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Cartogram Assignment

Remapping the World's Population
Visualizing data using cartograms
By Benjamin D. Hennig, John Pritchard, Mark Ramsden, and Danny Dorling, Department of Geography, the University of Sheffield

This article as a PDF .

Figure 1: Worldmapper Population Cartogram

The Worldmapper project has successfully produced a series of maps to visualize data concerning a range of issues facing the modern world based on the idea of density-equalizing maps. With this approach, ArcGIS 9.3 plays a crucial role as an interface to convert suitable raster datasets and produce updated cartograms. The data is converted using ArcMap's ArcToolbox, while the cartograms were calculated using a geoprocessing tool available from Esri's ArcScripts site. The final visualization was performed in ArcMap. This article introduces and evaluates further new mapping approaches that move depictions beyond their simple descriptive form. It gives an insight into these new developments, focusing on subnational-level data that has, until now, been neglected.

Worldmapper and Its World Population Cartogram

The world population cartogram demonstrates the first attempt to include sub-national density data. In the first stage of the Worldmapper project, a wide range of maps depicting various human dimensions of the world have been published on the project's Web site ( Since the publication of the first new world population cartogram in 2006, nearly 600 maps have been produced, going far beyond the depiction of the world's population and covering topics such as education, poverty, and pollution. The Worldmapper cartograms show the data for 200 territories, thus making this new view on the world to some extent an arbitrary view: territorial borders are artificial and are subject to change. Furthermore, the assignment of territories in Worldmapper is arbitrary as different thoughts on these territories might exist. Therefore, the world population cartogram was taken as an example to test different ways to calculate these cartograms beyond the territorial borders. [Additional information on the calculations used in and the design of existing Worldmapper cartograms is given in "Worldmapper: The World as You've Never Seen It Before," by Danny Dorling, Anna Barford, and Mark Newman, published in the September 2006 issue of IEEE Transactions on Visualization and Computer Graphics.]

Data and Cartogram Calculation

Data used in this work was derived from the Socioeconomic Data and Applications Center (SEDAC) of Columbia University, New York. The Gridded Population of the World (GPW) database contains the distribution of the world's population on a gridded base (, including population data and estimates from 1990 to 2015. This data is available in resolutions of up to 2.5 arc minutes, leading to a population grid of 8,640 x 3,432 pixels. Data from the year 2000 has been used to make results comparable to the original Worldmapper population cartogram.

Figure 2: Grid-Based World Population Cartogram (2000)
© Copyright 2009 SASI Group (University of Sheffield)

This raster format data was imported to ArcGIS, converted to polygons, and combined with further metadata (e.g., country labels) to match grid cells for further visualization tasks. The cartogram script uses a 4,096 x 2,048 pixel-sized lattice for its map results.

The cartogram itself was calculated using the Cartogram Geoprocessing tool created by Tom Gross of Esri and available from the Esri ArcScripts site ( It uses density-equalizing methodology developed by Mark Newman and Michael Gastner at the University of Michigan. Unlike the Worldmapper cartograms that distort an initial projection of the boundaries of the territories, each population grid is treated as a separate part for the calculation, not taking any territorial information of borders into account. Thus each grid cell marks a border so that distinct shapes of countries are intentionally of no interest in the calculation.

Changes in the distortion of the resulting cartogram thus are only possible by adjusting the factor to smooth the original density. In addition, data from the USA has been extracted from the 2.5 arc minutes population grid and is calculated separately in the same way to produce a more detailed view of the resulting grid and its interval variation.


The resulting cartograms require some final visualization steps to adapt them to appear similarly to the original Worldmapper cartograms. The polygons of the calculated world population cartogram are dissolved according to their affiliation to the Worldmapper territories and colored according to the distinctive Worldmapper color scheme. The gridlines in the USA cartogram are preserved to show the degree of distortion within the grid.

A Redrawn World Population Cartogram

Compared to its predecessor (Figure 1), the redrawn World Population Cartogram (Figure 2) shows considerable differences. For example, in China the sparsely populated Himalayan regions can be distinguished from the densely populated eastern coastal regions. Internal variation within the United States and Mexico can also be recognized. Somewhat harder to identify but still evident are north-south differences in Great Britain and west-east differences in Germany. Hence, our goal to take the varying distributions of population on a subnational level and make them visible on a global view has been achieved. However, subnational variation can be difficult to analyze in more detail because the grid cells are eliminated to sustain the view on the global scale. In addition, more distinctive national shapes are far more distorted than in the original cartogram, which for some users might appear odd when interpreting such maps.

