I might just dabble some more myself: this tile’s finder is much more like me than the serious mathematicians he enlisted to prove his tile’s aperiodicity. What we still don’t yet have, though it has not yet been proven impossible, is an aperiodic mono tile which tiles WITHOUT flipping or reflection. The tile itself is also, I must add, only one of a large set of such tiles, oh yes!
It might be a craze which comes and goes, getting its 15 minutes of fame, or it might linger for years, decades, being infinite in possibilities. Textiles: clothing, curtains and drapes, tablecloths, carpets. Yes, there’s an awkwardness at the edges which you don’t have with squares, because here you have to cut off pieces to make a straight edge, or live with an irregular one. The aforementioned bathroom tiles, or ones for the kitchen or elsewhere. It’s early days yet, but I expect this shape to revolutionize the world of tessellation, or tiling, in general.
Also, because this is a purely mathematical object, there’s no way to copyright it, just as there isn’t with, say, a square. Simply because it allows infinite tiling variations to each one of us. This is so much more interesting as a bathroom tile than, say, squares, triangles or hexagons (the only regular shapes which can tile the plane regularly). A rather technical preprint article on the find, yet to be peer reviewed, but getting plenty of attention, is here. Its simplest version is made of 8 identical sixth parts of a hexagon, and has 13 sides, as in the illustration. If I had found a shape which seemed to tile aperiodically, how would I even prove it rigorously? I don’t have the mathematical education to do that.
I dabbled some years ago, trying a shape which was half a square (diagonally cut) joined to an equilateral triangle. Its finder? One David Smith, 64, of East Yorkshire, UK, a “shape hobbyist,” as he calls himself. But never did he, or anyone until now, find that single tile which would do the job. Yes, the big mathematics news of the week is the discovery of the hitherto elusive “einstein”, or monotile (so THAT’S what the great Albert’s surname means!), which can tile the plane (2 dimensions) aperiodically, in other words, in ways which never repeat themselves.Īnother great, Roger Penrose, spent decades on the search, narrowing it down to pairs of tiles (for example, “kites” and “darts”) which can tile aperiodically.
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