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[Dorfimedes]

Did anyone else read in the news about the theory that all universes are contained in black holes?  While begging the issue of what the very "topmost" universe's black hole is in, it does support the "turtles all the way down" maxim.

http://www.foxnews.com/scitech/2012/05/17/every-black-hole-contains-new-universe/

Just thought I'd throw that in since the topics of curved space came up and universes arose.

I don't want to sound like the time cube guy, but I've been telling people for a while now that the universe could very well have a fractal structure. But this... This is just incredible. IRL inception?

[WealthyRadish]

Saw Fox's new slogan, nearly fell out of my chair.

Back on topic...
For natural walls, my guess is that it's more they squeeze through a crack, as mentioned, whereas smoothed/constructed walls actually show space between diagonals. Octagons wouldn't work, as they always would leave an impassable pillar in the corner. No shape would work that could represent 8 directions of movement on a square grid, so thinking of things geometrically isn't a good idea.

Having natural walls use the same varied tiles as constructed/smoothed walls would fix this, but would require quite a few new tile sets for something rather minor.

Edit: Looking back over the OP, it looks like the idea is that mined tiles are squares, and natural tiles are octagons. That makes more sense, but rock layers would need to have periodically placed pockets, which is rather contrived. If it is solid, are you saying that the dwarves mine out the corners on the surrounding blocks?

[Lagslayer]

Perhaps the tiles are hexagonal. Try wrapping your head around that one.

[biomatter]

I always assumed that walls didn't actually consume an entire square, and thus there was plenty of space to move through diagonals. It's the only way I can justify "One Natural Wall -> One Boulder -> Four Blocks -> Four Walls". They must be thin walls...

[FearfulJesuit]

Perhaps the tiles are hexagonal. Try wrapping your head around that one.

That would make for an interesting update, like the one from Civ IV to Civ V.

[cybergon]

Try and put four octagons together so that they perfectly interlock. It's impossible, there will always be an annoying diamond in the center... Fucking shapes, how do they work.

A bit late replying to this, but yeah I get what you say. What happens is that this space actually doesn't exist between the tiles until the miner digs it out, like this:



Then if we're talking about building walls, think of it as if it were in reverse, builders fill that space in when they place the first orthogonal wall, then the fourth wall just fits in perfectly.