Cartograms, because they distort our normal view of things, are wonderfully rich research and teaching tools. A distance cartogram shows relative travel times and directions within a network. An area cartogram is a map in which some variable is used instead of the land area in each polygon to compute the size of that polygon. Many of us remember using graph paper to make rectangular area cartograms as undergraduates (but perhaps I am dating myself). Today, one can use Web GIS and desktop GIS to create cartograms. For example, nearly 700 variables can be mapped on www.worldmapper.org, and the data can be downloaded as Excel spreadsheets and analyzed within ArcGIS.
To dig deeper and make your own cartograms, with the ability to do bivariate analysis within a GIS environment, use the ArcScript cartogram tool that Tom Gross in the ESRI Applications Prototype Lab created, on: http://arcscripts.esri.com/details.asp?dbid=15638. How can a GIS, which focuses on the accurate spatial representations of features, be used to create cartograms? Try this script and find out!
Once you install the cartogram tool, inside ArcMap, access ArcToolbox. Create a toolset, add the cartogram tool, and run it. The intuitive interface allows specifying input and output, and even comes with a nice assortment of international population and other variables to practice on. You can distort the base layers so that your cartogram can include the distorted layers for reference. I did this for cities, a 30-degree world grid, and a satellite image of the Earth to see these reference layers overlaid on my cartogram.
In this example, I chose to map the total CO2 emissions by country in 2004, in millions of metric tons, from the US Energy Information Agency. What patterns do you notice?
The cartogram map layer has to be written into a geodatabase, but otherwise, the tool has few restrictions. I am very pleased cartographically with the results, and the methodology of how the cartograms are generated is well documented.
What other variables and scales could you map and analyze as cartograms?