To answer Gimlao's question:
The four-square concentric rings are in the forest level with the "totem" statue, where you temporarily lose your ability to rotate the world in 3D. Not sure if they're normally visible there in first-person view, but a pair of contributors at GameFAQs found the image file in that level when they decoded the game's resources.
My general theory (spoilerish):
the rings represent the same place in space, at different points in time. The largest set of rings is in the past in the 2D ruins, and the smallest single square is in the "present" (at the top of the Village.) It's where you meet the Hexahedron at the beginning, so maybe this links to the Tome haiku about the point of origin. It could also mean that the mobius "loop" in the candle room with its zero and one squares represents the beginning and end of time, or time folded back on itself?
That's interesting that the paintings link to the square locations!