Cartogram

Kartenanamorphote (not Kartogramm) of Germany, with the states and districts resized according to population.

A cartogram is a map in which some thematic mapping variable – such as travel time, population, or Gross National Product – is substituted for land area or distance. The geometry or space of the map is distorted in order to convey the information of this alternate variable. They are primarily used to display emphasis and for analysis as nomographs.^[1]

Two common types of cartograms: area and distance cartograms. Cartograms have a fairly long history, with examples from the mid-1800s.^[2]

Area cartograms

Area cartogram of the 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.

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.^[3][4][5]

Area cartograms may be contiguous or noncontiguous. The area cartograms shown on this page are all contiguous, while a good example of a noncontiguous cartogram was published in The New York Times.^[6][7] The online resource SHOW®, provided by Mapping Worlds, creates discontiguous cartograms for different geographies (United States, Japan and World at this time) interactively, allowing users to quickly compare various characteristics. 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 about 700 contiguous area cartograms is available at Worldmapper,^[8] a collaborative team of researchers at the Universities of Sheffield and Michigan.

Production

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,^[9][10] Cart,^[11] and the Cartogram Processing Tool (an ArcScript for ESRI's ArcGIS), which all use the Gastner-Newman algorithm.^[12][13] An alternative algorithm, Carto3F,^[14] is also implemented as an independent program for non-commercial use on Windows platforms.^[15] This program also provides an optimization to the original Dougenik rubber-sheet algorithm.^{[16] [17]}

Algorithms

See also

• Choropleth map
• Contour map
• Thematic map

References

Further reading

• 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: 114–115. 
• 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.

External links

Wikimedia Commons has media related to Cartograms.

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