Density-equalizing map projections: Diffusion-based algorithm and applications

Abstract

Map makers have for many years searched for a way to construct cartograms—maps in which the sizes of geographic regions such as countries or provinces appear in proportion to their population or some similar property. Such maps are invaluable for the representation of census results, election returns, disease incidence, and many other kinds of human data. Unfortunately, in order to scale regions and still have them fit together, one is normally forced to distort the regions’ shapes, potentially resulting in maps that are difficult to read. Here we present a technique for making cartograms based on ideas borrowed from elementary physics that is conceptually simple and produces easily readable maps. We illustrate the method with applications to disease and homicide cases, energy consumption and production in the United States, and the geographical distribution of stories appearing in the news.