“Eureka! Eureka!” shouted Messrs Huffman, Nelson and Field because when there are new tiles there are new maps to be made. Non-professional mathematician David Smith, along with academic researchers in the UK and US, believe they have discovered this elusive aperiodic monotile which they have dubbed ‘the hat’ and reported in a paper that describes their proofs. The question of whether a single aperiodic monotile exists that can tesselate space has dumfounded mathematicians for decades but, recently, it appears to have been solved. Penrose tiling is a form of aperiodic tiling in this respect but it actually uses two different monotiles since you cannot tesselate space using only one of them. The counter is an aperiodic monotile where there is no repetition across a surface. You can also find symmetry in these tilings. Most of our cartographic tessellations use what are called periodic monotiles – that is, when placed across a surface they generate a repeatable pattern.
But a new shape has recently been developed, and this is what had piqued our interest, and conversation. Ordinarily we use nice regular shapes that create clear, organized and ordered surfaces for our maps. The search for tessellating shapes is essentially a branch of mathematics that us cartographers find a convenient use for. But surely every shape has been found that can be used for tessellating space in a way that completely covers the surface of the map, leaving no gaps? Apparently, no…
Anyway, I digress, but the point of this is that we each have history with this storied thematic mapping technique.
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