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.

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.
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?


Jason also made a spherical Voronoi map with a dataset of world airports:

There’s an Observable version here if you want to see an implementation using d3-geo-voronoi:

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 ( On a world scale these numbers can get quite large - it looks like 33 capitals are closer to Vladivostok than Moscow is (

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

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