From Wikipedia, the free encyclopedia
Cartogram 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 are 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.
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, while a good example of a noncontiguous cartogram was published in The New York Times.[7][8] 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,[9] a collaborative team of researchers at the Universities of Sheffield and Michigan.


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]


Year Author Algorithm Type Shape preservation Topology preservation
1973 Tobler Rubber map method area contiguous with distortion Yes, but not guaranteed
1976 Olson Projector method area noncontiguous yes No
1978 Kadmon, Shlomi Polyfocal projection distance radial Unknown Unknown
1984 Selvin et al. DEMP (Radial Expansion) method area contiguous with distortion Unknown
1985 Dougenik et al. Rubber Sheet Distortion method [18] area contiguous with distortion Yes, but not guaranteed
1986 Tobler Pseudo-Cartogram method area contiguous with distortion Yes
1987 Snyder Magnifying glass azimuthal map projections distance radial Unknown Unknown
1989 Cauvin et al. Piezopleth maps area contiguous with distortion Unknown
1990 Torguson Interactive polygon zipping method area contiguous with distortion Unknown
1990 Dorling Cellular Automata Machine method area contiguous with distortion Yes
1993 Gusein-Zade, Tikunov Line Integral method area contiguous with distortion Yes
1996 Dorling Circular cartogram area noncontiguous no (circles) No
1997 Sarkar, Brown Graphical fisheye views distance radial Unknown Unknown
1997 Edelsbrunner, Waupotitsch Combinatorial-based approach area contiguous with distortion Unknown
1998 Kocmoud, House Constraint-based approach area contiguous with distortion Yes
2001 Keim, North, Panse CartoDraw[20] area contiguous with distortion Yes, algorithmically guaranteed
2004 Gastner, Newman Diffusion-based method[4] area contiguous with distortion Yes, algorithmically guaranteed
2004 Sluga Lastna tehnika za izdelavo anamorfoz area contiguous with distortion Unknown
2004 van Kreveld, Speckmann Rectangular Cartogram[21] area contiguous no (rectangles) No
2004 Heilmann, Keim et al. RecMap[19] area noncontiguous no (rectangles) No
2005 Keim, North, Panse Medial-axis-based cartograms[22] area contiguous with distortion Yes, algorithmically guaranteed
2009 Heriques, Bação, Lobo Carto-SOM area contiguous with distortion Yes
2013 Shipeng Sun Opti-DCN[17] and Carto3F[15] area contiguous with distortion Yes, algorithmically guaranteed
2014 B. S. Daya Sagar Mathematical Morphology-Based Cartograms area contiguous with local distortion, but no global distortion No

See also


  1. ^ Tobler, Waldo (March 2004). "Thirty-Five Years of Computer Cartograms". Annals of the Association of American Geographers. 94 (1): 58–73. doi:10.1111/j.1467-8306.2004.09401004.x. JSTOR 3694068. 
  2. ^ Johnson (2008-12-08). "Early cartograms". Retrieved 2012-08-17. 
  3. ^ Paull, John & Hennig, Benjamin (2016) Atlas of Organics: Four Maps of the World of Organic Agriculture Journal of Organics. 3(1): 25-32.
  4. ^ a b Michael T. Gastner; Mark E. J. Newman (2004). "Diffusion-based method for producing density equalizing maps". Proceedings of the National Academy of Sciences. 101 (20): 7499–7504. arXiv:physics/0401102Freely accessible. Bibcode:2004PNAS..101.7499G. doi:10.1073/pnas.0400280101. PMC 419634Freely accessible. PMID 15136719. 
  5. ^ Gallery of Data Visualization - Bright Ideas
  6. ^ UNEP GRID Ardenal: Anamorphic Maps
  7. ^ Johnson (2011-02-22). "Noncontiguous cartograms in OpenLayers and Polymaps". Retrieved 2012-08-17. 
  8. ^ Cowan, Sarah; Doyle, Stephen; Heffron, Drew (2008-11-02), "Op-Chart: How Much Is Your Vote Worth?", New York Times, retrieved 2012-08-17 
  9. ^ Worldmapper:The world as you've never seen it before
  10. ^ ScapeToad
  11. ^ The Art of Software: Cartogram Crash Course
  12. ^ Cart: Computer software for making cartograms
  13. ^ Cartogram Geoprocessing Tool
  14. ^ Hennig, Benjamin D.; Pritchard, John; Ramsden, Mark; Dorling, Danny, "Remapping the World's Population: Visualizing data using cartograms", ArcUser (Winter 2010): 66–69 
  15. ^ a b Sun, Shipeng (2013), "A Fast, Free-Form Rubber-Sheet Algorithm for Contiguous Area Cartograms", International Journal of Geographic Information Science, 27 (3): 567–93, doi:10.1080/13658816.2012.709247 
  16. ^ Personal Website of Shipeng Sun
  17. ^ a b Sun, Shipeng (2013), "An Optimized Rubber-Sheet Algorithm for Continuous Area Cartograms", The Professional Geographer, 16 (1): 16–30, doi:10.1080/00330124.2011.639613 
  18. ^ a b Dougenik, James A.; Chrisman, Nicholas R.; Niemeyer, Duane R. (1985), "An Algorithm to Construct Continuous Area Cartograms", The Professional Geographer, 37 (1): 75–81, doi:10.1080/00330124.2011.639613 
  19. ^ a b Heilmann, Roland; Keim, Daniel; Panse, Christian; Sips, Mike (2004). "RecMap : Rectangular Map Approximations". Proceedings of the 10th IEEE Symposium on Information Visualization: 33–40. doi:10.1109/INFVIS.2004.57. 
  20. ^ Keim, Daniel; North, Stephen; Panse, Christian (2004). "CartoDraw: a fast algorithm for generating contiguous cartograms". IEEE Trans Vis Comput Graph. 10 (1): 95–110. doi:10.1109/TVCG.2004.1260761. 
  21. ^ van Kreveld, Marc; Speckmann, Bettina (2004). "On Rectangular Cartograms". In: Albers S., Radzik T. (eds) Algorithms – ESA 2004. ESA 2004. Lecture Notes in Computer Science. Springer, Berlin, Heidelberg. 3221. doi:10.1007/978-3-540-30140-0_64. 
  22. ^ Keim, Daniel; Panse, Christian; North, Stephen (2005). "Medial-axis-based cartograms". IEEE Computer Graphics and Applications. 25 (3): 60–68. doi:10.1109/MCG.2005.64. 

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

  • Cartogram Central
  • Worldmapper collection of world cartograms
  • Classified Ads on the French Leboncoin social web site and their regional distribution
Retrieved from ""
This content was retrieved from Wikipedia :
This page is based on the copyrighted Wikipedia article "Cartogram"; it is used under the Creative Commons Attribution-ShareAlike 3.0 Unported License (CC-BY-SA). You may redistribute it, verbatim or modified, providing that you comply with the terms of the CC-BY-SA