Cartograms

Cartograms: (infrequently used as a synonym for thematic map, but implies distortion)

Basic rule of choropleth mapping is that you cannot manipulate SIZE, cartograms attempt to escape this limitation. They may be an exception that proves a rule...

space distorted based on some redefinition of distance (from a point)
as in "functional distance" such as time of travel.
linear cartograms are relatively simple when performed from a central focus.

Area Cartograms:

The size of an area is rescaled to be proportional to the attribute.
Manipulate the graphic variable size to communicate magnitude of a variable.

Basic constraints:

positive values - zero means the area vanishes, negative means what?
Minimum perceptual size (scale of cartogram) is given in attribute value
Skewed distributions are difficult
Recognition of shapes

Discontinuous Method

Each area (polygon) scaled by shrinking towards its center
Largest value is shown at full size (no expansion)
Polygons lose contiguity, but retain identifiable shape

Continuous Method

Goal: make each area proportional to the attribute, while retaining connectivity and general geographic orientation

• Tobler's algorithm: place outlines on surface of variable, flatten the distribution based on regular sampling of the surface. Iterate. (imperfect convergence, eg. states of US after 99 trials still only .6 corr.)
• Dougenik's algorithm: generate gravitational field with attractive (shrinking) forces and repulsive (expanding) forces at centers of polygons. Iterate. Converges much more rapidly. US States after 8 iterations
• Other approaches, distort each polygon serially (depends on order)

Use of cartograms: as base for other (related) variables

A cartogram should be constructed for the raw magnitude underlying the phenomenon studied. In the case of US Presidential Elections it is Electoral Votes, in economic studies it could be gross regional product or employment in some general sector. Then another attribute (% vote for Kennedy) is shown in the distorted zones.

Cartogram resource: UC Santa Barbara