Down to Earth: A Population Cartogram of the United States

Figure 3: Grid-Based Population Cartogram of the Contiguous United States (2000)

To counter the loss of familiar national boundary shapes, a separate population cartogram is produced for the contiguous United States (Figure 3) and several other countries. The shape of the cartogram has more detail compared to the shape of the USA on the world population cartogram. This is because more grid cells are used in the calculation of the cartogram and no other polygons (e.g., from the European continent) influence the calculation. The different scale also allows the visualization of each grid cell so that subnational variation can be recognized. An "original" map of the USA with its familiar shape is shaded in underneath the grid to aid interpretation.

This visualization on a different scale is an improvement that goes far beyond the current capabilities of the Worldmapper project by using gridded base data to allow a different view of population distribution not only worldwide but also within separate regions. By using cartogram techniques, a different view on the regional variations of human geography is created, which can hardly be achieved with traditional mapping techniques.



Explore Data Using a Free Tool

The Cartogram Geoprocessing tool, available from ArcScripts, can be used for creating cartograms in ArcMap. A cartogram is a transformation of a map that uses some variable instead of land area to expand or contract the area of the original polygons based on an attribute value. Cartograms are often used for displaying population data. The Cartogram Geoprocessing tool was developed by Esri staff member Tom Gross. It uses the density-equalizing methodology developed by Mark Newman and Michael Gastner at the University of Michigan. A new version of the Cartogram Geoprocessing tool released in May 2009 allows the tool to be used in a Python script. This new version uses the currently selected data and honors definition queries. Visit arcscripts and search on the keyword cartogram.

The most significant obstacle to the realization of gridded depiction for Worldmapper will be the vast quantity of different topics covered and availability and reliability of data. Reliable gridded social and economic data for the whole world is rarely available and rarely of such good quality as the population data. The estimation of missing national data for some topics has already been a serious matter in the existing Worldmapper cartograms. Such estimations will not meet the demands of gridded datasets, so new ways of data estimation are needed.

Current approaches to estimate data commonly use the GPW data, and these have the potential to be adapted to Worldmapper's requirements. Revised gridded cartograms offer great potential to enhance the variety of Worldmapper's visualization capabilities. A different view of the "real" location of the depicted topic can present a better understanding of human action and human patterns on the globe.

However, distortions associated with the gridded method are a disadvantage and undermine the purpose of Newman and Gastner's algorithm to preserve the familiar shapes of countries. The potential of the gridded approach and the desire to preserve the familiar shapes must therefore be carefully balanced. Nevertheless, much potential lies in adding more user interactivity and detail to Worldmapper. Grid-based cartograms have the advantage of allowing a user to zoom in to view national and regional details, within a global context. As one of the authors, Danny Dorling, has commented, "Our maps could be made more interactive, certainly, and there are probably many other features that could be added."

GIS technology is a key tool to make this happen. A GIS environment not only facilitates data conversion and calculation of cartograms but also allows different geographic scales to be brought together under one map. An easy transfer to popular digital globes can thus be realized, allowing viewers to identify the regional dimension of a subject. Separate regional editions of gridded population cartograms can be generated to visualize the regional variation of population distribution.

For additional information, contact

Benjamin D. Hennig
Sheffield S10 2TN
United Kingdom
Tel.: +44 114 222 7900
Fax: +44 114 279 7912
Related Web sites: and


The authors thank the Leverhulme Trust for funding the Worldmapper project. The trust played no role in the submission or preparation of this work.


Dorling, Danny (2007), "Worldmapper: The Human Anatomy of a Small Planet," PLoS Medicine 4(1), 13�18.

Dorling, Danny, Anna Barford, and Mark Newman (2006), "Worldmapper: The World as You've Never Seen It Before," IEEE Transactions on Visualization and Computer Graphics, 12(5), 757�764, doi:10.1109/TVCG.2006.202.

Gastner, M. T., and M. E. J. Newman (2004), "Diffusion-Based Method for Producing Density Equalizing Maps," Proc. Natl. Acad. Sci. USA 101, 7499�7504.

Gaffin, S. R. et al. (2004), "Downscaling and Geo-spatial Gridding of Socio-economic Projections from the IPCC Special Report on Emissions Scenarios (SRES)," Global Environmental Change 14(2), 105�123.

Hay, S. I., A. Graham, and D. J. Rogers (2006), Global Mapping of Infectious Diseases: Methods, Examples and Emerging Applications, Academic Press, London.

