Underville, Xana's homeworld, is a set of 2⁶⁴ cubical rooms. That's about 1.8×10¹⁹, which seems like an immense number, but it's not incomprehensibly huge; the total volume of Underville is about 0.8 times the size of the moon. The rooms connect at the edges, and each room connects to four others, but not in any way that makes coherent Euclidean sense. Deep Down Town is the part of Underville Xana's from, and it's the set of rooms along the path from Elseways to Inver City, plus their neighbors.
@bj Makes sense to me! Are all the cubes the same size? Or are there some small rooms and some massive open areas?
-F
@Felthry Every cube is the same size - 1 meter on a side. At mouse scale, though, that's a nice comfortable size to build in.
@Felthry One rule that is consistent, though, is that there are no one-way doors. If you go from room A to B through a specific door, then going backwards will always take you back to A.
@bj Hm. Are there doors that go from A to A?
-F
@bj Also, is every cube accessible from every other cube, or could there be isolated bits?
-F
@Felthry Only as special cases. There are exactly two rooms with self-loops. And to answer your other question, every cube is accessible from every other in a maximum of 64 steps. If you know what path you're taking, you can be anywhere in Underville in minutes, even if you're only going as fast as a mouse on foot can.
@Felthry This works because of the way rooms are tied to bit strings, 64 bits long. The exits correspond to the actions of pushing a bit onto either end of a string and dropping one off the other end, which is why there are 4 (0-start, 0-end, 1-start, 1-end) and why they're reversible. The only self-loops are in the all-0 and all-1 rooms. This is also why you can get anywhere in at most 64 steps; if you know your destination bit string, you just take the exits to shift it in one bit at a time.
@Felthry The latter. Every cube has four exits to other cubes somewhere in its walls, but they don't have to be in any specific place. Since the whole thing is a non-Euclidean mess anyway, you can get rooms with all four doors on a single wall and all leading to places that "should" overlap.