Why are cartograms so distorted

Though three years old, the maps are incredibly eye-opening, reflecting everyting from alcohol consumption to HIV prevalence to toy exports. The Marginalian participates in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn commissions by linking to Amazon.

In more human terms, this means that whenever you buy a book on Amazon from any link on here, I receive a small percentage of its price, which goes straight back into my own colossal biblioexpenses. Privacy policy. TLDR: You're safe — there are no nefarious "third parties" lurking on my watch or shedding crumbs of the "cookies" the rest of the internet uses. This is the basis for a cartogram — a diagrammatic form of map that distorts the geography to overcome some of the problems of heterogenous reality.

Author and Citation Info:. Field, K. Wilson ed. Topic Description:. Definitions cartogram: a diagrammatic map type that represents the mapped area by distorting the geometry of the feature itself non-contiguous cartogram: adjacencies are compromised as areas shrink or grow; individual area shapes are preserved but they become detached from the overall map contiguous cartogram: adjacencies are maintained but shape is distorted to accommodate the mapped variable graphical cartogram: maintains neither shape, topology or location; instead using non-overlapping geometric shapes e.

Introducing Cartograms 2. One of the disadvantages of the cartogram is that it inevitably changes the visual representation of geography. This has consequences as the map attempts to balance statistical accuracy, geographical accuracy and topological accuracy. In some respects any cartogram could be thought of as a unique map projection — one that is modified by the data variable being mapped.

As with any map projection that tries to warp 3D space onto a 2D surface, some distortion is inevitable. Cartograms therefore contain inherent distortions as they strive to minimize the natural distortions caused by our perception of real geography. The French engineer Charles Minard is largely credited as the first to use the term cartogram Friis, Minard was a pioneer of statistical graphs and charts in the mids.

Many early statistical maps were also referred to as cartograms and the term was used interchangeably with many forms of thematic map until the early s. While maps and atlases had begun to use cartograms of some types, perhaps the earliest example of its use in a general English-speaking publication was in The Washington Post in Joseph R.

Grundy used a cartogram to illustrate his belief that State-based voting powers were unfair as they all had markedly different populations. Hence, voting strength would also be different and the map was an attempt to show the sizes of each State on the basis of population and Federal Taxes. Haack und H. It was publicly on sale at newsagents in Germany targeted at a general audience and consists of a highly detailed electoral cartogram of the general election in the German Empire at the time.

In the early s Raisz also noted the difficulty in accurately defining cartogram due to its use as a general term for many thematic maps. He also illustrated his text books with examples of a land-equal area cartogram. He used rectangles representing geographical divisions of the Census and States proportional to their population.

These value-by-area cartograms became relatively well defined through their inclusion in textbooks by Dent and Slocum The s also saw further development through the work of Danny Dorling whose abstract non-contiguous cartograms became a popular way to show data by throwing the shackles off geography altogether.

Michael Gastner and Mark Newman created an algorithm that managed the two seemingly impossible objectives of warping geography by a data variable while at the same time managing to maintain shape to a reasonable degree Gastner and Newman, Their density-equalizing contiguous cartogram technique provided a way to maintain the topological principle of adjacency while keeping some of the shape of the original unit areas.

The development of cartograms since the early s has progressed as improvements have been made in the various algorithms. Hennig adapted the Gastner-Newman algorithm to incorporate intra-area warping.

This allowed areas to be warped in a way that caters for their heterogeneity. More recently, cartograms have appeared with increasing frequency in the mainstream media. For instance, Gridded cartograms have become popular graphical ways to report election results.

They tessellate shapes, for instance squares or hexagons, of uniform size to create abstract illustrations where some other visual variable is used to symbolize the data variable itself, for instance through shading each shape much like a choropleth map. Though it is not guaranteed, many gridded cartograms are actually contiguous adjacencies between all pairs of enumeration units are preserved. However, they are not continuous as an explicit transformation is not defined for all points Kronenfeld, Tobler and Nusrat and Kobourov provide excellent and detailed reviews of the history of cartograms.

Non-contiguous cartograms are the simplest type where the shapes of the enumeration units are simply resized according to the denominator used Olson, Typically this results in an over-lapping or non over-lapping map Figure 1. In a non-contiguous cartogram topology adjacency and connectivity is sacrificed to preserve shape and enable recognition of geographical areas.

