Wednesday, May 6, 2020

Doors, Shores, and Parallel Zones: a guide to the boundaries between worlds

So you're jumping around between parallel dimensions.  But what's the crossover like?

Here's a quick taxonomy, sorted in increasing order of smoothness.



(Also known as gates, portals, wormholes, cosmic glory holes, or rifts. )

An enclosed frame holding a flat region of warped space which is connected to a paired surface elsewhere in the cosmos. Any particle which passes through the frame is transported to the other world. (Some doors connect to an intermediary demiplane, and so resemble a tunnel.)

These are the most common and easiest-to-understand type of planar boundary, and most cross-dimensional spells work by opening these doors.

The defining characteristic of this kind of boundary is that local space is entirely normal close to the boundary and then experiences a discontinuity.

d6 doors found in the Plates of Flavor:

  1. A small pond of cream found in the Plate of Sweets. Jump in and you'll pop out of a similar pond in the Plate of Meats. Unfortunately, the pond has a tendency to move around when no one is paying attention to it.
  2. An elephant-sized peach pit lays in the deserts of the Plate of Seed. Small tunnels dot its surface, just large enough to crawl through. Most of the tunnels are shelter to vermin, but one opens out into a giant half-eaten peach in the valley of unripened fruit. 
  3. The city of Everything Bagel, found at the center of the Great Buffet of the outer plates, is just riddled with doors. Nobody actually lives there except for the Lady of Propane. All the other people bustling about were just unfortunate enough to have a random portal open up connected to their refrigerator or shower drain or something like that.
  4. If you dig deep into the crust of the pastry plains, sometimes you'll find a pocket of filling connecting to some other world. A custard pocket connecting to the plain of sweets. A pocket of garbage connecting to the prime material. Etc.
  5. Dionysus has a big inter-dimensional portal that he just uses to dump half-eaten chicken wings.  No clue where the other end opens up.
  6. Dump enough fish sauce into any whirlpool and it will briefly transform into a portal to the shallow sea.

Hyperbolic Shores

A transition into another world with noticeable spatial distortions, but no discontinuities.

For example, you're in the Boiling Oil Ocean, cruising around on your turnip barge. You see an island made of meat off in the distance, giant billowing fingers dressing its shores. After cruising around a bit, the island doesn't seem too large. But when you land and go to explore its interior, you find that it's infinitely large and in fact contains the entire Elemental Plate of Meat.

Meanwhile, from the Meat side of things, you approach a lake of oil. You can easily walk around the entire thing in a matter of hours, but can't see across to the shore on the other side. The lake, is in fact, the entirety of the infinite Plate of Oil.

Another common kind of shore are the ones that form in large book collections. As we all know, a dense enough concentration of knowledge can cause spacial distortions, making libraries and bookstores bigger on the inside or even connecting them to L-space. Because such distortions are noticeable, but locally continuous, they count as Shores.

Parallel Zones

Characterized by a transition to another world despite the lack of absolutely any sort of spatial distortion.

You know, that crazy fairy kind of stuff where you're walking in the woods down a path you've travelled many times before, but it's unusually spooky this time and then somehow you find yourself trapped in an endless twilight forest. And it turns out it's because the vice-archduchess of the fey or whomever wanted to look at your hat was lined with beaver pelt from a particular magical beaver is seeking its revenge. Okay, we're back. It's fine.

Tuesday, May 5, 2020

Mathpost: Coordinates on a tesselating hexagonal world.

Turn back now, if ye be looking for some narrative content. This be nothin' but a big wad of barely polished geometry.

Basic idea is that you live on a giant flat plane that loops. (As in this story) Go far enough in any direction, and you'll end up back where you started. Navigational systems evolve to meet the needs of the people using them. What kind of system of coordinates would be useful for navigating on a looping hex?

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Rectangular Coords

X: Y:

Hexline Offset Coords

A: B: C:

 Unit length is equal to the inner radius of the hex.

(X,Y) coordinates are the standard Cartesian kind.

(A,B,C) coordinates are "Hexline Offsets". Basically, choose 2 opposite edges of the hex perimeter, and draw parallel lines first through the origin and then through your point. The absolute value of coordinate is the ratio of (the distance between the point and the line through the origin) and (the distance between the center and the perimeter line)

Further Explanation 

More detailed unpolished explanation below.

Neither the images nor text were optimized, so everything is a bit too large.