Thursday, 21 May 2015

Hexagonal Tile Map of New Zealand Electorates

Tile grid maps are a great way to represent thematic data for regions of equal importance. Tile grid maps use a simple regular tessellation (triangles, rectangles, or hexagons) to represent geographic regions. The tiles are positioned to create recognisable shapes that approximately conserve the correct relative positions of the features.

During the 2015 election in Britain hexagonal tile choropleths were the map de jour. As typified by this example from Bloomberg. Danny DeBelius gives some examples from the USA  here. Chris McDowall experiments with New Zealand electorates here

Given that I am a hexagon fan and love a good spatial meme,  here is my hexagonal tile choropleth map of New Zealand electorates.

Why regular tiles?

Choropleth maps generally consist of accurately represented geographic features that are coloured or textured to represent a theme that varies spatially. Quantitative totals can be represented in choropleth maps by normalising the value by area. However, strict adherence to geographic accuracy can make maps misleading when the regions of interest are very different sizes but of similar importance. In addition, it is very difficult to normalise nominal data.

Tile grids, however, offer simple geometries of equal area whilst still imparting a sense of the spatial variation of the theme being mapped.

Electorate maps are a good example. The electorates of New Zealand contain similar voting populations and are each represented by a single 'electorate' seat in the New Zealand parliament. However, the large rural seats dominate a geographically accurate choropleth map.

Cartograms mitigate this bias by distorted and resizing shapes to reflect some statistical measure whilst retaining topological accuracy. Cartograms are typically combined with colour to represent multiple variables. They can also be used to equalise the areas of the regions in a choropleth, effectively normalising nominal data. However, this can create maps that, although interesting, are quite confusing and very complicated. This is where the uniformity of grid tile maps come in.

How the map was made

The arrangement of electorates into tiles was a manual and subjective process. I am sure analytical methods are possible but I suspect it would be difficult to retain the legibility of the map without  human input in the design.

The dominance of Auckland in the population distribution of New Zealand created some problems. Two issues I found were that Hamilton and Taupo were pushed further south than I would like and Bay of Plenty is inland. In the South Island, Christchurch extends all the way to the West Coast. Maybe you could do better? I would love to see alternative layouts.

The cells of the hexagonal grid were sized such that the total area covered by the 64 electorate hexagons was similar to New Zealand's actual area. The size of the tiles is not important but consistency did allow easy comparison between the tile grid and true geography.

My first version of the tile map was generated from the centroids of the equalised cartogram shown above. Where more than one centroids were in a single hexagonal tile, I moved one to the nearest available tile. Then I joined the centroids to the hexagonal tiles using a spatial join, keeping only the joined features. I continued to experiment with different layouts until I was happy with the result. Finally I made a separate map for the Maori seats. Square and triangular versions are in development.

But how would one represent the all important party vote? That question will be addressed in a future post.


Shapefiles of my hexagonal tile map of NZ electorates can be downloaded here. I have also included a blank tessellation of hexagons, approximately centred in Wellington if you would like to make your own arrangement. All data sets are in NZTM2000.

Creative Commons License
This work by @MAPdruid is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

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