World Capitals Voronoi (2014) | Hacker News Reader

World Capitals Voronoi (2014)

jasondavies.com

92 pointsodyssey744 comments

Another example of how real world data is always messier than a neat model:

Vatican is entirely encircled in Rome, therefore any area outside Vatican is closer to Rome than the Vatican, yet if we look at them as point sources, as this map does, you see a lot of other area closer to Vatican.

> Vatican is entirely encircled in Rome, therefore any area outside Vatican is closer to Rome than the Vatican

this is only true if the rule is "any point inside the area". if the rule is "any point on the border", then your comment fails here:

    +--rome-border
    |
    |
    | x (closer to vatican border)
    |
    +--vatican-border

The official city limits of Rome extend quite far out into the countryside (all the way to Ostia), so by this reckoning, I think the Vatican area would encompass the lion's share of the buildings/population.

Amen. I work in geophysical computing where there is no such thing as neat data.

It's interesting to see how some of the boundaries drawn by this end up lining up with historical territories. For instance, in this map much of the American southwest comes under Mexico, which it largely was a part of during the middle of the 19th century. Scotland and Wales also fall under Ireland, which also makes sense given their common Celtic ancestry. And Vatican City has much more territory in Italy, which it did throughout much of the last millennium as the Papal States.

Except that the Vatican is fully within Rome so, actually, nowhere in Italy is closer to the Vatican than to Rome...

Or, nowhere else in the world is closer either.

You made me curious to find out the antipode of the Vatican City (41.903°N,12.454°E): the nearest land point is Waitangi, Chatham Islands, New Zealand (43.9°S, 176W) according to: https://www.geodatos.net/en/antipodes/vatican/vatican-city (not 41.903W, -167?W, which is in the ocean).

Good points. With regard to the last one, the result depends strongly on how one deals with the Vatican City being an enclave of Rome.

I'd guess it just uses the central point of each city.

Some things I'd love to see:

- a difference metric between this coverage and the actual map (and country breakdown of same)

- a weighted version ([1]) with weights chosen to optimize the above distance metric.

The latter is in itself is a fun math problem -- the gradient on such an objective clearly exists (and the numerical gradient is fairly cheap). But can you prove anything about its structure? Is there a closed form that could be derived from the map information?

[1] https://en.wikipedia.org/wiki/Weighted_Voronoi_diagram

What I'd suggest trying is to use the accessibility of the terrain (there are such maps out there) and find the closest capital city according to that. This is basically a global travel time map and I would not be too surprised if that matches some borders rather well.

Jason also made a spherical Voronoi map with a dataset of world airports: https://www.jasondavies.com/maps/voronoi/airports/

There’s an Observable version here if you want to see an implementation using d3-geo-voronoi: https://observablehq.com/@d3/world-airports-voronoi

It’s incredible that these were created almost 10 years ago and yet so little of the internet uses d3 or similar interactivity these days.

What do you mean by “so little of the internet uses d3 or similar interactivity”?

D3 is not as ubiquitous as one might think. Outside newsroom graphics departments most visualizations consumed through the browser are published using low-effort crappy BI tools like Power BI and Tableau or some generic charting libraries. So still even in 2023 when you see something that’s been meticulously crafted using a low-level approach (like D3) that allows that slick native feel it’s very impressive.

I just mean I don’t see as many websites using d3 as I’d expect given how amazing it is

I remember seeing your Obama 2013 budget article and being giddy. I just wish I saw more of that.

The most surprising bit for me (because it really depends on the world being round) is Alaska - parts of which are closest to Tokyo, Reykjavik, or Ottawa. (No part of Alaska is closest to Washington.)

In the US, the southwesternmost bit of Virginia is closer to 9 other state capitals than to Virginia's capital of Richmond (https://cardinalnews.org/2022/02/28/ewing-is-closer-to-nine-...). On a world scale these numbers can get quite large - it looks like 33 capitals are closer to Vladivostok than Moscow is (https://mathematica.stackexchange.com/questions/159041/how-m...).

Actually you know what, it is kinda weird that New Zealand doesn't have a claim to half of Antarctica.

Part of Antarctica does use New Zealand's time zone:

https://brr.fyi/posts/sunset

New Zealand does have a claim containing McMurdo Station. It doesn't have much land since Ross Sea gets close to South Pole.

The unclaimed Marie Byrd Land is next to Ross Dependency. New Zealand would have good claim. But the nearby countries mostly claimed areas directly south.

It does claim a slice

Would be interesting to use the centroid of the current country as well.

Jason has created some very nice maps, go check them out.

Fun fact from this map, if I’m not mistaken, Greece is the only country touching three continents (Europe, Africa and Asia.

Wonder if the Voronoi map functions in the Java/Net Topology Suite also accounts for the curvature of the Earth like Jason's maps do.

So pleasing

I love Voronoi diagrams (and Dirichlet sets.) been in my toolbox for a long time. used in a few of my games and game prototypes.

Canada seems to me to come out the big winner.

I keeps pretty much all its territory and it absorbs a significant chunk of the USA.

I wonder which country got the biggest relative bump in territory. Vatican City is probably a contender, and Timor-Leste nabbed a huge part of Australia.

I think Iceland and New Zealand are also contenders. Iceland absorbs all of Greenland, large portion of Nunavut, and a sizable chunk of Alaska. New Zealand grabs a large part of Antarctica.

I think though if Nuuk were to be included the dynamics of Iceland would change significantly, and similar if you include New Zealand’s already claimed territory on the Antarctic, then their gains are less impressive.

Some of the small European countries like Monaco, Lichtenstein, San Marino, Andorra and the Vatican do quite well for themselves.

Percentage wise Andora is killing it!

Looking further Brunei and East Timur are also huge winners.

I think it is because it is slightly to the west of Washington D. C., and there is no country to the north of Canada.

If, say, Chicago is the capital of the US, I think a lot of Canada will end up being closer to Chicago than Ottawa.

Wonderful visualisation, always wondered this one. I wish the nodes had the names of the capitals.

They do, if you hover the mouse pointer.

South Africa is cheating by having three capitals.

very interesting, in some places the influence of cultures, language is close to the border

"Holy Sea"

The funny thing about the Vatican, in addition to the misspelling, is that it highlights the flaws of Voronoi when points are close together.

Good eye.

How is Mongolia larger than Russia?

According to Wikipedia: Mongolia is approximately 1,564,116 sq km, while Russia is approximately 17,098,242 sq km, making Russia 993% larger than Mongolia.

This has nothing to do with real borders, but with the distance to the nearest capital (that's how Voronoi diagrams work)

For instance, that shows that more than half of Russia territory is closest to the capital of Mongolia (which is Ulaanbaatar) than to Moscow, that's the point.

Thanks for clarification.

This map doesn't preserve area, it only says which capital is closest by distance.

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