In the redistricting discussions last week several GOP-designed districts were described as "pinwheels", i.e. 3-4 perfectly compact districts that come together and intersect at a point inside a city. I've played around with this a little and I'm actually not convinced pinwheels are an unnatural feature, even if the maps were being designed by a blind algorithm.
Tl;dr - if you take a metropolitan statistical area that has enough people for N districts, and you subtract ~750k people (one district) from each of the densest areas in the MSA, what's left will look like swiss cheese, so the remaining districts won't be as compact.
Conversely, if you divide the MSA into N roughly compact shapes with the densest areas running between or at the intersection of the pseudo-districts, you can be sure of getting N compact districts by transferring people between districts with minimal effect on their shape.
So non-pinwheel compact districts are possible sometimes (when the swiss cheese map that's left after you subtract the K densest urban districts just happens to split cleanly into N-K compact pieces), but pinwheel compact districts are always possible (usually many options, too)
This isn't to say the pinwheel shapes in the current wave of redistricting weren't intentional retaliation for the Virginia map: at least some of them were. (Thank god.) But you should expect them even in randomly-generated fair maps, because they solve a real geometric problem.
I'm all in favor of giving 800k-citizen municipalities their own districts as often as possible once Dems stop their insane gerrymanders, but in many MSAs with unusual geography (coasts, deserts, corners) or multiple urban clusters, pinwheels are inevitable and proper.
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