Redrawing the map using math leads to some beautiful results

The boundaries of states are so engrained in our minds that it can be hard to look at the earth without dividing it into political regions. But there are many other ways of looking at our planet. For example, what would the map of the world look like if each country only controlled all the land closer to its capitol city than any other country's capitol? Some might argue that it'd produce "mathematically perfect" borders.
Data visualization freelancer Jason Davies has had fun exploring these ideas using mathematics. With algorithms and the right datasets, he splits the planet into regions that contain only the land nearest a certain point — say, a capitol city. Maps made with this technique are called Voronoi diagrams, and he's made m...
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