Maps shape our perception of geographical realities, albeit often imperfectly. A world map, for instance, relies on some form of projection that transfers — with inevitable distortion — the unbounded surface of the globe to the bounded page. Mark Newman has taken this idea of distortion a stage further, producing a world map that gives each territory a size proportional to its population.
The idea of such density-equalized ‘cartograms’ is not new, and can be applied to a host of variables, besides population, whose distribution is geographically uneven. The innovation in Newman's map (pictured) is the use of the diffusion equation, familiar from the physics of heat transfer and molecular mixing, to produce a map that smooths out population density, but keeps geographical distortion to a minimum.
The map follows on from work in which Newman and Michael T. Gastner applied the diffusion technique to (among other things) maps depicting the results of the 2000 US presidential election (Proc. Natl Acad. Sci. USA 101, 7499–7504; 2004). For the world cartogram, a grid of 4,096 by 2,048 squares was overlaid on a rectangular world map based on a cylindrical equal-distance (plate carrée) projection. A starting population-density function was computed by dividing the population of each country equally between the squares covering its territory.
Population was then allowed to diffuse away from areas of higher density to those of lower density, with national boundaries moving such that the net population flow through them was zero at all times. The displacement of the boundaries was recalculated throughout the diffusion process by integrating the diffusion-velocity field, until the population density was equalized over the land surfaces. Constituent parts of non-contiguous territories (such as nations divided between several islands) were treated as separate entities, and the oceans and unpopulated Antarctica were treated as a sea of uniform population density equal to the average density of the populated land areas. This ensured an end result that maintained the semblance of familiar geographical relationships.
Apart from the domination of Asian nations — China and India alone account for about a third of the world population of some 6.6 billion — the map throws up many other interesting facets. The Americas are diminished; Russia and Canada, the two largest geographical territories, are reduced to Arctic buffer zones. Australia all but disappears, especially when compared with its near neighbour Indonesia.
The value of Gastner and Newman's technique lies in its intuitiveness and the relative simplicity of the algorithm, which requires a computation time of minutes. The diffusion method may also be extended readily to three dimensions, to create, for example, a three-dimensional ‘homunculus’ in which each part of the body is scaled according to the size of the brain region devoted to it. The potential of such techniques for producing startling representations that challenge our preconceptions seems — unlike world maps — unbounded.
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