Pointilist cartography

The Washington Post have published an article that explores alternative methods for mapping elections. "Toward a more perfect 2016 presidential election results map" does an excellent job of establishing the problem of mapping totals in massively different geographical units. They don't really explain you have to normalize the totals but, instead, leap to the population-equalizing density cartogram as one alternative before quickly dismissing it as hard to read.

They then offer a map that takes precinct level data and scales the results by number of votes.

What they seem to have done is created a proportional symbol map with very small circular symbols that have been scaled across a ridiculously small size range. They've used a lot of transparency to allow overlapping symbols to build a composite patch of more opaque colour in areas with a lot of small geographical areas.

This is pointilist cartography (note, I said pointilist, not pointless). Proportional symbol maps are not new. Neither are dot density maps. This version isn't particularly innovative but it does do a very good job of mitigating the perceptual problems of widely varying geographical areas. Each place gets the same symbology treatment and, so, the map provides a well balanced mix of red and blue with a lot of white space in between. They used a symbol treatment that goes from red through white to blue with the intermediate colours reserved for marginal precincts. I like this approach. It avoids the unusual purple often used for areas that are finely balanced. It means the map brings focus to those areas that are more partisan. Of course, with a shift in the symbology you could bring focus to marginal areas if that was the map you wanted to show.

A similar approach is to use solid fills for small areas and then show larger areas as small circular symbols. Mixing the techniques on a single map can be useful and also mitigates the visual impact of large areas. Here's an illustration using the technique that I recently made for my forthcoming book. The top is a standard choropleth with a diverging colour scheme. The bottom is the pointilist version.

So, overall I really like this kind of approach to deal with perceptual issues. But the article does hide a more interesting problem. The opening paragraph is at pains to say we've been over this ground before. We have - ad nauseam. Yet so many prefer the standard choropleth and, worse, sometimes with totals. But when they suggest it's a problem for the 'designer' that's where the real problem lies. Everyone these days is a bloody 'designer'. But everything is designed. I always balk when someone tells me they're a designer. A designer of what precisely? Furniture? Buildings? UI? Maps? A cartographer knows how to map election data. They know the problems and they know the solutions that best deal with particular visual issues to get to a map that matches a particular narrative. Far too many 'designers' are busy scrambling to try and figure out how to overcome problems that have already been figured out.

Talk to a cartographer. That's their job. They know what they're doing and likely have a good solution. Pointilist cartography isn't new. I'm pleased to see articles like the one I note here picking up these techniques. I just hope they get used a little more rather than being marginalized by 'designers' who default to the standard choropleth.

Brewdog: Stick to the Beer

I've written about non-normalized choropleths before (e.g. here and here and here) but when one of my favourite breweries makes the mistake I feel compelled to mention it again.

Brewdog are setting up in the USA. This is a good thing because their beer is spectacularly good. I have become an investor in their USA Equity for Punks campaign to support their efforts. But they need a cartographer because their maps are spectacularly bad.  They've been running this map showing how investors are spread across the US.

Clearly they're mapping totals as a choropleth which as most who know me will know gets me really rather upset. I mentioned this to Brewdog but their reply suggest (a) they don't get it and (b) they don't care.

Yes, I get that it's a bit of a fun but that's not actually a good excuse for making a crap map.  I could make some shitty home brew just for fun as well but what's the point of that? I'd rather try and do the job right and make something that tastes good. They've also used a poor blue to red colour scheme but that's a different argument. Anyway, I have offered to help them correct it so just because I can, here's a couple of efforts whipped up in less than an hour.

Here's the (incorrect) totals version as a choropleth in Punk IPA colours:

And here's the same data of the number of investors, normalized by the number of people over 21 (drinking age) in each State to create a 'Punks per Million' map. I guessed on roughly what the data might be from their original map:

Compare thee two maps. You see - because the population of each state differs massively and the size of States differs massively, using totals inevitably skews the map numerically and visually and you get a warped sense of reality. Texas will always come out as a lot. Montana always not. But actually, as a proportion of the population, there are more Punk investors in Montana than Texas. Ohio still gets shown as having the most investors because they have a lot (as totals) and as a proportion of their population and that's where the new brewery is. But California isn't a stand-out because it has roughly the same Punks per million as Oregon and even Wyoming.

Still want to map totals? Well use a proportional symbol map:

There you go - now you can clearly see the huge difference in the pattern of investment between states. And if you want to Punk out the map...well go right ahead:

And yes, I used the same bottletop technique on this quick map as I did on the much larger Breweries of the World map which, if you want a copy, can be downloaded here.

