MapCarte 349/365: Density equalizing cartogram by Michael Gastner and Mark Newman, 2004

MapCarte349_cartogramThe so-called Holy Grail of cartograms was solved by Michael Gastner and Mark Newman and published in 2004. To this point, cartograms had largely been abstract maps; they took various geometric shapes such as circles and then re-sized and re-positioned them. The result was a map without a map…there was very little of the underlying geography depicted and in some respects they were simply spatial graphs, or the thematic part of a thematic map without any sense of the geography that they more normally sit atop of.

At the heart of a cartogram is the use of symbols to represent geographic regions in proportion to the variable being mapped. To do this, one normally has to severely distort shapes or revert to geometric symbols. These can make such maps difficult to read because they no longer look like the very places they are supposed to represent. Gastner and Newman brought a new approach to the calculation of their cartogram by making use of elementary physics. This in itself was innovative since they borrowed logic and algorithms from the science of physics and applied it to cartography. They demonstrated their work using data from the 2000 U.S. Presidential election which illustrates how the U.S.A. map is modified by the share of the vote, thus giving equal visual weight to the key data being mapped as well as retaining the general impression of a map of the U.S.

The technique is referred to as density equalising because it uses a variable to normalize the map shape. It’s almost the inverse of a choropleth whereby one would normalize the data values to take account of the size of area; instead the actual values are mapped but the size of the areas are modified so they are visually equivalent in prominence. The result was an elegant solution to the search for a cartogram that allowed the user to show different magnitudes by area and at the same time preserve shape sufficient enough to make it recognisable. In effect, the map is warped yet shared boundaries are retained in their correct topological state. The map retains the essential elements of the original shapes and leaves readers with the ability to recognise the shapes.

Cartograms are visually arresting as images. Gastner and Newman’s work produced a new technique that enables them to be just that bit more understandable.

You can read their original paper here.

MapCarte 278/365: Socio-economic tectonics by Kenneth Field, 2014



Forgive the fact it’s one of mine but others feel it worthy of inclusion…

The standard way of illustrating socio-economic data for countries on a world map would be a choropleth. Options, of course, exist, to show data in a different way including proportional symbols or cartograms. All of these techniques are perfectly reasonable but all suffer from one problem, namely that it’s up to the map reader to make visual comparisons between areas shaded differently or symbolised differently. The focus is on how one place compares to another. What if the question is based on trying to understand how similar or dissimilar neighbours are?

This map looks specifically at the relationship between bordering countries to create a set of proportional line symbols that represent their dissimilarity…let’s call it a proportional adjacency map (any better ideas?). It’s a sort of linear cartogram.  Thinner lines mean countries share a very similar value for the variable. Thicker lines mean adjacent countries are very dissimilar. Additional ‘boundaries’ have been added to show how countries differ when they are separated by a stretch of sea or ocean.



The map shows twenty key socio-economic indicators, four for each of five broad themes. The use of small multiples gives a sense of how different countries vary across different measures. The only colour used on the map simply provides a motif for each of the five themes. Additionally, there is a note for each variable to express which two adjacent countries are most similar, and which are most dissimilar. The title is simply designed to capture attention and provide a metaphor for the socio-economic fracture zones that crisscross the planet.

The style of the map has been deliberately kept subdued so only the coloured fracture zones stand out. It demonstrates that if we’re trying to map a specific characteristic of data that isn’t well supported by conventional techniques then sometimes we have to make a new technique or modify one to suit our purposes. In many ways this map tehnique is the counter to a choropleth and literally fills in the gaps.

You can download a full size print version of the map here.

MapCarte 275/365: The population and the state capitals by Carlos Lemos, 2010


Click image above to go to web map

The word infographic has become a part of the lexicon used to describe information delivered using graphics. Maps have always been information graphics and although this example is described as an infographic it’s actually a map; an abstract, interactive web map, but a map nevertheless. It deals with spatial information and organises it in a manner that assists the communication of the message the author wishes to impart.

