New Aperiodic Monotile

[Camer the Dragon]

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

[Master Raiden]

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

[Camer the Dragon]

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