So, Brewdog. I like your beer a lot. You take great care to make it right. I like maps a lot and I take great care to make them right. You stick to brewing and I'll keep drinking your beer. I'll stick to making maps. If you want some help with the maps, just drop me a line.

Grid-O-gram

I had the pleasure of working with Mamata Akella when I first started at Esri. Mamata went on to work for the National Park Service and is now at CartoDB where she seems able to flex her design wings with thematics. This is fertile space in mapping in general and it seems never a week goes by without someone re-inventing a thematic mapping technique, occasionally with a new twist. Mamata's latest map caught my attention.

In response to her call for comments I hope she won't mind me using this blog as a space in which to offer my opinion and insight so here's a critique of the map above.

It's visually arresting. It's one of those maps you immediately stop and look at so it does a great job of getting people to pause and spend some time with it. That's probably the point so it's already done it's job. Because it lacks a title or any popups or marginalia one quickly gets lost though. As Mamata explains, it's a test and, no doubt, not designed to be used as a fully fleshed out project but it would be useful to include the basics.

It's the 2012 US election data. A well worn dataset that's just about exhausted most techniques. I spent some time with it myself a couple of years ago creating a gallery of various thematic map types. But with the 2016 election on the horizon many will be experimenting with new or modified techniques to prepare for that mapping extravaganza (me too...but you'll have to wait for that).

So what's going on in this map? Mamata calls it a 'modified cartogram'. Symbol size is total vote. Colour is the winner (red=republican, blue=democrat). Units are counties.

First off - I like the appearance and I like that it's in an equal area projection (Albers). It's eye-catching and somewhat different. I then quickly get uncomfortable with the function and how the data processing encodes meaning. Clearly the real geographic boundaries have been processed. My sense is a regular grid of rectangles has been used in which to bin the counties that fall within. That explains the regular grid and also the irregular number of symbols per location.

Geographical boundaries have been replaced by an abstract geography. It's referred to as a cartogram, likely because of this abstraction but a cartogram it is not. Cartograms distort space but they don't aggregate in an irregular fashion. Think Gastner-Newman, Dorling, Demers or a basic non-contiguous cartogram which all treat geography in different ways but which do not apply a binning technique as an interim step. Further, cartograms don't have overlaps. Mamata's symbols do overlap. It's therefore difficult to know how many counties are represented by each location and it's difficult to ascertain the distortion of the underlying geography which will inevitably be greater in areas with larger numbers of smaller counties. It's adding in a visual complexity that isn't necessary even though it gives a neat (as in regular - pleasing to the eye) looking final appearance.

I don't particularly like the way transparent overlaps on the symbols yield overlaps with darker shades - to me that visually implies 'more' yet is purely an artifact of symbol size bleeding into an adjacent symbol and not necessarily a function of geography at that place or overlapping geographies. Of course, when we're talking about mixing blues and reds it gets even more difficult to visually disentangle. That''s not a problem simply on this map though. I wrote about it before in regard to proportional symbol maps.

So it's a gridded proportional symbol map? Looks that way. Are symbols stacked? Possibly - in which case a lot of colour is missing due to occluded symbols which changes the ratio of blue:red colour across the map as a whole. If the data is really represented as rings then OK, we're seeing everything but it's also hard to determine why some symbols have more transparency applied than others (strength of vote?).

There's no labels which makes it difficult to describe the pattern verbally and causes even more problems if you don't actually know this is the USA. When you zoom in, the map refreshes with some very big changes in symbol size and larger white spaces so the structure we see for the whole is lost. This makes it hard to retain a mental image of pattern at one scale and compare it to that at another and we very quickly lose where we are on the map.

If it's a proportional symbol map then why not just use geography, even if you discount the boundaries and make a proportional symbol map?

I'll tell you why - they just ain't sexy enough in today's modern mapping landscape. So that's why Mamata experiments. It's why I experiment too. Sometimes we hit, sometimes we miss in our search for something just a little bit unique to develop cartography and showcase the tools and technology of our trade.

For my money this is a miss. I like the look but I think it complicates the subject matter and confuses the cognitive process of understanding the patterns in the data. For me, form should never outperform function. Cartography really is, at its very essence, that art and science of marrying form and function in harmony. You've got to get both right to make a good map.

Back to it being a cartogram - no. It isn't. But maybe Mamata's created a grid-O-gram?

