Cartograms

Cartograms are maps in which symbol sizes represent some measured quantity. Maps that use areapreserving projections can be considered cartograms; however, the term usually refers to a combination of statistical map and graph distorted to represent social phenomena. This involves a coordinate transformation [Page 20]to ensure that aspects of the original geography are preserved, while areas representing the chosen phenomenon and symbols do not overlap.

It is impossible to retain the locations, shapes, and adjacencies of the original map in a cartogram. Various techniques aim to minimize errors in these characteristics and aid recognition, while ensuring computational efficiency. Cartograms are used in spatial analysis, modeling, and geovisualization when studying social phenomena. Most are equal population cartograms, whereby the sizes of discrete areas relate to the numbers of inhabitants.

Figure 1 shows a choropleth map and a noncontinuous population cartogram shaded by land area, with darker areas having fewer people. The people in the smaller, but more densely populated zones are evidently visually underemphasized in the choropleth map—indeed, it may be difficult to believe that these are maps of the same phenomenon.

Hand-drawn cartograms gained popularity in the 1930s, but examples have been reported from as early as 300AD. Various analog techniques exist for producing equal population maps, including use of a rolling pin and modeling clay and thousands of ball-bearings. Tobler developed some of the early mathematical techniques for describing cartogram transformations. We can now compute cartograms for large numbers of areas using these and other methods.

Figure 1 Land Area (Choropleth) Map and Noncontinuous Population Cartogram of Leicestershire, U.K

Source: cdv Software—1991 U.K. Boundary Data are Crown Copyright.

Both maps are shaded by land area. Circle size in the right-hand figure is proportional to population.

Cartograms may be continuous or noncontinuous. The former are space-filling, and a single transformation is applied to a region of interest. Topology is preserved, but shapes are distorted. This may make it difficult to recognize zones and compare area sizes (see Figure 2). Noncontinuous cartograms, such as that shown in Figure 1, contain gaps. Some resize areas according to population and map them at their original locations, retaining shape and location, but not contiguity. Similar to Figure 1, Daniel Dorling's New Social Atlas of Britain uses circle symbols to represent populations for each area, keeping symbols as near to the positions of the original zones as possible, while maintaining adjacencies between neighbors.

You can see a huge range of detailed cartograms and other graphics in the New Social Atlas of Britain. Online resources that use cartograms include the WorldMapper project, which explored global inequalities with a different cartogram for each day of 2006. Michael Gastner's cartograms of the 2004 U.S. presidential election map voting patterns according to population. Bettina Speckmann and Adrian Herzog's online applications generate cartograms. Daniel Keim's group has developed a number of techniques for generating cartograms and pixel-repositioning techniques to address overplotting issues in large, pixel-based geospatial data sets on large displays.

Figure 2 Land Area (Choropleth) Map and Continuous Population Cartogram of Leicestershire, U.K.

Source: cdv Software—1991 U.K. Boundary Data are Crown Copyright.

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