SamTherapy opened this issue on Apr 04, 2023 · 6 posts
SamTherapy posted Tue, 04 April 2023 at 2:20 AM
https://www.theguardian.com/science/2023/apr/03/new-einstein-shape-aperiodic-monotile
Following on from the recent thread about texture bombing, here's a new discovery that features a shape which tiles but never in any repeating pattern.
Coppula eam se non posit acceptera jocularum.
NikKelly posted Tue, 04 April 2023 at 6:04 AM
https://phys.org/news/2023-03-geometric-tiled.html
This has their base hexagonal grid, with the additional guide-lines (@ 0º,30º,60º,90º) to give 6 LH + 6 RH right-angle triangles per hex and simplify construction.
Though not much of a 'Recreational Mathematician', I was stunned by its minimal elegance...
Y-Phil posted Tue, 04 April 2023 at 9:37 AM
Why is your link opening two windows, one with an onion-related site?https://www.theguardian.com/science/2023/apr/03/new-einstein-shape-aperiodic-monotile
Following on from the recent thread about texture bombing, here's a new discovery that features a shape which tiles but never in any repeating pattern.
𝒫𝒽𝓎𝓁
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Sunfire posted Tue, 04 April 2023 at 11:44 AM
I can actually see a repeating pattern in the first image in that article. It does not repeat horizontally or vertically but instead diagonally.
NikKelly posted Tue, 04 April 2023 at 1:00 PM
But it does not have to, unlike hex+pent, or Penrose's kites etc...
The 'Grauniad' has a reputation for oopsies...
;-)
SamTherapy posted Tue, 04 April 2023 at 2:24 PM
I spotted that but the surrounding, lighter coloured tiles are different, if they'd picked a wider range, you'd be able to tell easier.I can actually see a repeating pattern in the first image in that article. It does not repeat horizontally or vertically but instead diagonally.
Coppula eam se non posit acceptera jocularum.