Inf@Vis!

The digital magazine of InfoVis.net.
[Number 197]

Cartograms
by Juan C. Dürsteler

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.

See the illustrated version at
http://www.infovis.net/printMag.php?num=197&lang=2

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 (http://www.infovis.net/printMag.php?num=79&lang=2) ). 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.

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.

WorldMapper (http://www.worldmapper.org/) 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 (
http://www.ncgia.ucsb.edu/projects/Cartogram_Central/) website by the
National Center for Geographic Information and Analysis (NCGIA) we can
consider three main types of cartograms:

* 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.

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

o 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.
__________________________________________________________
(c) J.C. Dürsteler 2000 - 2008 Barcelona, Spain.
All rights reserved

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--
==========================================
J. T. Johnson
Institute for Analytic Journalism -- Santa Fe, NM USA
www.analyticjournalism.com
505.577.6482(c) 505.473.9646(h)
http://www.jtjohnson.com tom@...

"You never change things by fighting the existing reality.
To change something, build a new model that makes the
existing model obsolete."
-- Buckminster Fuller
==========================================


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