Non-contiguous cartograms are essentially proportional symbol maps where the area of each geographical unit is scaled proportionate to the data value.

While the recognition of individual shapes can be maintained, position warps location and distorts the overall appearance of the map as a whole. Figure 1. Presidential election results as a non-overlapping non-contiguous cartogram. Contiguous cartograms maintain connectivity between adjacent geographical areas but have a tendency to dramatically distort shape. Perhaps the most widely used is the Gastner-Newman cartogram otherwise known as a population-density equalizing cartogram; Gastner and Newman, which does an excellent job of retaining some character of the general shape of individual areas Figure 2.

However, the degree of distortion often renders the map difficult to interpret due to the abandonment of familiarity.

Of course, they are attention grabbing and if used in a web map, data could still be retrieved through a hover or popup which can counter the visual jarring.

Figure 2. Presidential election results as a population-density equalizing cartogram. Graphical cartograms are a third type which effectively create proportional symbols for the data values and then reorganize them in some way. The Dorling cartogram is perhaps the most well-known, which uses proportional circles, organized to provide the best adjacency as possible Figure 3; Dorling, An alternative is the Demers cartogram which uses squares instead of circles and thus reduces the gaps between shapes Figure 4; Bortins et al.

However, whereas the Dorling cartogram attempts to limit the distance of the eventual position of each object from its original position, the Demers sacrifices distance to maintain contiguity as far as possible. Figure 3. Presidential election results as a Dorling cartogram. Figure 4. Presidential election results as a Demers cartogram. The gridded or tessellating mosaic cartogram is a compromise cartogram that ignores geographical shape but attempts to maintain a more uniform topology that enables people to find familiar places without the need for perfect maintenance of adjacencies Cano et al.

Squares and hexagons tend to be the preferred shape for gridded cartograms. In a gridded cartogram, each area is symbolized by the same-sized shape regardless of geographical reality. Different symbol fills can be used to show higher or lower values of the data variable being mapped, using the same processes for classification and symbolization as a choropleth map Figures 5 and 6.

Because the shapes used are uniform in size, they can also provide a framework for incorporating graphs to create gridded cartogram of small multiples Figure 7. Figure 5.

Below is an example of a Dorling cartogram, using the same population of California counties example. Another Dorling-like cartogram is the Demers Cartogram, which is different in two ways.

It uses squares rather than circles; this leaves fewer gaps between the shapes. Secondly, the Dorling Cartogram attempts to move the figures the shortest distance away from their true locations; the Demers cartogram often sacrifices distance to maintain contiguity between figures, and it will also sacrifice distance to maintain certain visual cues The gap between figures used to represent San Francisco Bay in the Demers Cartogram below is a good example of a visual cue. The 25 Most Populated Counties in California are labeled in each of the two cartograms below for reference.

Pseudo-cartograms or false cartograms are representations that may look like cartograms but do not follow certain cartogram rules. Perhaps the most famous type of pseudo-cartogram was developed by Dr. Waldo Tobler. In this case, instead of enlarging or shrinking the objects themselves, Tobler moves the object's connections to a reference grid such as latitude or longitude in order to give the same effect.

This maintains good directional accuracy in the cartogram if county A is directly north of county B, it will still remain directly north in the cartogram. Note in previous examples, such as the Dorling Cartogram, this is not always true however, this is a false cartogram because it creates extensive error in the actual size of the objects. Let us consider this error where it becomes very clear, in the case of the California population.

Mono County is a very lowly populated county, with only 13, people but by pure coincidence it lays at the same latitude as San Francisco County , people and at the same longitude as Los Angeles County 9,, people.

It would be impossible to expand the latitude and longitude lines to make Los Angeles and San Francisco the appropriate size without in turn, expanding Mono County as well. In the same way, the lines cannot be contracted to make Mono County the appropriate size without making San Francisco and Los Angeles too small. Tobler uses a root mean square calculation to find the "best fit" or cartogram that is "close enough. That is, let a computer make a pseudo-cartogram, and from this a cartographer can create a contiguous cartogram by hand.

This also proves to be very effective. What is a Cartogram?