Cartogram Types

"Everything is related to everything else, but closer things are more closely related." - Waldo Tobler



What is a Cartogram?

Borden D. Dent in the fourth edition of his book "Cartography Thematic Map Design" begins his chapter on cartograms this way:

"Erwin Raisz called cartograms 'diagrammatic maps.' Today they might be called cartograms, value-by-area maps, anamorphated images or simply spatial transformations. Whatever their name, cartograms are unique representations of geographical space. Examined more closely, the value-by-area mapping technique encodes the mapped data in a simple and efficient manner with no data generalization or loss of detail. Two forms, contiguous and non-contiguous, have become popular. Mapping requirements include the preservation of shape, orientation contiguity, and data that have suitable variation. Successful communication depends on how well the map reader recognizes the shapes of the internal enumeration units, the accuracy of estimating these areas, and effective legend design. Complex forms include the two-variable map. Cartogram construction may be by manual or computer means. In either method, a careful examination of the logic behind the use of the cartogram must first be undertaken."

A cartogram is a type of graphic that depicts attributes of geographic objects as the object's area. Because a cartogram does not depict geographic space, but rather changes the size of objects depending on a certain attribute, a cartogram is not a true map. Cartograms vary on their degree in which geographic space is changed; some appear very similar to a map, however some look nothing like a map at all. There are three main types of cartograms, each have a very different way of showing attributes of geographic objects- Non-contiguous, Contiguous and Dorling cartograms.
Quick glossary of terms:
Geographic Object: Some thing that exists in geographic space, like a country, a city, a river or a house.
Attribute: Some characteristic of a geographic object; such as a country's population, its literacy rate, or Gross National Product.


A non-contiguous cartogram is the simplest and easiest type of cartogram to make. In a non-contiguous cartogram, the geographic objects do not have to maintain connectivity with their adjacent objects. This connectivity is called topology. By freeing the objects from their adjacent objects, they can grow or shrink in size and still maintain their shape. Here is an example of two non-contiguous cartograms of population in California's counties.

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The difference between these two types of non-contiguous cartograms is a significant one. The cartogram on the left has maintained the object's centroid (a centroid is the weighted center point of an area object.) Because the object's center is staying in the same place, some of the objects will begin to overlap when the objects grow or shrink depending on the attribute (in this case population.) In the cartogram on the right, the objects not only shrink or grow, but they also will move one way or another to avoid overlapping with another object. Although this does cause some distortion in distance, most prefer this type of non-contiguous cartogram. By not allowing objects to overlap, the depicted sizes of the objects are better seen, and can more easily be interpreted as some attribute value.


In the previous section we referred to the connectivity between objects, or topology. In a non-contiguous cartogram topology was sacrificed in order to preserve shape. In a contiguous cartogram, the reverse is true- topology is maintained (the objects remain connected with each other) but this causes great distortion in shape.
This leads to the single most difficult, but intriguing problem in creating cartograms. The cartographer must make the objects the appropriate size to represent the attribute value, but he or she must also maintain the shape of objects as best as possible, so that the cartogram can be easily interpreted. Here is an example of a contiguous cartogram of population in California's counties. Compare this to the previous non-contiguous cartogram.

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This type of cartogram was named after its inventor, Danny Dorling of the University of Leeds. A Dorling cartogram maintains neither shape, topology nor object centroids, though it has proven to be a very effective cartogram method. To create a Dorling cartogram, instead of enlarging or shrinking the objects themselves, the cartographer will replace the objects with a uniform shape, usually a circle, of the appropriate size. Professor Dorling, for the reason described above in the non-contiguous cartogram section, suggests that the shapes not overlap but rather be moved so that the full area of each shape can be seen. Below is an example of a Dorling cartogram, using the same population of California counties example.
Another Dorling-like cartogram is the Demers Cartogram, which is different in two ways. It uses squares rather than circles; this leaves fewer gaps between the shapes. Secondly, the Dorling Cartogram attempts to move the figures the shortest distance away from their true locations; the Demers cartogram often sacrifices distance to maintain contiguity between figures, and it will also sacrifice distance to maintain certain visual cues (The gap between figures used to represent San Francisco Bay in the Demers Cartogram below is a good example of a visual cue.) The 25 Most Populated Counties in California are labeled in each of the two cartograms below for reference.

click for a larger image


Pseudo-cartograms (or false cartograms) are representations that may look like cartograms but do not follow certain cartogram rules. Perhaps the most famous type of pseudo-cartogram was developed by Dr. Waldo Tobler. In this case, instead of enlarging or shrinking the objects themselves, Tobler moves the object's connections to a reference grid such as latitude or longitude in order to give the same effect. This maintains good directional accuracy in the cartogram (if county A is directly north of county B, it will still remain directly north in the cartogram. Note in previous examples, such as the Dorling Cartogram, this is not always true) however, this is a false cartogram because it creates extensive error in the actual size of the objects.
Let us consider this error where it becomes very clear, in the case of the California population. Mono County is a very lowly populated county, with only 13,000 people but by pure coincidence it lays at the same latitude as San Francisco County (777,000 people) and at the same longitude as Los Angeles County (9,519,000 people.) It would be impossible to expand the latitude and longitude lines to make Los Angeles and San Francisco the appropriate size without in turn, expanding Mono County as well. In the same way, the lines cannot be contracted to make Mono County the appropriate size without making San Francisco and Los Angeles too small.
Dr. Tobler uses a root mean square calculation to find the "best fit" or cartogram that is "close enough." This technique is sometimes used to pre-process a contiguous cartogram. That is, let a computer make a pseudo-cartogram, and from this a cartographer can create a contiguous cartogram by hand. This also proves to be very effective.



This site is funded by the USGS, created by Ian Bortins and Steve Demers under the direction of Dr. Keith Clarke, hosted and maintained by NCGIA.

Last Edited 7/31/02