  Map makers have long 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 other analogous 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. Many
methods for making cartograms have been proposed, some of them extremely
complex, but all suffer either from this lack of readability or from other
pathologies, like overlapping regions or strong dependence on the choice of
coordinate axes. Here we present a new technique based on ideas borrowed from
elementary physics that suffers none of these drawbacks. Our method is
conceptually simple and produces useful, elegant, and easily readable maps. We
illustrate the method with applications to the results of the 2000 US
presidential election, lung cancer cases in the State of New York, and the
geographical distribution of stories appearing in the news.

Data Analysis, Statistics and Probability;Physics and Society