Penrose Binning

Some months ago, I came up with a little joking idea: what if, instead of hexagonal or square bins, cartographers used Penrose tiles?

A Penrose tiling is a form of tessellation. It’s fun and unique in that it fills the entire plane, but has no repeats. Wikipedia has more detail about how these things are cool. Mostly, I thought of them because they look interesting and are sort of regular, without being too regular.

So for fun, I made a couple of maps using Penrose bins.

Density [Converted]-01

Population Density

US/Canada Atlas of Design sales

US/Canada Atlas of Design sales

Land Cover

Land Cover

I can think of no proper cartographic use for Penrose binning, but it’s fun to look at, and so that’s good enough for me.

To create the tiles, I found an SVG of a Penrose tiling here: Then I pulled it into QGIS and resized it to fit appropriately on the US and part of Canada when in an Albers Equal Area conic (CM: -96º, SP1: 20º, SP 2: 60º). Then I did zonal statistics in ArcMap (for population density and land cover) or a spatial join in QGIS (for the point data of Atlas of Design sales).

If you want to give it a try yourself, I’ve put the shapefile here:

While I can’t think of a use for this presently, who knows what the future will hold? Silly little experiments like this sometimes become valuable later on.