What is a Cartogram?
Borden D. Dent in the fourth edition of his book "Cartography
Thematic Map Design" begins his chapter on cartograms this
way:
"Erwin Raisz called cartograms 'diagrammatic maps.' Today
they might be called cartograms, value-by-area maps, anamorphated
images or simply spatial transformations. Whatever their name,
cartograms are unique representations of geographical space. Examined
more closely, the value-by-area mapping technique encodes the
mapped data in a simple and efficient manner with no data generalization
or loss of detail. Two forms, contiguous and non-contiguous, have
become popular. Mapping requirements include the preservation
of shape, orientation contiguity, and data that have suitable
variation. Successful communication depends on how well the map
reader recognizes the shapes of the internal enumeration units,
the accuracy of estimating these areas, and effective legend design.
Complex forms include the two-variable map. Cartogram construction
may be by manual or computer means. In either method, a careful
examination of the logic behind the use of the cartogram must
first be undertaken."
A cartogram is a type of graphic that depicts attributes of geographic
objects as the object's area. Because a cartogram does not depict
geographic space, but rather changes the size of objects depending
on a certain attribute, a cartogram is not a true map. Cartograms
vary on their degree in which geographic space is changed; some
appear very similar to a map, however some look nothing like a map
at all. There are three main types of cartograms, each have a very
different way of showing attributes of geographic objects- Non-contiguous,
Contiguous and Dorling cartograms.
Quick glossary of terms:
Geographic Object: Some thing that exists in geographic space, like
a country, a city, a river or a house.
Attribute: Some characteristic of a geographic object; such as a
country's population, its literacy rate, or Gross National Product.
NON-CONTIGUOUS CARTOGRAMS
A non-contiguous cartogram is the simplest and easiest type of
cartogram to make. In a non-contiguous cartogram, the geographic
objects do not have to maintain connectivity with their adjacent
objects. This connectivity is called topology. By freeing the objects
from their adjacent objects, they can grow or shrink in size and
still maintain their shape. Here is an example of two non-contiguous
cartograms of population in California's counties.
The difference between these two types of non-contiguous
cartograms is a significant one. The cartogram on the left has maintained
the object's centroid (a centroid is the weighted center point of
an area object.) Because the object's center is staying in the same
place, some of the objects will begin to overlap when the objects
grow or shrink depending on the attribute (in this case population.)
In the cartogram on the right, the objects not only shrink or grow,
but they also will move one way or another to avoid overlapping with
another object. Although this does cause some distortion in distance,
most prefer this type of non-contiguous cartogram. By not allowing
objects to overlap, the depicted sizes of the objects are better seen,
and can more easily be interpreted as some attribute value.
CONTIGUOUS CARTOGRAMS
In the previous section we referred to the connectivity between
objects, or topology. In a non-contiguous cartogram topology was sacrificed
in order to preserve shape. In a contiguous cartogram, the reverse
is true- topology is maintained (the objects remain connected with
each other) but this causes great distortion in shape.
This leads to the single most difficult, but intriguing problem in
creating cartograms. The cartographer must make the objects the appropriate
size to represent the attribute value, but he or she must also maintain
the shape of objects as best as possible, so that the cartogram can
be easily interpreted. Here is an example of a contiguous cartogram
of population in California's counties. Compare this to the previous
non-contiguous cartogram.
DORLING CARTOGARMS
This type of cartogram was named after its inventor, Danny Dorling
of the University of Leeds. A Dorling cartogram maintains neither
shape, topology nor object centroids, though it has proven to be a
very effective cartogram method. To create a Dorling cartogram, instead
of enlarging or shrinking the objects themselves, the cartographer
will replace the objects with a uniform shape, usually a circle, of
the appropriate size. Professor Dorling, for the reason described
above in the non-contiguous cartogram section, suggests that the shapes
not overlap but rather be moved so that the full area of each shape
can be seen. Below is an example of a Dorling cartogram, using the
same population of California counties example.
Another Dorling-like cartogram is the Demers Cartogram, which is different
in two ways. It uses squares rather than circles; this leaves fewer
gaps between the shapes. Secondly, the Dorling Cartogram attempts
to move the figures the shortest distance away from their true locations;
the Demers cartogram often sacrifices distance to maintain contiguity
between figures, and it will also sacrifice distance to maintain certain
visual cues (The gap between figures used to represent San Francisco
Bay in the Demers Cartogram below is a good example of a visual cue.)
The 25 Most Populated Counties in California are labeled in each of
the two cartograms below for reference.
PSEUDO-CARTOGRAMS
Pseudo-cartograms (or false cartograms) are representations that
may look like cartograms but do not follow certain cartogram rules.
Perhaps the most famous type of pseudo-cartogram was developed by
Dr. Waldo Tobler. In this case, instead of enlarging or shrinking
the objects themselves, Tobler moves the object's connections to a
reference grid such as latitude or longitude in order to give the
same effect. This maintains good directional accuracy in the cartogram
(if county A is directly north of county B, it will still remain directly
north in the cartogram. Note in previous examples, such as the Dorling
Cartogram, this is not always true) however, this is a false cartogram
because it creates extensive error in the actual size of the objects.
Let us consider this error where it becomes very clear, in the case
of the California population. Mono County is a very lowly populated
county, with only 13,000 people but by pure coincidence it lays at
the same latitude as San Francisco County (777,000 people) and at
the same longitude as Los Angeles County (9,519,000 people.) It would
be impossible to expand the latitude and longitude lines to make Los
Angeles and San Francisco the appropriate size without in turn, expanding
Mono County as well. In the same way, the lines cannot be contracted
to make Mono County the appropriate size without making San Francisco
and Los Angeles too small.
Dr. Tobler uses a root mean square calculation to find the "best
fit" or cartogram that is "close enough." This technique
is sometimes used to pre-process a contiguous cartogram. That is,
let a computer make a pseudo-cartogram, and from this a cartographer
can create a contiguous cartogram by hand. This also proves to be
very effective.
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