Equal Area Cartograms

Choropleth maps are extremely popular (e.g. try image search on Bing or Google). But choropleth maps have many short comings including:

  1. Small areas may be invisible (e.g. Dubai, Singapore)
  2. Identification of a particular region or finding a named target can be difficult. (e.g. see the National Geographic literacy survey from 2006: many young adults cannot identify significant countries on a world map).
  3. Countries with large land area dominate the display (e.g. Canada, Russia).

Here is an example showing the Prevalence of HIV in 2010 from World Health Organization:

Cartograms are a different approach that modify geographic shapes to size the regions (e.g. countries) based on a data value. However, for the analytic task, small values and/or null values may be important. Say, prevalence of HIV by country: if you are analyzing health-care data, the low values and the null values are important, and you don’t want those to disappear.

In general, there are many types of visualizations that use the size (or area) to convey data, including bar charts, area charts, pie charts, bubble charts, treemaps and more. There are times when this may be inappropriate – perhaps the viewer needs to be able to focus equally on the small items. Perhaps the tiny bar represents the most important project, or most important country for the purposes of the analysis – it could be missed if using size to convey data attribute. 

Returning to the choropleth and cartogram, consider a tweak to the cartogram: the Equal Area Cartogram. In an equal area cartogram, the primary consideration is that every item has the same size, while preserving all the other aspects associated with cartograms, such as local proximity (i.e. the countries that were beside each other are still beside or fairly close to each other). Now, all countries are visible (addressing problem #1); and are equally visible (addressing problem #3). Furthermore, depending on the cartogram approach, since there is a minimum size, each item can be explicitly labeled (addressing problem #2). Other visual attributes can be used to encode data of interest, such as color. This example uses color to encode population in an equal area cartogram labeled using 3 letter country ISO codes.


(Interactive version here – you can get a better sense of how compact/crowded Europe is).

Freed from using size and shape, there are now more opportunities to encode data using a variety of visual attributes. The example below is an experimental visualization encoding data using a variety of font attributes, including font weight (i.e. boldness), italics and caps:


This is experimental, because there is a lot going on all at once:

  • Labels indicate countries via their 3 letter ISO country code.
  • Labels are located based on a equal-area cartogram to preserve relative spatial relationships
  • Label color is based on region. If no HIV data is available, the the label color is grey.
  • Font weight indicates health expenditure (as a percentage of GDP). First world countries tend to be heavy-weight because a significant portion of GDP is spent on health care. e.g. JPN, USa
  • Font capitalization indicates life expectancy. ALL_CAPS indicates long life, all_lower indicates shorter lives. Unfortunately, most of Africa is lowercase. e.g. bdi, moz.
  • Font italics indicates the Prevalence of HIV. All italics indicates a high proportion of HIV. While there are many italics in Africa; high prevalence can also be seen in Haiti (Hti) and Jamaica (JAm).

The combination of these many attributes enables complex queries to be made visually, for example:

  • Are there countries with high HIV and short lives, even though they spend a significant portion of GDP on health care? Answer yes: e.g. see Rwanda (rwa) or Sierra Leone (sle). 
  • Is health care spending consistent among countries with long lives and similar rates of HIV?
    Answer: I’m not answering this one for you: feel free to explore the image and comment.

In summary, when considering high level maps that are meant to compare values across regions, consider going beyond a choropleth or one of many types of distortion cartograms all the way to an equal area cartogram. At a minimum, you’ll be able to show each country clearly and the data associated with the country, and the labels will help the viewer identify those countries.


About richardbrath

Richard is a long time visualization designer and researcher. Professionally, I am one of the partners of Uncharted Software Inc. I am also pursuing a part-time PhD in data visualization at LSBU. The opinions on this blog are related to my personal interests in data visualization, particularly around research interests related to my PhD work- this blog is about exploratory aspects of data visualization not proven principles.
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