Artificial reality - The Visualization of Spatial Social Structure - page 69

Population cartograms will continue to gain in popularity as they become
easier to employ and better understood in general. 11 For visualizing the spatial
distributions of social structure there is no alternative, if we wish to see the
detail of substance. A traditional map can take many projections, and so too can
population cartograms. An infinite number of correct population cartograms can
be constructed for any aspect of any set of places.

3.4 The nature of space

Vision is therefore, first and foremost, an information-processing task,
but we cannot think of it just as a process. For if we are capable of
knowing what is where in the world, our brains must somehow be
capable of representing this information - in all its profusion of color
and form, beauty, motion and detail.

(Marr, 1982, p. 3)

Cartograms are normally made by slowly stretching some parts while squash-
ing others, until the places' sizes are in proportion to their populations, instead
of being in proportion to their land area.
This process can be tempered by deciding that the topology of the space
should be preserved throughout the transformation. In other words, these places,
which were neighbouring, should remain so after transformation and those that
were not so should not become neighbours. Most creators of cartograms aim
to create a topologically and geometrically correct contiguous area cartogram.
Even so, it is still possible to create a multitude of these for any given area.
Recently Gastner and Newman's algorithm has allowed the widespread creation
of cartograms, which also appear conformal (maintaining compass directions
locally), reducing this multitude down, but it remains useful to look at other
options and other constraints that may be helpful. 12
Further constraints can be added to creating cartograms other than preserv-
ing topology, scaling areas appropriately and attempting to maintain compass
directions where possible. The most common are that the outer boundary of the
area be preserved and that the lengths of interior boundaries be minimised, so
creating a cartogram, the shape of which looks familiar and whose interior is

11 Not all writers favour the use of cartograms. Despite the format being very rare even in the
1930s there were objections to these types of graphic: 'Such maps, however, are not superior to the
dot or bar maps ... for showing distributions of size. In many cases the method ... would result
in the states being so distorted that little if any resemblance of their true shapes would remain, and
even their relative positions would be inaccurate. It is much more difficult to compare the irregular
areas on such maps than it is to compare either circles or bars' (Riggleman, 1936, pp. 179 - 180).
12 Dorling, Barford and Newman, (2006). See also the on-line atlas www.worldmapper.org.