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Cartograms – Classification and Terminology Polish Cartographical Review Vol. 51, 2019, no. 2, pp. 51–65 DOI: 10.2478/pcr-2019-0005 Received: 01.02.2019 ANNA MARKOWSKA Accepted: 20.05.2019 Institute of Geodesy and Cartography Geoinformation and Cartography Warsaw, Poland orcid.org/ 0000-0001-8446-6171 [email protected] Cartograms – classification and terminology Abstract. The author discusses new classifications of cartograms. Cartographic anamorphoses terminology and a multi-level classification, including not only cartograms but also anamorphical projections, have been proposed. The selected area cartograms’ classes were discussed in detail and compared. Keywords: cartograms, area cartograms, cartograms’ classification 1. Introduction rature considers cartograms mostly as maps which are the result from a purposeful modifi- A cartogram1 is a form of cartographic pre- cation of traditional maps, mainly choropleth sentation for which there is no unified termino- and diagram maps (R. Szura 1989), i.e. “maps logy and full classification. Earlier divisions of of visibly distorted geometry – in comparison cartograms, both Polish and foreign, were in- to Euclidean geometry – but better suited to complete. Anamorphical projections and ana- reader requirements connected to map’s func- morphic pseudomaps were often omitted. The tion” (A. Michalski, P. Tymków 2011, p. 19). author aims to discuss the terminology referring In the literature there appear various terms to cartograms, present a proposed multi-level referring to area cartograms. The most common classification of cartographic anamorphoses English terms are cartogram and value-by- and compare classes of area cartograms. -area map. The term cartogram was originally used for graphic presentation of statistical data, in cartographic meaning it was first used in 2. Cartograms – terminology 1851 to name a series of maps Cartogrammes a foyer diagraphiques by C.J. Minard (H. Friis A cartogram is a map, on which one feature 1974). Today the English term cartogram refers – distance (distance cartograms) or area (area to maps elaborated in a “scale other than a true cartograms) is distorted proportionately to the scale” (V.S. Tikunov 1988, S. Mayhew 2004, value of a given phenomenon (A. Faliszewska B.D. Henning 2011). 2011). According to J.C. Muller (1982, 1983), if In the sixth volume of The history of carto- cartograms are a particular type of projection, graphy… (M. Monmonier 2015) other terms for all traditional maps can be treated as carto- area cartograms are listed: anamorphosis, dia- grams, and traditional equal-area maps can be gramic maps, map-like diagrams, varivalent pro- treated as area cartograms. However, the lite- jections, density equalized maps, isodensity maps, mass-distributing (pycnomirastic) map projections. Terms of cartograms often relate to 1 In Polish terminology the term “kartogram anamorficzny” the shape of basic units, e.g. rectangular carto- has been used for many years to describe area cartogram (R. Szura 1989). The Polish term “kartogram” means “cho- gram (E. Raisz 1934) or circular cartogram, more ropleth map”. often known as Dorling cartogram (D. Dorling 52 Anna Markowska 1996). Terms of many area cartograms contain 3. Cartograms – classification the name of the algorithm used in their prepara- tion. When W. Tobler (2004) wrote about compu- For the purpose of map classification, seven ter elaboration of area cartograms, he mentioned classification criteria were set. The criteria are J. Dougenik, N. Chrisman and D. Niemeyer divided depending on which map class they (Continuous Area Algorithm, 1985) or Gastner- can be referenced: -Newman (Diffusion-based Method, 2004) algo- • cartographic anamorphoses: rithms. It is possible to find other names related A) mathematical basis, to algorithms used to generate cartograms B) transformed object, (A. Markowska, J. Korycka-Skorupa 2015), e.g.: C) transformed method; − algorithm of W. Tobler from 1973 (Rubber- • area cartograms: -map Method) and from 1986 (Pseudo-carto- D) graphic continuity; gram), E) graphic presentation; − algorithm of D. Dorling from 1990 (Cellular • anamorphical projections: Automation Algorithm), F) grid transformation; − algorithm of D. House and C. Kocmoud • distance cartograms: from 1998 (Continuous Area Cartogram Using G) the main distortion point’s location. the Constraint-based Method). Since the publication of W. Tobler’s (2004) A. Mathematical basis article there have appeared new algorithms, Division according to mathematical accuracy and therefore new terms referring to cartograms, of transformation was established as the main e.g. gridded cartogram (B.D. Henning 2011), criterion of classification of cartographic ana- circular-arc cartogram, rectilinear cartogram, morphosics (Z. Mudrych 