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+--- Thread: New Aperiodic Monotile (/showthread.php?tid=4332)
New Aperiodic Monotile - Camer the Dragon - 2nd June 2023
Lads wake up new aperiodic monotile dropped
The shapes tile a 2d infinite surface with no gaps with a never-repeating pattern when flips aren't permitted, with the two shapes on the right having a never-repeating pattern regardless of if flips are allowed or not
They were looking for a shape like this for 60 years after Penrose Tiling, they had found one a few months ago but this one required flips to tile with a never-repeating pattern, this one does it without flips
RE: New Aperiodic Monotile - Master Raiden - 7th June 2023
It's pretty cool how this stuff works.
I get how the tiling can be aperiodic when you flip the first shape, but how do the other two shapes work without flipping? Where's the irrationality in that case?
Also, I fully expect you to have these as your bathroom tiles some time in the near future
RE: New Aperiodic Monotile - Camer the Dragon - 7th June 2023
(7th June 2023, 7:41 AM)Master Raiden Wrote: It's pretty cool how this stuff works.
I get how the tiling can be aperiodic when you flip the first shape, but how do the other two shapes work without flipping? Where's the irrationality in that case?
Also, I fully expect you to have these as your bathroom tiles some time in the near future
All 3 work aperiodically without flips
It's just that if you flip the first one you can make a periodic tiling but the other two you can't
Lmao would be a good bathroom tile