The math behind Gravity’s Rainbow (Part 7): Rotational symmetry

I didn’t do a math post in quite some time, so here is a quick one to get back into the game. It’s about some mathematical imagery in the Putzi’s section of Gravity’s Rainbow:

Other souls move, sigh, groan unseen among the sheets of fog, dimensions in here under the earth meaningless—the room could be any size, an entire city’s breadth, paved with birds not entirely gentle in twofold rotational symmetry, a foot-darkened yellow and blue, the only colors to its watery twilight.

Pynchon, Thomas. Gravity’s Rainbow (S.606).

What I’m interested here are those birds with their “twofold rotational symmetry”. At first I thought he was talking about a tiling that tessellates the plane and that it would look similar to an Escher painting:

But that does not quite work because the birds in the painting don’t have perfect rotational symmetry and the symmetry is not twofold. And the comment about them not being “entirely gentle” seems also out of place.

So instead I created this picture to visualize how I think it would look like based on the description:

It’s a bird-eat-bird world.

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