Cartogram

A cartogram is a map projection that uses purposeful distortion to represent some terrestrial phenomena on a geographic map. In this sense, Mercator's projection is a cartogram because it distorts distances to represent loxodromic (rhumb line) directions, and all maps have some distortion of the two-dimensional surface of the earth. In more conventional parlance, there are three main types. One of these uses a metric scale other than kilometers to represent distance on the map, generally from one or two places. The map scale may be in minutes of travel time, dollar costs, or other units of inconvenience. The most common type is centered at a specific place. On a normal map, the same relation often is shown by isochrones or isotims. To show simultaneous relationships from more than two places on one graphic requires an approximation, usually calculated using a trilateration, multidimensional scaling, or least squares.

The second common type of cartogram stretches space according to the density of some distribution on the earth, often population or resources by country. Within this class, there are three subtypes. One of these is the rectangular cartogram of Erwin Raisz, also called a value-by-area map. A second subtype is the noncontiguous cartograms introduced by J. Olson. The more common variant is represented by a continuous map, also called a contiguous cartogram. This latter group, a generalization of the equal area class of map projection, has been the subject of numerous construction algorithms, including many recent ones using computers. This is in part because the single defining equation is not sufficient to render a unique solution. In some cases, the value-by-area property is relaxed to better preserve recognizable shapes.

The most common use of contiguous cartograms is as a graphic display to contrast the geographic distribution of some phenomenon in comparison with the conventional map. On occasion, a second geographic variable is shown (often by distinct colors) on the cartogrammatic base map, for example, per capita income on a world population cartogram. Another use, most common in epidemiology, is to present the geographic arrangement of some distribution of concern to examine whether or not clusters are related or dependent on the distribution of people. Cartograms may also be used as an anamorphose designed to solve a specific theoretical problem.

The third map subtype maintains topological relations but not metric distances. The classic example is the London subway diagram, where the order of stations is correct but the distances between them are not. Early railroad advertising maps were similar.