces are balance (springs of equal length), the object will appear to have no weight along that axis (up/down). Moving it from side-to-side (left/right, forward/backward), it will still weigh the same, and still take as much work to move.

Now, the item will want to stay and return to its balanced state in the up/down direction. If you pull it down (or push it up), the object will start to oscillate around the balance point, becoming a pendulum. Over time, the object will move less and less distance with each oscillation, coming to rest in the middle.

Make the object a 4-gravity alloy, and it will travel a circular path (instead of a straight one). Make it a 6-gravity alloy, and it will orbit the balance point.

If you want real fun, mix the alloys in ratios other than 50/50.

 

[Olive]

Isn't this really just a 8 room dungeon with a twist? And if so, how can you really put much int here? Won't the PCs kill everything in each of the 8 rooms and then just get bored looking around it?

 

[Gutboy Barrelhouse]

Ahhh, Piratecat, thanks for bringing back fond memories.
Read both of the Tesseract pieces in Best of Dragon and the idea captivated me for a long time.
Stuck a few in my dungeons through the years.
Went totally mad and mapped the inner planes on one, linked to the outer planes mapped on another. Yep, I stuck the whole dang multiverse on a couple of tesseracts.
Let's not forget Heinlein's He Built A Crooked House. Great story.
Favorite memory of tesseract in my dungeon: PCs had opened all the doors and so, could see their own backs four rooms away. Mistook that for bad guys, shot arrows which hit themselves in the back! Priceless.

 

[The Goblin King]

In the movie Hypercube the rooms had different Time traits! I only watched the end but I know a time loop of some kind was created. A room where time slowed to a crawl would be an incredibily nasty thing to do.

 

[MerakSpielman]

Hypercube was a poorly done movie, IMHO. It had its moments, though. Like when the heroine character stabs the crazy dude in the eye - leaving the knife there - and slams a door on him, then hears a noise behind her and sees the crazy dude holding the knife to the neck of her friend, except he's clearly 20-30 years older, with a big scar over one eye, saying, "I've been waiting a long time for this moment" or something.