Update: Inevitably, whenever I do one of these critiques I get called out for it being on a map made by someone who works somewhere that I don't. First, Mamata asked for comments. Second, I couldn't care less where she works and this IS NOT about the tech she used. None of my critiques are about the tech. It's about the cartography. Sure, tech affords opportunities or constraints but I don't care one bit about who uses what. This is not about scoring points. I don't publicly critique maps made by colleagues at the place I work because there are better mechanisms for me to use to try and effect change from within. And surely, if anyone thinks it's a good idea openly calling out your employer and those who you work with, you must work in an incredibly forgiving place. I do call co-workers maps out all the time using appropriate avenues. They critique mine too...often in very stark terms. Critique is good. Using different mechanisms to get the job done is important for cartography whomever you work for. So - don't get irate just because Mamata and I work at different companies. It's irrelevant. And yes, many maps I see made by friends, colleagues or whomever are truly awful and I tell them that. Silence in a public space can often be deafening.

The Economist ponders map types

The Economist recently asked for reader opinions on the types of map used to portray the data it uses. It focused on the choice between cartograms, choropleths and proportional symbol maps.  I added comments which are reprinted below but you should read the original article here first.


Poor mapping gives the wrong message. Most are unaware of map theory so mistakes go unnoticed; misinformation is propagated. That said, asking readers their opinion is like a doctor asking a patient what medicine they prefer. The doctor has the conferred expertise to make a sound judgment.  The same is true here so my comments are based on my professional experience to add to the mix.

Population equalized area cartograms are impactful but difficult to decipher because of massive distortions.  We’re atuned to see our world in a particular way (normally through the hideously distorted Mercator lens) so when familiar shapes are further modified we struggle.  Numerous alternatives use circles, squares, hexagons and non-contiguous areas which gives choice.  I like cartograms but am used to them, know how to construct them and don’t have difficulty in deciphering the content.  They work best for global datasets where continents can be seen.  For headline grabbing infographics then a cartogram is hard to beat but one way of giving readers visual comfort is to add a second, smaller map using a more conventional method for comparison.

Cartograms rescale geography to account for differences in size of areas used to report data values.  If a conventional map type is used that maintains geography, this difference often isn’t accounted for and the map is worthless. The classic example is the choropleth that maps totals. Consider the number of medals that Team GB won at London 2012.  Greater London has a population of 8278251 with 10 medal winners (0.12 medals per 100,000 people). Cardiff has 346100 people and 4 medal winners (1.16 medals per 100,000 people).  A map of totals shows Greater London as visually dominant and Cardiff much less so when the reverse is true. Normalized results allow proper per capita comparisons across the map that account for underlying populations.  The classification scheme used is also vital as it can dramatically alter appearance. There are many choices (natural breaks, equal interval, quantile, standard deviation etc.) and each dataset requires exploration to avoid imbuing false patterns.  Choropleths are bland but they do their job. Make good use of other design principles to combine functionality with a useful aesthetic.  Your colours are poor. Green for non-export markets confuses and neutral grey would be a better choice.  You use light peach, through orange/pink to a heavily saturated red last seen during the cold war on propagandist maps! It’s visual noise. Adding Catalonia in burgundy makes it seem part of the choropleth spectrum yet isn’t. Good colours go a long way to making the map work. Legends are important to see the classification scheme but the map should be able to tell the headline story without one. All choropleths suffer from dominant large areas so where possible use an equal area projection; and inset maps for those parts of the map that contain small geographic areas.

Your proportional symbols are too similar, leading to the impression that exports are similar.  Greater variation in symbol size would help.  Transparency deals with overlaps but won’t always work where large data values occur in smallest areas. Colours could be improved and a neutral background would help with contrast. Humans aren’t good at estimating differences between areas.  How many people can accurately tell if one circle is double the size of another? There are ways to adjust for our underestimation but which introduces further complexity.

You might consider dot density, dasymetric  or, for this subject a flow map would suit.  Flow lines from Catalonia to neighbouring countries could be scaled by width to indicate proportions.  My rudimentary reworking of Minard’s flow map of British Coal Exports shows how flow can be represented. If you’re presenting maps online then consider hover and click events to reveal data values or additional information. This pairs back the map to essential graphics while allowing people to delve into the content interactively.

So the answer isn’t straightforward.  Consider each dataset independently of preconceived ideas about map type.  Think about the story you want to tell to inform your choice.  Once chosen, the next trick is to design it to work effectively and marry form and function meaningfully.  This isn’t easy and is the main reason why so many poor maps are made. Sometimes a table or a graph is much more useful.  Sometimes you might combine graphs with the map or combine map types. The map should be informed by a decisions that bring together useful graphic components in a well-thought out composition. There’s no substitute for looking at how others tackle thematic cartography. Learn what works, understand what doesn’t and your maps will evolve into purposeful products regardless of map type.