Lemos shows the distribution of the population of municipalities in relation to the capital of each Brazilian state. It illustrates the urban hierarchy too in a clean, efficient graphical manner. It’s a cartogram that dispenses with the real geography in favour of a version that ignores everything except the crucial aspects…population sizes illustrated as proportional symbols, organised in a linear fashion, by state.

The map’s use is supported by a simple yet elegant functionality including data display returned via a hover rather than a click. You can zoom to disentangle the symbols giving clarity to each spoke of the map. Transparency is well used and gives a sense of density.

Simple. Effective. Enthralling and informative. Maps do not need to be graphically complex to impart their information but they do need to be engaging.

MapCarte 225/365: Is Barack Obama President? By The Guardian, 2012


Infographics are all the rage. In fact, maps have always been information graphics. Sometimes, though, maps and mapping ideas can be used in extremely innovative ways to help create what might be termed a modern infographic.

Take this illustration from The Guardian’s coverage of the 2012 Presidential election. It has the two candidates holding a handful of balloons. At first glance there’s very little map-like about this infographic but the balloons are, in fact, a Dorling cartogram. Each balloon represents a US state, coloured to show strength of vote, with the shared States being held by both candidates in the middle and the more partisan States being held well away from their opponent.

Each balloon is a perfect proportional circle and hovering over the balloon reveals further details.



The combination of illustration and the use of a statistical and highly abstract map form is a great way to present data in a new and interesting way and perfect for journalistic purposes.

The approach is supported by a clean look, effective typography and bold numbers to clearly inform the key facts. The balloons float into the screen and reorganise just as if filled with helium (or a metaphor for hot air perhaps?). There’s very little visual clutter on the page.

Take a look at the interactive version of the Obama map here or, for the sake of being equal, the Romney version here.

MapCarte 180/365: Worldmapper by Worldmapper, 2006


Cartograms seem to be one of those map types that garner polarised opinion. There are as many who find them compelling and highly useful as there are those who find any reason to debunk their utility.

The WorldMapper project, a research project spearheaded by Danny Dorling and Benjamin Hennig have done much to bring the value of the Gastner-Newman cartogram, in particular, to global attention. Taking a range of global indicators, they have produced well over 200 maps showing all manner of socio-economic indicators that illustrate global inequalities. The web site allows individual maps to be seen and also downloaded as an executive briefing document combined with brief notes, graphs and other allied information. There’s even a published book of the maps.

The maps rely on the cartogram to deliver the message. Only colour is added to help identify the different continents and to anchor the eye.


Hennig has gone further with the idea and developed a variant he calls a gridded cartogram. While a conventional gastner-Newman cartogram modifies the size and shape of an area relative to a mapped value, the gridded version incorporates additional detail so that individual grid cells are morphed according to relative internal quantities. The result is a display of internal heterogeneity that the standard Gaster-Newman approach does not support.


A great example of the use of cartograms and the development of further cartographic research. More details on Worldmapper at the web site here. Details of the gridded cartograms are on Benjamin Hennig’s research page, Views of the World, here.

MapCarte 164/365: The Beautiful Game by Kenneth Field, 2010


One from me…

There’s a world of difference between designing maps for inclusion in small format publications which are designed to be viewed at about 18 inches and a large format poster designed to catch the attention of someone as they pass by, perhaps fleetingly, in a gallery. This map was designed for the latter, the original being A0 size.

The poster displays the global distribution of national professional football teams. The use of a Dorling cartogram technique scales the symbols to the number of professional teams in that country. The cartogram neither maintains topology, shape of feature centroids yet we are still able to pick out that it’s a world map since most adjacent countries touch each other. The map could have been presented using a choropleth or some other standard mapping technique but when you want maximum visual impact you need to design something far more eye-catching.

