Cartogram
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 mid1800s.^{[2]}
Contents
Area cartograms
An area cartogram is sometimes referred to as a valuebyarea 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, densityequalizing 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 scaleddown 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. Scaleddown cartograms (from the NY Times example) are strictly shapepreserving. 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 shapepreserving 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.
Production
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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 addons 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 GastnerNewman algorithm.^{[13]}^{[14]} An alternative algorithm, Carto3F,^{[15]} is also implemented as an independent program for noncommercial use on Windows platforms.^{[16]} This program also provides an optimization to the original Dougenik rubbersheet algorithm.^{[17]} ^{[18]} The CRAN package recmap provides an implementation of a rectangular cartogram algorithm.^{[19]}
Algorithms
This table includes a list of references, related reading or external links, but its sources remain unclear because it lacks inline citations. (November 2014) (Learn how and when to remove this template message)

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  PseudoCartogram 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  GuseinZade, 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  Combinatorialbased approach  area contiguous  with distortion  Unknown 
1998  Kocmoud, House  Constraintbased approach  area contiguous  with distortion  Yes 
2001  Keim, North, Panse  CartoDraw^{[20]}  area contiguous  with distortion  Yes, algorithmically guaranteed 
2004  Gastner, Newman  Diffusionbased 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  Medialaxisbased cartograms^{[22]}  area contiguous  with distortion  Yes, algorithmically guaranteed 
2009  Heriques, Bação, Lobo  CartoSOM  area contiguous  with distortion  Yes 
2013  Shipeng Sun  OptiDCN^{[17]} and Carto3F^{[15]}  area contiguous  with distortion  Yes, algorithmically guaranteed 
2014  B. S. Daya Sagar  Mathematical MorphologyBased Cartograms  area contiguous  with local distortion, but no global distortion  No 
See also
References
 ^ Tobler, Waldo (March 2004). "ThirtyFive Years of Computer Cartograms". Annals of the Association of American Geographers. 94 (1): 58–73. doi:10.1111/j.14678306.2004.09401004.x. JSTOR 3694068.
 ^ Johnson (20081208). "Early cartograms". indiemaps.com/blog. Retrieved 20120817.
 ^ Paull, John & Hennig, Benjamin (2016) Atlas of Organics: Four Maps of the World of Organic Agriculture Journal of Organics. 3(1): 2532.
 ^ ^{a} ^{b} Michael T. Gastner; Mark E. J. Newman (2004). "Diffusionbased method for producing density equalizing maps". Proceedings of the National Academy of Sciences. 101 (20): 7499–7504. arXiv:physics/0401102 . Bibcode:2004PNAS..101.7499G. doi:10.1073/pnas.0400280101. PMC 419634 . PMID 15136719.
 ^ Gallery of Data Visualization  Bright Ideas
 ^ UNEP GRID Ardenal: Anamorphic Maps
 ^ Johnson (20110222). "Noncontiguous cartograms in OpenLayers and Polymaps". indiemaps.com/blog. Retrieved 20120817.
 ^ Cowan, Sarah; Doyle, Stephen; Heffron, Drew (20081102), "OpChart: How Much Is Your Vote Worth?", New York Times, retrieved 20120817
 ^ Worldmapper:The world as you've never seen it before
 ^ ScapeToad
 ^ The Art of Software: Cartogram Crash Course
 ^ Cart: Computer software for making cartograms
 ^ Cartogram Geoprocessing Tool
 ^ Hennig, Benjamin D.; Pritchard, John; Ramsden, Mark; Dorling, Danny, "Remapping the World's Population: Visualizing data using cartograms", ArcUser (Winter 2010): 66–69
 ^ ^{a} ^{b} Sun, Shipeng (2013), "A Fast, FreeForm RubberSheet Algorithm for Contiguous Area Cartograms", International Journal of Geographic Information Science, 27 (3): 567–93, doi:10.1080/13658816.2012.709247
 ^ Personal Website of Shipeng Sun
 ^ ^{a} ^{b} Sun, Shipeng (2013), "An Optimized RubberSheet Algorithm for Continuous Area Cartograms", The Professional Geographer, 16 (1): 16–30, doi:10.1080/00330124.2011.639613
 ^ ^{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
 ^ ^{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.
 ^ 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.
 ^ 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:10.1007/9783540301400_64.
 ^ Keim, Daniel; Panse, Christian; North, Stephen (2005). "Medialaxisbased 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: McGrawHill, 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, "Diffusionbased method for producing densityequalizing 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): 2532.
 Tobler, Waldo. "ThirtyFive Years of Computer Cartograms." Annals of the Association of American Geographers. 94 (2004): 5873.
 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
 Classified Ads on the French Leboncoin social web site and their regional distribution