A distorted map in which regions are drawn not to an areal scale but to some other scale such as population. Some cartograms attempt to retain the shape of the geographical region they represent; others, such as the rectangular cartogram illustrated opposite, use a single shape to represent all regions of equal importance.


Broadly defined as a map using statistical symbols, a more specialist usage defines a cartogram as a type of map transformation based on a scale other than a true scale. For example, a voting map of Britain may show the size of counties in relation to the numbers of voters in each electoral unit, or an economic cartogram of the world may show countries drawn in proportion to their per capita GNP. Certain ‘rules’ are followed, as far as possible: the shapes of the countries and regions involved are preserved, although often stylized, and they are positioned in the correct geographical locations with respect to each other. Obviously, distortions occur, but the trick is to preserve the original shapes and positions enough to make the units recognizable; computers have helped in this, but the best examples are still produced by hand.
A map showing the distribution of a population by area.

A cartogram is a map in which some thematic mapping variable – such as travel time or Gross National Product – is substituted for land area or distance. The geometry or space of the map is distorted in order to convey the information of this alternate variable. There are two main types of cartograms: area and distance cartograms.
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An area cartogram is sometimes referred to as a value-by-area map or an isodemographic map, the latter particularly for a population cartogram, which illustrates the relative sizes of the populations of the countries of the world by scaling the area of each country in proportion to its population; the shape and relative location of each country is retained to as large an extent as possible, but inevitably a large amount of distortion results. Other synonyms in use are anamorphic map, density-equalizing map and Gastner map.[1][2][3]
A distance cartogram may also be called a central-point cartogram or isochronic cartogram. This form is typically used to show relative travel times and directions from vertices in a network. Compare the maps of travel time for the London Underground below.
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One of the first cartographers to generate cartograms with the aid of computer visualization was Waldo Tobler of UC Santa Barbara in the 1960s. Prior to Tobler's work, cartograms were created by hand (as they occasionally still are). A number of software packages generate cartograms.
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