Cartogram

Area cartogram of the conterminous United States, with each county rescaled in proportion to its population. Colors refer to the results of the 2004 U.S. presidential election popular vote. See also Purple America.)

Cartogram of Germany, with the states and districts resized according to population

Area cartogram of the world with each country rescaled in proportion to the hectares of certified organic farming[3]

An area cartogram is sometimes referred to as a value-by-area map or an isodemographic map, the latter particularly for a population cartogram, which illustrates the relative sizes of the populations of the countries of the world by scaling the area of each country in proportion to its population; the shape and relative location of each country is retained to as large an extent as possible, but inevitably a large amount of distortion results. Other synonyms in use are anamorphic map, density-equalizing map and Gastner map.[4][5][6]

Area cartograms may be contiguous or noncontiguous. The area cartograms shown on this page are all contiguous, where all areas are connected together and continuously deformed, while a good example of a noncontiguous cartogram was published in The New York Times[7][8], where each area is disconnected from the rest, and is scaled while maintaining the area's shape. This method of cartogram creation is sometimes referred to as the projector method or scaled-down regions.

Cartograms may be classified also by the properties of shape and topology preservation. Classical area cartograms (shown on this page) are typically distorting the shape of spatial units to some degree, but they are strict at preserving correct neighborhood relationships between them. Scaled-down cartograms (from the NY Times example) are strictly shape-preserving. Another branch of cartograms introduced by Dorling, replaces actual shapes with circles scaled according to the mapped feature. Circles are distributed to resemble the original topology. Demers cartogram is a variation of Dorling cartogram, but it uses rectangles instead of circles, and attempts to retain visual cues at the expense of minimum distance. Schematic maps based on quad trees can be seen as non shape-preserving cartograms with some degree of neighborhood preservation.

A collection of contiguous area cartograms is available at Worldmapper,[9] which was started by a collaborative team of researchers at the Universities of Sheffield and Michigan.

A linear cartogram of the London Underground, with distance distorted to represent travel time from High Barnet station

While an area cartogram manipulates the area of a polygon feature, a linear cartogram manipulates linear distance on a line feature. The spatial distortion allows the map reader to easily visualize intangible concepts such as travel time and connectivity on a network. Distance cartograms are also useful for comparing such concepts among different geographic features. A distance cartogram may also be called a central-point cartogram.

A common use of distance cartograms is to show the relative travel times and directions from vertices in a network. For example, on a distance cartogram showing travel time between cities, the less time required to get from one city to another, the shorter the distance on the cartogram will be. When it takes a longer time to travel between two cities, they will be shown as further apart in the cartogram, even if they are physically close together.

Distance cartograms are also used to show connectivity. This is common on subway and metro maps, where stations and stops are shown as being the same distance apart on the map even though the true distance varies. Though the exact time and distance from one location to another is distorted, these cartograms are still useful for travel and analysis.

Cartogram showing Open Europe estimate of total European Union net budget expenditure in euros for the whole period 2007–2013, per capita, based on Eurostat 2007 pop. estimates (Luxembourg not shown).
Net contributors

  −5000 to −1000 euro per capita

  −1000 to −500 euro per capita

  −500 to 0 euro per capita

Net recipients

  0 to 500 euro per capita

  500 to 1000 euro per capita

  1000 to 5000 euro per capita

  5000 to 10000 euro per capita

  10000 euro plus per capita

One of the first cartographers to generate cartograms with the aid of computer visualization was Waldo Tobler of UC Santa Barbara in the 1960s. Prior to Tobler's work, cartograms were created by hand (as they occasionally still are). The National Center for Geographic Information and Analysis located on the UCSB campus maintains an online Cartogram Central with resources regarding cartograms.

A number of software packages generate cartograms. Most of the available cartogram generation tools work in conjunction with other GIS software tools as add-ons or independently produce cartographic outputs from GIS data formatted to work with commonly used GIS products. Examples of cartogram software include ScapeToad,[10][11] Cart,[12] and the Cartogram Processing Tool (an ArcScript for ESRI's ArcGIS), which all use the Gastner-Newman algorithm.[13][14] An alternative algorithm, Carto3F,[15] is also implemented as an independent program for non-commercial use on Windows platforms.[16] This program also provides an optimization to the original Dougenik rubber-sheet algorithm.[17] [18] The CRAN package recmap provides an implementation of a rectangular cartogram algorithm.[19]

Cartograms can also be constructed manually, either by hand or in a computer-assisted environment. Block cartograms are constructed by arranging geometrically regular equal-sized blocks, with the number of blocks allocated to each district proportional to the population variable. Several examples of block cartograms were published during the 2016 U.S. presidential election season by The Washington Post,[20] the FiveThirtyEight blog,[21] and the Wall Street Journal,[22] among others.

• Choropleth map
• Contour map
• Thematic map

• Campbell, John. Map Use and Analysis. New York: McGraw-Hill, 2001.
• Dorling, Daniel. "Area cartograms: Their use and creation." "Concepts and Techniques in Modern Geography series no. 59." Norwich: University of East Anglia, 1996.
• Gastner, Michael T. and Mark E. J. Newman, "Diffusion-based method for producing density-equalizing maps." Proceedings of the National Academy of Sciences 2004; 101: 7499–7504.
• Gillard, Quentin (1979). "Places in the News: The Use of Cartograms in Introductory Geography Courses". Journal of Geography. 78 (3): 114–115. doi:10.1080/00221347908979963.
• Hennig, Benjamin D. "Rediscovering the World: Map Transformations of Human and Physical Space." Berlin, Heidelberg: Springer, 2013.
• House, Donald H. and Christopher Kocmoud, "Continuous Cartogram Construction." Proceedings of the IEEE Conference on Visualization 1998
• Paull, John & Hennig, Benjamin (2016) Atlas of Organics: Four Maps of the World of Organic Agriculture Journal of Organics. 3(1): 25–32.
• Tobler, Waldo. "Thirty-Five Years of Computer Cartograms." Annals of the Association of American Geographers. 94 (2004): 58–73.
• Vescovo, Victor. "The Atlas of World Statistics." Dallas: Caladan Press, 2005.

Wikimedia Commons has media related to Cartograms.

• Cartogram Central
• Worldmapper collection of world cartograms
• Classified Ads on the French Leboncoin social web site and their regional distribution
• Cartograms about Brazil