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The digital magazine of InfoVis.net

Cartograms
by Juan C. Dürsteler [message nº 197]

Cartograms are distorted maps where the area corresponding to each region is proportional to the value of some variable of our interest. Its visual power and its capacity  to reveal information are prominent.
USElections08.png (143218 bytes)
Conventional map of the presidential elections in USA. Each colour patch corresponds to the winning vote in each state. In red the republican vote, in blue the democrats.  Each state has the size corresponding to its geographic surface. Big states with a small population have less influence than conversely.  
Source
: As can be seen in the interesting article Maps of the 2008 US presidential election results of the University of Michigan
Click on the image to enlarge it.

The historical presidential elections of the past November 4, 2008 caught the interest of the planet during some long hours while the counting of votes in each county and state progressed. I had the opportunity to live it while it happened since I landed in Nashville, Tennessee just that afternoon.  

Most of the TV channels showed the results by using geographical maps of the US' states coloured in red (voting > 50%  for the republicans) or blue (> 50% for the democrats). This gave the impression of quite a leveled result while the vote computation indicated a constantly increasing advantage in favour of Obama over McCain. 

The day after, with a percentage of votes counted close to 100% the distance between the two candidates was vast. Nonetheless many newspapers and TV channels were still using the misleading map of the US where the area of each state was proportional to its surface, not to the electoral votes it provides, which is what the colours would try to represent.  

In that sense we where in front of a map with a high lie factor (see number 79). It would be different for each state but in any case quite high since the value of the visual variable (the coloured area) does not correspond with the actual value of the variable we intend to show (electoral votes). This way a state with a large geographical surface and few inhabitants (consequently with little electoral votes) will get an area disproportionate to its electoral relevance.  

This is the case of Montana, the fourth biggest US state in surface with 376.978 Km2 and the 44th in inhabitants with approx.  940.000, that provide only 3 electoral votes. California, the third in surface with 410.000 Km2 is, nevertheless, the most populated, with 38 million of inhabitants and provides 55 electoral votes. By representing both of them according to their geographical surface they visually appear equally important while the electoral relevance of California is 18 times bigger. The lie factor in this comparison is, then, of 18!. 

Fortunately there are other ways of visualisation that pursue a bigger correspondence between what you see and what you intend to show. A specially interesting example are cartograms.

USElectionsShade08.gif (64438 bytes) USElectionsCartoShade08.gif (50931 bytes)
Map of the elections in a per county basis. Each colour element corresponds to the percentage of votes in each county. Red for republican vote, blue for democrats. 

Source: As can be seen in the interesting article Maps of the 2008 US presidential election results of the University of Michigan
Click on the image to enlarge it.

Cartogram of the presidential elections in USA. In this representation the size is proportional to the electoral votes of each county. This corrects the effect of the left side map where counties with large surface and few electoral votes get more relevance than the real one.  
Source: As can be seen in the interesting article Maps of the 2008 US presidential election results of the University of Michigan
Click on the image to enlarge it.

A cartogram is a type of graphic, similar to a map, where the geographic limits and the area they contain are distorted as a function of the value of certain georeferenced variable  that we want to represent.  

A variable is georeferenced when it can be associated to geographic coordinates. For example the population of a country can be associated to the latitude and longitude of the towns where they belong.

For example a cartogram of the global population will show the countries with a a size proportional not to their area but to their population. 

Area.png (142954 bytes) Poblacion.png (154068 bytes)
Cartogram of the global surface. In this case it coincides, logically, with the usual mapamundi. 

Source: As can be seen in the  WorldMapper website.  
Click on the image to enlarge it.

Cartogram of the global population.  In this representation size corresponds with relative population, in respect to the global total, living in each country.  Notice how China and Japan are considerably bigger than in the typical surface map. 
Source
: As can be seen in the WorldMapper website.  
Click on the image to enlarge it.

WorldMapper is a site devoted to the elaboration of  cartograms of many interesting metrics, from population to poverty and wealth, food consumption and production, etc. It's a more than commendable source for cartograms and (sometimes stunning) information about our world.

According to the Cartogram Central website by the National Center for Geographic Information and Analysis (NCGIA) we can consider three main types of cartograms:

CartogramaNoContiguoNoSup.gif (24408 bytes) CartogramaNoContiguoSup.gif (20675 bytes) CartogramaContiguo.gif (25348 bytes) CartogramaDorling.gif (11746 bytes) CartogramaDemers.gif (6176 bytes)
Non Contiguous Non Overlapping Cartogram.
Source: As can be seen in the  Cartogram Central website.  
Click on the image to enlarge it.
Non Contiguous Overlapping Cartogram:
Source: As can be seen in the  Cartogram Central website.  
Click on the image to enlarge it.
Contiguous Cartogram:
Source: As can be seen in the  Cartogram Central website.  
Click on the image to enlarge it.
Dorling Cartogram
Source: As can be seen in the  Cartogram Central website.  
Click on the image to enlarge it.
Dorling (Demers variant) Cartogram
Source: As can be seen in the  Cartogram Central website.  
Click on the image to enlarge it.
  • Non contiguous Cartograms. In this case each one of the entities that constitute the cartogram do not need to maintain the connectivity (the topology) with its neighbours. Consequently it can maintain the shape although its relative size can change according to the value of the variable it represents.

    • Non Overlapping.  A non overlapping cartogram puts the  pieces apart so that they do not overlap. 

    • Overlapping.  An overlapping cartogram lets the non contiguous pieces maintain the original location of their centroids (the centroid  is the weighted center point of the figure) so that the pieces that have increased in size respective to others due to larger value of the variable to show can overlap other pieces 

  • Contiguous Cartograms. Here the connectivity has to be maintained. Correspondingly the shape of each piece is distorted to maintain the connectivity with the rest of connecting pieces, yet maintaining its total surface still proportional to the value of the variable of our interest. This is the case of the cartograms in Worldmapper, for example.
  • Dorling Cartograms. This type of cartogram encompasses several methods where the shapes are substituted by geometrical figures like circles in the true Dorling Diagram or squares in the Demers cartogram. In these diagrams neither the shape, exact location nor centroids are respected. Yet they are also a powerful means of showing georeferenciated 

Geographic maps constitute one of the most known and usual visual metaphors. They are taught systematically in all the schools and configure since our childhood our visual conception of the world to the extent that if we look at an upside down map of the world it takes a certain time to recognise what we are seeing.  

Although a cartography is by no means an easy metaphor, its familiarity converts it into a powerful platform to represent visual information, beyond its primeval objective of representing, classifying and communicating localization information of spaces so vast that can not be directly embraced with the sight.

Cartogramas use the visual metaphor of cartography to enhance the power of representing georeferenced information that not necessarily is of geographic nature.  Maybe its power comes precisely from the fact that they are a step forward towards abstraction in visualisation, that respects to some extent nevertheless a well known and learned metaphor. Something we are needing if we want to access to a higher visual literacy.

Links of this issue:

http://www-personal.umich.edu/~mejn/election/2008/   Article Maps of the 2008 US presidential election results
http://www.infovis.net/printMag.php?num=79&lang=2   Num 79 on Visual Integrity
http://www.worldmapper.org/   WorldMapper website
http://www.ncgia.ucsb.edu/projects/Cartogram_Central/   Cartogram Central website
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