standard Area Cartogram Maps Explored

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Area cartogram maps are maps of non-absolute space where the areal extent is in proportion to some measured value.  Cartogram maps retain a partially accurate relative location and relative space, but the actual area of the individual polygons features are overrepresented or underrepresented based on the assigned values. Area cartograms are useful for visualizing relativity based on a common quantitative attribute such as population.

Cartograms were popularized by Erwin Raisz who published the first statistical cartograms of the United States.  Raisz was a professor of cartography at the Institute of Geographical Exploration at Harvard University and was most well known for his physical relief maps which were hand drawn. In 1934, Raisz published in the journal Geographical Review an article entitled, “The rectangular statistical cartogram” which popularized the use of cartograms as an educational tool for learning about geography.

Cartogram map showing national wealth for the United States by Erwin Raisz, 1934.

Cartogram map showing national wealth for the United States by Erwin Raisz, 1934.

The distinction of the first cartogram has been attributed to Émile Levasseur who produced cartograms for his 1868 and 1875 economic geography texts.

Non-contiguous Cartogram Maps

Cartograms that focus on the distortion of area by a specific value can visualized as contiguous or non-contiguous.  Non-contiguous cartograms look like exploded maps with the individual polygons placed separately from each other.  Unlike contiguous cartograms, non-contiguous cartograms tend to preserve the shape of the individual polygons but not the size or connectivity to other polygons.   The sacrifice in non-contiguous cartograms is the topology or contiguity with adjacent areas.

Noncontiguous cartogram showing population density within Europe. (Source: Vinny Burgoo).  Projection: Lambert Azimuthal Equal Area. Data: January 2008 population data from Eurostat.

Non-contiguous cartogram showing population density within Europe. (Source: Vinny Burgoo). Projection: Lambert Azimuthal Equal Area. Data: January 2008 population data from Eurostat.

Dorling Cartogram Maps

Dorling cartograms also sacrifice topology but the representation of geographic shape is completely abandoned.  Created by Danny Dorling of the University of Leeds in 1996, Dorling cartograms use circles to represent proportion.  The concept of circular cartograms was popularized and defined by Dorling’s article entitled, “Area cartograms: their use and creation.”  In the publication, Dorling posed the question, “If, for instance, it is desirable that areas on a map have boundaries which are as simple as possible, why not draw the areas as simple shapes in the first place?” and noted “circles as the simplest of all shapes.”  As a side noteDorling is also one of the founders of worldmapper.org which posts and collects cartogram maps.

Circular cartogram showing the proportion of French language wiki originations by country from 2007-2011.  Created by wiki user Moyogo.

Circular cartogram showing the proportion of French language wiki originations by country from 2007-2011. Created by wiki user Moyogo.

A close cousin to Dorling cartogram is the Demers cartogram which uses squares instead of circles to show proportion.  Demers cartograms also provides more contiguity between areas while also attempting to maintain the least amount of distance from the true centroid of the shape as compared to Dorling cartograms.

Contiguous Cartogram Maps

Contiguous cartograms maintain topology (i.e contiguity) but, as compared to non-contiguous cartograms, produce the greatest distortion in shape. Areas are bloated or shrunk depending on the proportional attributes assigned.  Mark Newman provides some interesting excamples of contiguous cartograms on his page “Images of the social and economic world.”

Cartogram showing the number of billionaires by state.

Cartogram showing the number of billionaires by state. Click on image for larger map.

 

Free Cartogram Map Tools

There are some free cartogram tools available for downloading that allow you to manipulate geographic data to produce cartograms.

ScapeToad uses the Gastner/Newman diffusion-based algorithm to preserve topological relationships while transforming geographic data into cartograms.  ScapeToad is written in Java so it’s cross-platoform compatible (i.e. can run in Windows, MacIntosh, and Linux) and uses shapefiles as the input and output data file formats.  The application is standalone.  Maps can be exported in SVG format.

MAPresso is another Java based application that has a cartogram component.  Geographic data can be visualized as circle cartograms based on Dorling.  Data input is via text files or directly inputted into the app.  Data export options are minimal, the download page mentions, “An output as a file is not in the focus of the applet, there is a provisional possibility to produce an encapsulated PostScript file (EPS). The distorted geometry of a cartogram process can be exported in ArcGIS generate format.”

Cart is a C++ program written by Mark Gastner that uses a technique described in the 2004 journal article, “Diffusion-based method for producing density equalizing maps.” Cart is a standalone program but there are ArcGIS and MapInfo addins available that allow users to create cartograms within GIS software programs. Frank Hardisty has a Java version of the cartogram program that runs online.

Protovis is a graphical visualization toolkit  using Javascript (no longer under active development) that has a Dorling cartogram component. The same team is now actively developing d3.js which offers a non-contiguous cartogram component.

Related Cartographic Resources


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1 Comment

  1. Population density is not an appropriate value for a cartogram. It would have to be absolute population value, while relative data is not suitable for cartograms (i.e. wrong, comparable to using absolute values as choropleth shadings in maps – many people doing it does not make it more correct).

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