Webb, Richard (2006), "Cartography: A Popular Perspective," Nature 439, 800.

Area cartogram maps are maps of non-absolute space where the areal extent is in proportion to some measured value.  Cartogram maps retain a partially accurate relative location and relative space, but the actual area of the individual polygons features are overrepresented or underrepresented based on the assigned values. Area cartograms are useful for visualizing relativity based on a common quantitative attribute such as population.

The First Cartograms

The distinction of the first cartogram has been attributed to Émile Levasseur who produced cartograms for his economic geography related books in the 1860s and 1870s.

The Rise in Popularity of Cartograms

Cartograms were popularized by Erwin Raisz who published the first statistical cartograms of the United States.  Raisz was a professor of cartography at the Institute of Geographical Exploration at Harvard University and was most well known for his physical relief maps which were hand drawn. In 1934, Raisz published in the journal Geographical Review an article entitled, “The rectangular statistical cartogram” which popularized the use of cartograms as an educational tool for learning about geography.

Cartogram map showing national wealth for the United States by Erwin Raisz, 1934.

Non-contiguous Cartogram Maps

Cartograms that focus on the distortion of area by a specific value can visualized as contiguous or non-contiguous.  Non-contiguous cartograms look like exploded maps with the individual polygons placed separately from each other.  Unlike contiguous cartograms, non-contiguous cartograms tend to preserve the shape of the individual polygons but not the size or connectivity to other polygons.   The sacrifice in non-contiguous cartograms is the topology or contiguity with adjacent areas.

Non-contiguous cartogram showing population density within Europe. (Source: Vinny Burgoo). Projection: Lambert Azimuthal Equal Area. Data: January 2008 population data from Eurostat.

Dorling Cartogram Maps

Dorling cartograms also sacrifice topology but the representation of geographic shape is completely abandoned.  Created by Danny Dorling of the University of Leeds in 1996, Dorling cartograms use circles to represent proportion.  The concept of circular cartograms was popularized and defined by Dorling’s article entitled, “Area cartograms: their use and creation.”  In the publication, Dorling posed the question, “If, for instance, it is desirable that areas on a map have boundaries which are as simple as possible, why not draw the areas as simple shapes in the first place?” and noted “circles as the simplest of all shapes.”  As a side noteDorling is also one of the founders of which posts and collects cartogram maps.

Circular cartogram showing the proportion of French language wiki originations by country from 2007-2011. Created by wiki user Moyogo.

A close cousin to Dorling cartogram is the Demers cartogram which uses squares instead of circles to show proportion.  Demers cartograms also provides more contiguity between areas while also attempting to maintain the least amount of distance from the true centroid of the shape as compared to Dorling cartograms.

Contiguous Cartogram Maps

Contiguous cartograms maintain topology (i.e contiguity) but, as compared to non-contiguous cartograms, produce the greatest distortion in shape. Areas are bloated or shrunk depending on the proportional attributes assigned.  Mark Newman provides some interesting excamples of contiguous cartograms on his page “Images of the social and economic world.”

Cartogram showing the number of billionaires by state. Click on image for larger map.


Free Cartogram Map Tools

There are some free cartogram tools available for downloading that allow you to manipulate geographic data to produce cartograms.

ScapeToad uses the Gastner/Newman diffusion-based algorithm to preserve topological relationships while transforming geographic data into cartograms.  ScapeToad is written in Java so it’s cross-platoform compatible (i.e. can run in Windows, MacIntosh, and Linux) and uses shapefiles as the input and output data file formats.  The application is standalone.  Maps can be exported in SVG format.

MAPresso is another Java based application that has a cartogram component.  Geographic data can be visualized as circle cartograms based on Dorling.  Data input is via text files or directly inputted into the app.  Data export options are minimal, the download page mentions, “An output as a file is not in the focus of the applet, there is a provisional possibility to produce an encapsulated PostScript file (EPS). The distorted geometry of a cartogram process can be exported in ArcGIS generate format.”

Cart is a C++ program written by Mark Gastner that uses a technique described in the 2004 journal article, “Diffusion-based method for producing density equalizing maps.” Cart is a standalone program but there are ArcGIS and MapInfo addins available that allow users to create cartograms within GIS software programs. Frank Hardisty has a Java version of the cartogram program that runs online.


Protovis is a graphical visualization toolkit  using Javascript (no longer under active development) that has a Dorling cartogram component. The same team is now actively developing d3.js which offers a non-contiguous cartogram component.

Related Cartographic Resources