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Cartograms
July 14, 2016
They say, "
a picture is worth a thousand words." As a
scientist, I need to scan many
journal articles for relevance, and the best way to do this is by looking at the included
graphs and other
images. This is useful, especially, in
papers not written in
English, so my limited
foreign language skills are not overly taxed. That's why it's important for scientists to clearly render their images.
In our
computer age,
Information graphics (infographs) and
scientific visualization have become
research areas in themselves, but they have a long
history. When discussing graphical representation of data, it's
traditional to mention
Charles Joseph Minard's famous
cartograph, a 62 x 30
centimeter lithographic depiction of
Napoleon's 1812
Russian campaign that shows
troop numbers, their movement, and
temperature (see figure).
Charles Joseph Minard's cartograph of Napoleon's Russian campaign, 1812 (Click for larger image). The primary information conveyed is the continued troop loss during both the advance and the retreat, which is easily seen. The temperature is given on the Réaumur scale. In this temperature scale, the freezing point of water is 0 degrees, and its boiling point is 80 degrees. (Via Wikimedia Commons.)
While in
elementary school, my
daughter had an assignment to produce
charts and graphs of
data. Having a scientist father was a
burden most of the time, but it helped her in creating a novel
bar chart of the numbers of
bathroom fixtures in the
United States. Instead of bars, she produced arrays of
sinks,
toilets, and
bathtubs to lengths that matched their numbers. She was able to do this using a primitive "
photoshop" style
program that worked in the
Windows operating system of that time. This technique, as applied to a chart of membership in the major
science and
engineering professional associations, is shown below.
Membership in the four major science and engineering professional associations, the American Physical Society (APS), the Federation of American Societies for Experimental Biology (FASEB), the American Chemical Society (ACM), and the Institute of Electrical and Electronics Engineers (IEEE). I'm a member of the APS and the IEEE. (Created using Inkscape.)
Popular among
bloggers is the
word cloud, a representation of the
frequency of
keyword use in which the words themselves are sized according to their importance (see figure). While there are several online word cloud generators, the
free and open-source statistics programming language,
R, has a toolset that allows detailed development of word cloud representations.
A word cloud of Web 2.0 buzzwords.
(Modified Wikimedia Commons image.)
One of the more interesting data representations is the
cartogram, which is typically a
map in which the map elements have been distorted so that their
areas scale with a
variable, such as
population,
income,
carbon emission, etc. A simple cartogram of population is shown in the figure. A
review article on cartograms has been posted to
arXiv by
doctoral candidate,
Sabrina Nusrat, and
professor Stephen Kobourov of the
University of Arizona Department of Computer Science.[1]
A simple cartogram of the US population in 2010, as derived from US Census data. The huge size of New Jersey demonstrates the area scaling of such maps (Via US Census Web Site.)
As can be imagined, area cartograms can be created in a
panoply of pleasing forms that either attempt to reproduce the spatial arrangement of the original map by distorting its elements to scale with the variable of interest; or, to just place shapes of appropriate area on the
plane. As can be seen in the following example of Nusrat and Kobourov,
circles of appropriate area have been placed in the relative location of the
US states on the plane to indicate the
concentration of
Starbucks and
McDonald's locations.
Concentration of Starbucks and McDonald's locations in the United States. The circle size is indicative of the number of Starbucks coffee shops, while the intensity of the shading indicates the number of MacDonald's restaurants. The correlation is easily seen through this representation. (Figure 16 from ref. 2, used with permission.)[1-2])
Nusrat and Kobourov list quite a few cartogram techniques and
historical examples in their paper.[1-2] The example of the above figure is a
Dorling type cartogram, and it inspired me to attempt a similar cartogram program. My
C language program (
source code in my typical
amateur coding style can be found
here), accepts as an input a
CSV format file of states and some data attribute of the states, and it outputs an
SVG image as shown below.
A Dorling-type cartogram of the number of Representatives of each state. The radius of the circles is scaled, not their area. (Author's program)
Unlike a true Dorling cartogram, this program overlaps circles, thereby preserving the map shape. While this might be a valid reason, the actual reason is that this was easier to code. Some example data files are the
number of representatives in the house of representatives, and
population. A skilled programmer should be able modify the program to give a true Dorling representation, or experiment with other shapes.
References:
- Sabrina Nusrat and Stephen Kobourov, "The State of the Art in Cartograms," EuroVis 2016 - the 18th EG/VGTC Conference on Visualization, Groningen, the Netherlands (June 6-10, 2016). To appear, Computer Graphics Forum, vol. 35, no. 3 (2016).
- Sabrina Nusrat and Stephen Kobourov, "The State of the Art in Cartograms," arXiv, May 30, 2016.
- Some interesting maps, including a few cartograms, can be seen at the David Rumsey Map Collection, Cartography Associates.
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