The entire symbology  of the map is football related from the football sphere symbols that also contain team logos to the background of a football stadium. From a distance the football symbols seem to drop or dance about inside the stadium cauldron. National football association badges locate countries and symbols are grouped into FIFA confederations. The poster is designed to offer more than simple visuals though; it provides readers with a way to explore the structure of the game as well as the etymology of the term ‘football’ itself and how it varies globally with different vernaculars.

It deliberately uses saturated, vibrant colours that would not necessarily work for other presentations and in total it’s quite a visual assault on the eyes. Subtle it is not, but maps do not have to be subtle to be effective depending on the viewing environment. It won a few awards which is why it gets a mention in MapCarte. I even managed to add a little version of me sat in the stands just for fun.

Such one-off maps can have longeivity in a design sense too. I used a similar visual approach to a more recent map…the full history of the FIFA World Cup, published to coincide with the 2014 Brazil World Cup. This map used more conventional proportional symbols though still retained the football theme by adding a football design to the proportional symbols themselves along with a touch of shadow to provide some depth. An abstract basemap provides a simple backdrop:


You can view the web map here or download a copy of the full size print map here.

MapCarte 155/365: The carbon atlas by The Guardian, 2007

MapCarte155_carbonThere’s something very appealing about a well composed thematic map. The geometric character of the symbols often used as an overlay gives the work an abstract aesthetic whether they are draped across a real map of the world or not. Of of the central tenets of good thematic map design is that the underlying geography is really just a placeholder. Providing topographic detail is really nothing more than a distraction to the main event. The most explicit illustration of this is when the base map is disregarded altogether.

Here, The Guardian use a Dorling cartogram based on proportioanlly sized circles that convey both quantity of the phenomena being mapped as well as the geography itself. There’s no need for a base map as the position and adjacencies of the symbols work perfectly to tell the story. Cartograms are not to everyone’s taste though and they tend to find more favour outside North America than within which is in itself curious. They are often reserved for reporting of election results when the size and shape of real areas is secondary to the proportion of vote and the amount of red or blue one wants to paint across the map in true proportion.

They are also more heavily used in the media precisely because they are visually striking and attention-grabbing. The strong geometry coupled with bold colours used to differentiate between continents is particularly impactful. There’s a really good hierarchy of detail in the map from the large simple symbols through the typographic components providing facts to the small-print where we can read a little of the story. There’s a useful legend in the top right that relays the colour coding as well as an overall measure and the graphs and country list at the foot provide detail for those wanting to mine it.

A strong print graphic that The Guardian has used in subsequent years to good effect when updating the information.

MapCarte 153/365: The distribution of voting, housing, employment and industrial composition in the 1983 General Election by Danny Dorling, 1991

MapCarte153_dorlingOne of Edward Tufte’s often repeated quotes goes something like this… “The world is complex, dynamic, multidimensional; the paper is static, flat. How are we to represent the rich visual world of experience and measurement on mere flatland?”.  Indeed, this problem is at the heart of cartography and becomes prominent when we’re looking to map multivariate thematic data. With a palette of points, lines and areas and a range of visual variables it’s often difficult to concoct a way to mp the data without seriously compromising something. It’s a challenge to represent complex data using simple, easy to decipher graphics.

This example of a multivariate cartogram by Dorling does just that.  The cartogram that he created is based on the redistribution of proportional symbols such that they do not overlap. The underlying geographical structure is largely ignored though symbols are placed as close to their original position and in relation to their neighbours as possible. Here, the complex social landscape would normally be represented by a geometric symbol such as a circle which would be proportional to the population of the area they represent. Dorling goes one step further though by using Chernoff Faces to ascribe additional information.

Sizes of faces are proportional to the electorate and shape, eyes, nose and mouth each display additional socio-economic variables allowing a theoretical maximum of 625 different faces.  In reality only a fraction of these permutations exist, each coloured in one of 36 trivariate colours. Maps such as this require a clear legend. Dorling makes the legend larger to support the fact that this map requires readers to refer to it frequently. While this idea might be contrary to a lot of cartographic design theory (symbols should be capable of being interpreted with minimum recourse to the legend), such multivariate symbology needs clear unambiguous explanation.

