Cartograms

A cartogram is a map on which the underlying geography has been distorted to convey the distribution of some thematic variable. If the distorted features are linear, such as the lines of a subway system modified to show travel times, then the cartogram is termed a linear, or distance, cartogram. Without a qualifier, cartogram typically refers to the value-by-area cartogram, in which polygonal features, such as state or country boundaries, are reduced or enlarged based on a variable such as population (see Figure 1). Such area cartograms take two major forms—contiguous and noncontiguous—and have been used primarily within the domains of political cartography and epidemiology.

The first use of the area cartogram technique is difficult to pinpoint, but early examples were produced in France and Germany in the late 19th and early 20th centuries. Early cartograms were produced using manual and mechanical methods. In the 1960s, Waldo Tobler pioneered the use of computer programs in cartogram production, and several fully specified algorithms have been produced since then.

Area cartograms are typically classified as either contiguous or noncontiguous, though a full range of designs exists between these extremes. Fully contiguous, “rubber sheet” cartograms distort the shapes of units but maintain all border relationships from the original geography. Noncontiguous cartograms preserve the shapes of features, simply creating gaps between units to accommodate scaling. Both major types have [Page 339]distinct advantages and disadvantages, with the former design known for its compactness and the latter for its easily recognizable features.

Figure 1 Counties are sized by population and colored by the 2008 presidential election results. This contiguous cartogram was produced using a diffusion-based algorithm borrowed from particle physics.

Source: Map created by Michael Gastner, Cosma Shalizi, and Mark Newman of the University of Michigan.

For a cartogram to be effective, readers must be able to accurately recognize and estimate the areas of its features. The former task is hindered by the distorted, ballooned shapes found on many cartograms. Most cartographers attempt to maintain certain critical shape points along feature edges as visual cues to the original geographic space. Some, though, have taken the radical step of abstracting enumeration units to circles or squares, leaving only arrangement as a clue to the identity of cartogram features.

Area estimation in information graphics is typically poor, with most readers underestimating the size of symbols. Cartograms, which use the visual variable of area to convey information, are at a particular disadvantage. Rather than the circles and squares found on most proportional symbol maps, readers must estimate the areas of complex, sometimes multipart polygons.

Another factor in the effectiveness of cartogram communication is the distribution of the thematic variable chosen to map. A variable with a high correlation to land area will likely lead to an uninteresting cartogram. Cartograms are most effective at showing variables whose spatial distributions diverge markedly from land area.