1976). The term carto- table cartogram or mosaic cartogram (S. Nusrat, graphic anamorphosis is overriding in relation S. Koborov 2016). to cartograms. It includes all presentations Fig. 1. Cartograms’ classification Cartograms – classification and terminology 53 having certain anamorphic features, though they or distances between selected points can be may not be drawn up according to strict ma- introduced (fig. 1, criterion C). Both transfor- thematical rules or may not maintain spatial mations are proportional to the value of a phe- relations (fig. 1, criterion A): nomenon (J. Olson 1976). Two classes of − anamorphic maps (app. 1, pt 1) – presen- cartograms can be proposed: tations which have been made according to − area cartograms – maps on which the area mathematical and spatial rules; of individual spatial units is changed depend- − anamorphic pseudomaps (app.1, pt 2) – ing on the value of a phenomenon (app. 1, graphically close to anamorphic maps, but ela- pts 5a–10); borated in a more arbitrary way, often without − distance cartograms – maps on which the clearly determined mathematical rules or rules distance between selected points is changed connected to spatial relations. depending on the value of a phenomenon (app. 1, pts 4a–4b). B. Transformed object For distance cartograms a general division The second criterion of classification consi- is proposed according to the location of the ders if the anamorphic transformation is applied main points of distortion (fig. 1, criterion G): to the cartographical grid or to the thematic − monocentric distance cartograms – maps contents of the map (fig. 1, criterion B): on which the distance between the central − cartograms (app. 1, pts 4a–10) – anamor- point and given points changes with the value phic maps in which, depending on the value of of a phenomenon (e.g. distances between a se- the phenomenon, the area of individual areal lected metro station and next stations expressed units is changed (area cartogram) or the distance in the time of journey – app. 1, pt 4a); between selected points is changed (distance − polycentric distance cartograms – maps cartogram); which means that changes are in- on which the distance between a subsequent troduced depending on the thematic contents pair of points in a given network changes with of the map; the value of a phenomenon (e.g. distances − anamorphical projections (app. 1, pt 3) – between two subsequent stations of the War- anamorphic maps resulting from a transforma- saw metro expressed in the time of journey – tion of cartographical grid (J. Korycka-Skorupa, app. 1, pt 4b). et al. 2015). Anamorphical projections are a type of dis- tortion projections in which cartographical grid D. Graphic continuity is distorted (S. Grabarczyk-Walus 2007). In The author of a map performs various ope- this group of projections a local scale change rations during the process of cartogram elabo- is achieved by transforming linear elements of ration (B.D. Dent 1999, B.D. Dent et al. 2009 the map by specially selected transformational − fig. 2). In an anamorphical transformation functions. Areas around the selected center the area of both contiguous and noncontiguous are enlarged. Thus it is possible to observe cartograms is changed. In both classes of area more details in the reader’s area of interest. cartograms the area of base units is modified According to the type of distortion of the car- proportionately to the value of a phenomenon. tographical grid of the base map three classes In contiguous and noncontiguous cartograms of anamorphical projections can be indicated mutual location (orientation) of base units is (fig. 1, criterion F): preserved. Therefore changes of area or orien- − one-direction anamorphoses (distortion along tation cannot differentiate classes of area car- one axis of the rectangular coordinate system), tograms and should not be the criteria of their − two-direction anamorphoses (distortion along classification. two axes), Spatial continuity of presentation differentiates − radial anamorphoses (distortion in radial contiguous and noncontiguous cartograms. directions from a given central point). Therefore this characteristic was chosen as a criterion of classification of area cartograms. C. Transformed method Another aspect differentiating contiguous and In the process of editing the contents of a car- noncontiguous equiform cartograms is the tograms, the changes in the area of base units shape of base units. According to the scheme 54 Anna Markowska Fig. 2. The operations take to edit area cartograms (B.D. Dent 1999; B.D. Dent et al. 2009) (fig. 2) contiguous cartograms always have fied terms diagram cartograms, rectangular a changed shape of base units, while in non- cartograms, square cartograms or circle carto- contiguous
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