Artificial reality - The Visualization of Spatial Social Structure - page 77

created, appear continuous again - building Thiessen polygons around the circle
centres is simplest. Here every straight edge side of a polygon is equidistant
from the two nearest circle centres and hence every vertex is equidistant from
the three nearest circle centres.
With a circular cartogram we can now create a space of places and a space
that maintains, as far as is possible with circles, the original topology. 14 Such
a cartogram can be particularly useful for certain types of visualization, those
involving thousands of areas, as it presents a much clearer image than one that
would have to twist and wind to satisfy strictly all the topology conditions, all
of the time.

3.5 Producing illusions

So gravity can be explained by assuming that matter curves space.
But why should matter do this? Why should matter curve space?
One explanation is that space curvature is what matter is. William
K. Clifford first proposed this theory in an 1870 paper called 'On the
Space Theory of Matter'.

(Rucker, 1984, p. 82)

In this topic the density of people is used to curve the space they live in. What
places should now be chosen out of which to build these abstract spaces? How
will the choice of which hierarchy and division of areas to use alter the image
(Figures 3.12 and 3.13)? Many different cartograms, each based upon the same
population head count but drawn separately from all the major administrative
divisions of Britain, have been constructed to show how much the division of
space matters, and many are shown in these pages.
The answer to the question of robustness is that the choice of an areal unit
does not substantially alter the final shape of these images - this is a reassur-
ing outcome. In fact all thoughtfully constructed cartograms of Britain (or any
other territory) tend towards the same rough structure, which loosely implies
that an ideal solution exists. There is also a sense of aesthetic acceptance to be
realised. 15

14 The cartograms used in this work are pseudo-continuous: 'There are two types of contiguous
cartograms. The first is the pseudo-continuous cartogram. ... Pseudo-continuous cartograms depict
regions like a continuous map, but are endowed with the “pseudo” label (after Muehrke, 1978) due to
the generalization of the polygon's topological structure. This can be contrasted with the contiguous
cartogram, where the topology has been retained. ... ' (Torguson, 1990, p. 17).
15 The following papers document various attempts to control or automate the process: Hunter
and Young (1968), Hunter and Meade (1971), Skoda and Robertson (1972), Tobler (1959, 1973a,
1986), Olson (1976), Kadmon and Shlomi (1978), Eastman, Nelson and Shields (1981), Dougenik,
Niemeyer and Chrisman (1983), Nelson and McGregor (1983), Cuff, Pawling and Blair (1984),
Selvin et al . (1984), Dougenik, Chrisman and Niemeyer (1985), Kelly (1987), Cauvin, Schneider
and Cherrier (1989), Torguson (1990) and Dorling, Barford and Newman (2006).