Artificial reality - The Visualization of Spatial Social Structure - page 92

Box 3.4 Many-dimensional cartograms

Many different types of area cartogram can be imagined. Here are some
world scale examples:
.
One-dimensional: World Population over time

.

One-and-a-half-dimensional: World
Population over time by continent

Two-dimensional: World Population over space
by continent

.
.
Two-and-a-half-dimensional: World

Population with income as
perceived height

time distances between all places, when the two-dimensional space in which the
linear cartogram resides is itself warped in the third dimension.
What happens when we go beyond the two spatial dimensions and also
attempt to incorporate time? At one level an analogue to the one-and-a-half-
dimensional cartogram can be made. The linear cartogram where distance is
made proportional to travel time can be projected as a surface above an area
cartogram. Thus a two-and-a-half-dimensional linear area cartogram is created
as a surface of travel time above population space. 20
Even simple two-dimensional population space changes in time, dramatically
so over long periods. A series of area cartograms has been constructed for this
topic of the British electorate by parliamentary constituency from 1955 to 1987.
The ten images show the gradual deformation of the space as the electorate
grows nationally, the South East swelling in particular while the inner cities
shrink. The fact that the definition and number of places changed also over this
period was easily incorporated in the graphics.

20 Angel and Hyman (1972, 1976). Note that Section 7.6 in this topic gives more details.