The maps that MATHS made: Data artist redraws borders using algorithms instead of politics, language and culture
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Many wars have been waged defending a line on a map - or in a bid to draw a new one.
But one data visualisation specialist has created a number of intriguing maps carving up the world according to mathematical rules instead of politics.
Jason Davies, 29, from London, uses algorithms and datasets to divide our planet into new regions based around nearest 'point' such as a capital city or an airport, for example.
Flying high: Jason Davies uses algorithms and datasets to divide our planet into new regions based around a nearest 'point' which can be a capital city or an airport (pictured). On this map it is easy to see that the U.S. is well catered for in airports, while remote islands are not
JASON DAVIES ON VORONOI DIAGRAMS
'The Voronoi diagram is a beautiful piece of mathematics,' Mr Davies told MailOnline.
'It divides space into a number of regions, where each region contains all points closest to a particular seed. The seed points can be anything that has coordinates: capital cities, airports etc,'
Voronoi diagrams crop up in many places, including art and data visualisation.
'The most common Voronoi diagram works in 2D space, where the shortest distance from one point to another is simply a straight line.
However, on a globe, the shortest distance is along something called a geodesic.
'You can imagine this as stretching a string between two points on a football - it will be a curve in 3D'
In one map, he gives people an idea of what the world might look like if leaders only controlled the land closest to their capital city.
He uses a technique called Voronoi diagrams to pick out a set of 'seed points' – capital cities for example – then divides space into a number of regions so that there is one region for every seed, consisting of all points closer to that seed than any other.
This produces the mathematical borders and disregards language, culture and politics, which have traditionally been reasons to carve land up into countries and empires.
'The Voronoi diagram is a beautiful piece of mathematics,' Mr Davies told MailOnline.
In a right state? Mr Davies' map draws new state lines in relation to each state's capital. If his map were real, some states including California, Texas and Georgia would be much smaller, while others such as Florida, Arizona and West Virginia would gain territory
Divide and Conquer: This map gives people an idea of what the world might look like if leaders only controlled land closest to their capital city, rather than another country's capital. If this division came to be, Scotland would be ruled by the Irish government and countries such as Belgium and Holland would make territorial gains
His latest map divides the world into 2,980 regions based upon the location of medium and large airports across the world.
It is immediately obvious which parts of the planet are the wealthiest and most populated, with Europe and the U.S. for example being carved up into many more regions than parts of northern and central Asia or small islands..
The Voronoi airport map ensures that each region is closer to a particular airport than any other and highlights certain areas that are not well covered by air travel.
Whole world in his hands: Mr Davies' latest map divides the world into 2,980 regions based upon the location of medium and large airports across the world (pictured). It is immediately obvious which parts of the planet are the wealthiest and most populated
Drawing a line: Another Voronoi diagram divides the world according to its capital cities. Here, Mexico is substantially larger, while the U.S. has lost considerable ground as its capital, Washington DC is based on the East Coast. The Bahamas is also ruling part of Florida
HOW THE AIRPORT MAP WAS MADE
Mr Davies accessed a list showing the location of 2,980 medium and large airports
He wrote and and used a reusable library to compute spherical Voronoi diagrams in JavaScript, which is a computer programming language.
'It exploits several beautiful mathematical relationships, starting with something called a "3D convex hull", which leads to something called a "spherical Delaunay triangulation", and finally this leads to the spherical Voronoi diagram,' he said.
Polygons are created within the Voronoi diagram and Mr Davies then uses the data visualisation library called D3.js to make it interactive and create a zoomable globe.
The page which calculated the most remote points relative to the airports is under 300 lines of code and took Mr Davies just one evening to create.
However, it took him 'much longer' to make the library.
According to the map, the most remote airport in the world is Mataveri Airport on Easter Island. It is 1,617 miles (2,602km) from the nearest airport, which is Totegegie Airport on Totegegie Island in French Polynesia.
Another Voronoi diagram divides the world according to its capital cities and the same technique is used to determine the mathematical boundaries of different states in the U.S.
Mr Davies' map draws new state lines in relation to each state's capital. If his map were real, some states including California, Texas and Georgia would be much smaller, while others such as Florida, Arizona and West Virginia would gain territory.
Mr Davies said: 'My work is primarily intended to demonstrate the beauty of Voronoi diagrams, in particular for spherical space, which I think is somewhat unusual.'
He has written a reusable library to compute spherical Voronoi diagrams in JavaScript, which is a computer programming language.
'The majority of Voronoi diagrams are for 2D. I hope to inspire others to create more interesting and potentially thought-provoking maps using a reusable library,' he said.
Asia re-mapped: Mr Davies uses a technique called Voronoi diagrams to pick out a set of 'seed points' - capital cities for example (pictured) - then divides space into a number of regions so that there is one region for every seed consisting of all points closer to that seed than any other. India has lost considerable territory in this map
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