I do quite a bit of spatial analysis and mapping in my academic research, and some of it ends up on this blog. Over the past few years I've done quite a few 3D* maps - most recently one of population density in China. A comment by map-guru James Cheshire made me think about the 3D issue, hence this post, which attempts to say a little more about why I like using the third dimension, as it were. Also, there's not much about this stuff online at present. The two images below show population density in Europe at NUTS3 level, with a colour scale running from red (high density) to blue (low density). Click the images to enlarge.
*N.B. Data for some parts of Italy, Germany, and the UK are missing,
but that doesn't matter for now - this is just an example.
The reason I like the addition of the third dimension with this kind of dataset is that you can tell more about the differences between areas within the same statistical category. Essentially, it adds an additional dimension of information that you can not observe from the conventional 2D map above. This is particularly true of the most high density areas in the first map. There is of course an issue here about the relative size of areas and how this might change the population density of different places but that is a different matter since I'm not in control of NUTS3 definitions! For more on this kind of thing I'd recommend looking at Stan Openshaw's work and for more on the utility (or futility?) of choropleths generally Tobler (1973) is an excellent starting point. Gale and Halperin (1982) is also worth a look.
If we assume that the main purpose of a choropleth map is to present and discover spatial patterns then there is sometimes a strong case for using the vertical dimension and extruding polygons using a z-variable (I do this in ArcScene, in case anybody is interested). However, there are some complications and I don't think it is always appropriate to go 3D. For example, depending upon the spatial structure of your data extruded polygons in one area can obscure those in another. There is also the issue of the different size of areas and the way these might have an impact upon the level of extrusion - i.e. if we used 1km cells for the European population density map it would look rather different in 3D - though this is possibly another artifact of the modifiable areal unit problem, as described by Openshaw. I've patched together three different examples from my blog in the image below, just for comparison. Another option would be to follow the example of Ben Hennig and produce population-weighted cartograms.
When I produce these 3D maps (or visualisations) I'm not trying to create a geographically precise rendering of space but rather I'm attempting to draw attention to variations in a dataset in a way which 2D maps can only do to a limited degree. They are abstractions and simplifications but in terms of understanding the world I find it can be an improvement. There is a little bit about it in this Environment and Planning B paper I wrote but I plan to write more about this in the near future (the'near future' in geological terms of course).
*Also known as 2.5D in the GIS world, but I'll put that to one side for now...