The strength of the image is its overall impact as well as allowing readers to mine detail.  Faces evoke emotional reactions and show social differences we can easily interpret.  Sharp local divisions or gradual changes emerge.  While such glyphs can often overload a map image, Dorling combines them masterfully and the strong colours on a black background create additional contrast and impact and the recognisable shape of the Great Britain emerges.

Another of Tufte’s mantras is that you can symbolise complexity by giving detail. Here, Dorling makes a very efficient and simple looking graphic by providing a wealth of detail. It’s an art form to be able to represent complexity simply but maps can be very efficient ways of presenting multivariate data if done well.

MapCarte 125/365: Where on earth have you been? by The Guardian, 2014


A lot is currently being made of personalised geographies and maps that reflect our supposed desire to see content filtered in some way by what map-makers think we might want to see. Google are pioneering personalised content in Google Maps based on our search histories and other preferences. But there’s always been a far simpler way of understanding personalised geographies. Sometimes these are as basic as a world map in a pub where patrons are invited to place a pin to show their location…thus the map of the pub’s patronage takes shape. We may even have a map at home in which we place pins to show where we’ve been.

The Guardian, in collaboration with Kiln have created a simple application that allows us to create our personalised world of travel. The map requires you to input the countries you have visited and the number of times you’ve been there. It’s a simple interface to add your information and the map is then built. What this app does very well is not just default to a shaded choropleth but turn the data into a density equalizing cartogram. Countries visited are shown proportional to each other in size. The map is then presented as if on a folded piece of paper with a nicely constructed layout. You can print your map or share it.

Of course, what’s really going on is The Guardian is collecting data through the choices of our selections which is possibly the real purpose of the map. They still achieve that aim by making the application interesting, simple and designed to encourage participation.

Simple. Fun. Eye-catching. Visit The Guardian’s web site here to make your own personalised map.

MapCarte 121/365: Wahlland by Moritz Stefaner, 2013


Click the image to view the online web map

Following the mapping of elections has become almost as much of a spectacle as the elections themselves. Media outlets seem to fall over themselves trying to provide more detailed and expansive coverage than their rivals. Over the course of the last decade we’ve seen countless ways to map the detailed voting patterns as they are announced and the map takes shape. Proportional symbols, choropleths, a variety of cartograms and three-dimensional techniques have all been used in recent years.The map presented here hasn’t been widely used and takes a different graphical approach altogether.

Made as a web map and published by the online arm of German newspaper Die Zeit (The Times), the Wahlland map shows the Germand Bundestag elections of 2013. The electoral districts of Germany are arranged by their voting behaviour using a very abstract approach that is based on similarity of lifestyle, preference and attitude rather than geography. Each district is represented by a series of triangles arranged almost like a coxcomb chart over each district. Each segment maps the results (by size) for the party represented (by colour). Rather than simply mapping voter numbers the size maps the relative difference to the average result of that party overall. Only parties that are above average are mapped and the districts are arranged so that more similar districts are clustered. It’s a novel approach to mapping multivariate statistical data that shows not only the salient information of the results but in a way that adds value and provides some sense of the underlying geography and patterns being revealed. Which districts voted like each other? Are they geographically proximal or distant?

The design goes beyond by providing a very helpful legend (hidden until required) and also allows data to be seen through hovering over each segment. The map can be filtered by state or by party so the clusters are easily viewed and the subtle background shading works to anchor the eye to a cluster and give a hint as to the overall quantity of vote for a party. Geography is thrown to the wind but this is a novel and well crafted alternative to more traditional forms of mapping elections that is visually eye-catching and performs well. Even the way it draws is neat, smooth and easy on the eye.