The first true equal-area projection

[saga]

I've just made an amazing discovery. There are many existing projections that claim to be equal-area, but actually aren't. For example, the Equal Earth projection inflates Russia to be nearly twice the area of China, not equal as advertised. I knew I had to fix this state of affairs, so I went to work, and today I finally finished the first real equal-area map:



I know that when old results are overturned, there's bound to be some resistance from the community, but I'll tell you now that I'm not backing down from my discovery. If you all don't have my back, I'm sure Boston Public Schools will.

[justinkunimune]

This could easily be an XKCD comic. I love how eastern Europe looks kind of like an egg sac, and how China gets stretched out into a spindly tree shape.

[daan]

That’s a thing of beauty! Bravo!

— daan

[Atarimaster]

I wish I would have come up with THIS definition of “equal-area”!

[Milo]

Haha.

I guess that in formal terms, this would be considered a cartogram whose measured property is "number of governments".

(Well... not quite. Antarctica doesn't have a government, but is still represented at the same size as actual countries.)

[saga]

Yeah, it is a cartogram where every state (i.e., "sovereignt" as defined by the Natural Earth database) is given a population of 1. I used my cartogram algorithm with a few microstates excluded because they caused floating point errors.

[Milo]

with a few microstates excluded because they caused floating point errors.

Haha, not a problem most cartographers have to worry about often!

I see that this is a new cartogram algorithm published late last year, so it's a legitimately valuable new discovery, even if you chose a humorous way of presenting it.

It does seem to be a pretty good cartogram algorithm. It kinda has to be, for the result to only look mostly ridiculous, rather than totally ridiculous. (Having Africa near the center helps. It provides a calming effect when I get dizzy from looking at the rest of the map for too long.)

And I'm definitely getting dizzy from looking at Central Asia. I think that's the Persian Gulf that somehow got twisted upside down? And the Caspian Sea is the surprisingly-small isosceles triangle north of it? I do think Justin had the right idea about all of Eurasia looking like some kind of monstrous wasp. Japan is pretty much its antenna (it's close enough to the rest of the land that it's not obviously an island), while Scandinavia might be atrophied wings.

My favorite part is North America, though. With how those lame countries on the mainland (like the United States, who needs them?) get hollowed out to make room for a nice zoom-in of the Caribbean Islands. Particularly contrasting with how South America still looks slightly more normal.

If I could nitpick one thing, it's that's some peninsulas, such as Florida and Cape York, seem to elongated to a degree that isn't necessary to equalize the areas, since these peninsulas aren't actual normalized territories in their own right and are only small parts of the territories they belong to. I'm guessing that's what happening is that the algorithm is trying to make these peninsulas look like they're in the right place relative to nearby islands, prioritizing that above preserving the internal shapes of the landmasses they're part of. But it's weird that the algorithm would foist so much of the distortion onto these peninsulas specifically, rather than the attached landmasses, the islands, or the intervening seas.

[saga]

Thanks! I think it gives better results than any other existing cartogram algorithm, though the runtime is a lot longer. This case is pretty extreme compared to a population cartogram, so it's a good stress test.

The issue with peninsulas is from the limited resolution of the mesh. It's possible to increase the resolution, but that would seriously increase the runtime. It can also counterintuitively create cartographic problems, because it gives the geometry more opportunities to get messed up in intricate ways.