![]() It seemed obvious for this demonstration to honour Einstein’s theory of relativity (also known as his theory of gravity), so here is a simple map layer showing the Isostatic gravity anomaly for the contiguous U.S. You can also select tiles to delete to remove tiles you don’t need, or use tools such as Clip, or use a Spatial Join to select tiles that correspond to the geographical area you’re focussing on, and save the selection as a new dataset.Īnd then you are in a position to use the new tiles as a way to bin other data. Once added to your map you’re able to move, and scale the features using the edit tools to fit across the area which you want to eventually tile. You’ll likely want to make a copy of the data, and then use that for your own mapping needs. You can download the Einstein Tiles Master shapefile here. Once added, you can, of course, use Define Projection to save a version in the projection of your map. That means that whenever you add the shapefile to your map it will retain its geometry rather than being reprojected to whatever your map is using. Using the shapefile format means I can use a simple hack, and omit the. I wanted to be able to share the master set of tiles so others can use them in their own work, and for it to work across different projections I needed a way of sharing the file that contains no projection information. So I downloaded a large surface of nearly 140,000 individual tiles in their tessellated state, added them to ArcGIS Pro as a graphic, converted it to features and saved it as a shapefile. However, Smith and colleagues’ work is available under a Creative Commons license and they have helpfully developed an app that generates surfaces of Einstein tiles, including an svg output option. Except there’s no Einstein tile generator in ArcGIS Pro. ![]() “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… The grid is punctuated with small diagonals that twist this way then that – adjacent molecules are mirror images of themselves so the interact in controlled ways – After leaving it pegged overnight, the paper has sufficient memory to stay put, but a fine misting of water while pegged would, when dry, re-program the paper to stay put also.įun fold, pure procrastigami (which is why I originally bought the book), must do some more.Anyway, I digress, but the point of this is that we each have history with this storied thematic mapping technique. Then scale up – I took an A3 sheet, cut the biggest square I could, then divided into 16ths, and these saw how many molecules I could pack in there: Then we move to a simple tile of 2×2 molecules: 2×2 Cubes molecules I present the “ molecule” – that is the tileable unit: Cubes “molecule” Starting at the beginning, with the “Cubes Family”, this is “Cubes”, a deceptively simple tessellation of twisted cubes. Looking through my Origami Library, I realised I had bought “Origami Tessellations for Everyone” by Ilan Garibi back as the pandemic hit early last year, and realised I had yet to fold anything from it at all: A field of cubesĮarly last year was crazy times – bushfires, floods and then lockdown from Covid-19, this book got buried in my reading pile so it is time to begin the journey of exploring tessellations more formally.
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