Density-equalizing map projections: Di!u sion-based algorithm and applications

Map makers have for many years searched for a way to construct cartograms—maps in which the sizes of geographic regions such as coun- tries or provinces appear in proportion to their population or some sim- ilar property. Such maps are invaluable for the representation of census results, election returns, disease incidence, and many other kinds of hu- man data. Unfortunately, in order to scale regions and still have them fit together, one is normally forced to distort the regions' shapes, po- tentially resulting in maps that are di!cu lt to read. Here we present a technique for making cartograms based on ideas borrowed from elemen- tary physics that is conceptually simple and produces easily readable maps. We illustrate the method with applications to disease and homi- cide cases, energy consumption and production in the United States, and the geographical distribution of stories appearing in the news.