Flatland leaves out a lot of details of physics, anatomy, and general science. Everyone is just geometric shapes floating in an endless plain. Planiverse attempts to envision a 2D world with gravity, a food chain, and digressions on the unpleasant reality of being a creature whose digestive system only has a single orifice due to the topological restrictions of their reality.
I seem to recall something about "zippers" at a cellular level? It's been a while and my copy is long gone.
Edit: For some reason using a whole comment to say this got me muted from commenting at all, so I'll put it in an edit: Damn, that shoelace thing is really cool.
That's precisely why Flatland and the Planiverse are such interesting books. Making the step from 2D observing from 3D gives you a little bit of an intuition of how a 4D being would look at us as well as to how a 3D being would look at a 4D one.
It's like saying of us 3d creatures: "the butt doesn't have to be connected to the head, does it?"