I agree that many of these shots represent three dimensions in two quite well, often through a combination of a clear fore, middle, and background, aerial perspective, receding lines, and selective focus.
Take a look at this thread
where almost all the photos show what I mean by 3D look, where you see most things in focus AND have a real sense of depth -- roundness, plasticity, etc.
We've had a number of discussions about 3D on RFF, often devolving into debates about whether it exists or not. I'm not trying to revive that debate -- just showing that what we mean by 3D may differ.
Joe, I don't know if there is a recognized formula for one, but quite a few people have taken a stab at suggesting lenses that provide it, regardless of subject. I may have a list of some, if people are interested. Sherry K suggested that the round back element on some Leica lenses was responsible in those cases. Not sure if that explanation holds up.