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Comment by beeforpork | Hacker News Reader

Definitely nice for bathroom tiles! Staring at the wall while doing your business and failing to find a repeating pattern -- wonderful!

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The unique feature of the new tile isn't that it will tile aperiodically. It's that it will only tile aperiodically. If you just want an aperiodic tiling, you can achieve it with 2x1 rectangles. There's a big list of such patterns here:

https://tilings.math.uni-bielefeld.de/

examples:

https://tilings.math.uni-bielefeld.de/substitution/domino-va...

https://tilings.math.uni-bielefeld.de/substitution/tetris/

Thanks for posting this. It should be higher.

I can't believe NewScientist left that out of their headline.

>Bielefeld university

I'm not clicking that, I don't trust I'll be able to come back.

For the downvoters, I'm pretty sure this is supposed to be a veiled reference to the https://en.wikipedia.org/wiki/Bielefeld_conspiracy

I've heard of this injoke a lot, but it doesn't seem to have any real core of fun to it, it's just interesting because it's an injoke?

It is the earliest German bit of net culture to take an offramp from the information superhighway into regular culture - at least the earliest I know of. Maybe that gives it its staying power, humorous value aside.

Forcing aperiodicity makes the installation idiot-proof though.

If I recall (previously-submitted article - https://cp4space.hatsya.com/2023/03/21/aperiodic-monotile/ ), the shape has to be flipped upside down some fraction of the time. So you'd either need two tile shapes for a real bathroom, or your tiles would be a compromise between "both faces are easily cleaned" and "both faces stick firmly to the mortar".

> The ratio of unreflected to reflected tiles is φ^4 : 1

I just love this

Having a white tile and a blue tile would be fine, though. I'm really tempted by this, but I think I should start by tiling the garage floor or something rather than my whole living area.

Cool, but for some reason i find it pretty hard to look at?

stop looking at it :)

Sounds like a pretty tough job due to the lack of pattern. Either you have to follow a template or you run the risk of randomly tiling something that can't actually be extended further.

The tiles seem like they can only join at one spot to one spot so I don’t think it would even be possible to lay them incorrectly unless you straight were jamming incorrect sides together.

> First we produce a list of possible neighbours of the hat polykite in a tiling. There are 58 possible neighbours when we only require such a neighbour not to intersect the original polykite; these are shown in Figure B.1, with that original polykite shaded. The first 41 of these neighbours remain in consideration for the enumeration of 1-patches. The final 17 are immediately eliminated (in the order shown) because they cannot be extended to a tiling: either there is no possible neighbour that can contain the shaded kite (without resulting in an intersection, or a pair of tiles that were previously eliminated as possible neighbours), or we eliminated Y as a neighbour of X and so can also eliminate X as a neighbour of Y.

From the preprint. It is definitely possible to lay the tiles so that they do not tile anymore.

Wow that’s really something, thanks for the additional info

Who needs a never-ending smartphone feed if you can have a never-ending tile pattern to gaze upon!

It's been a looooong time ....

But I could see this making a "psychedelic" experience a bit more interesting.

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