Feel good moment. Spread the joy.

[saveasteading]

Not so long since this was a storage area with a passage still full of mud and cow manure.

Curtains up is a big moment.

 

The rest of the place is at first fix with pb coming behind it.

[Kelvin]

Well done to everyone involved. It looks excellent. Very homely. As you know by shear coincidence I’ve walked around that steading when it was derelict which was only a few years ago so can see how much work has gone into it. 

[Alan Ambrose]

Congrats

[MJNewton]

Looks lovely - well done.

 

Perfect time of year to be completing a room like that!

[ToughButterCup]

Looks wonderful.... probably because somebody has a good eye for color...?

[saveasteading]

50 minutes ago, ToughButterCup said:

somebody has a good eye for color

I was involved, I'll have you know!

Hundreds of swatches, reduced to the final 20. 

Mostly I just agreed with the final decision.

I'll admit that the purple features weren't my choice but it's inspired.

 

That view, if it wasn't for a mountain in the way, would be all the way to @ProDave and @Jenki. The Northern Lights shine above them.

[saveasteading]

I would also emphasise that I chose the floor tiles. It bothers me if I see repeats in a quasi natural product, especially if they line up.

 

Does that bother anyone else or is it my curse?

My Son-in-law realised he had it too when I mentioned it and daughter 'gets it'. They laid them so no similar tiles are near each other, and reversing helps too.

 

These tiles are in 18 patterns, so flipping makes it 36.

 

[joe90]

1 minute ago, saveasteading said:

Does that bother anyone else or is it my curse?

And my curse, being called OCD is normal for me (but I don’t care, it’s either right or not 😎)

[MJNewton]

53 minutes ago, saveasteading said:

Does that bother anyone else or is it my curse?

 

That sort of thing doesn't bother me.

 

It HAUNTS me!! 😂

[Kelvin]

I have that problem too but if there’s a creator they are benevolent as my eyesight is shit so can’t see it. 

[Jenki]

5 hours ago, saveasteading said:

That view, if it wasn't for a mountain in the way, would be all the way to @ProDave and @Jenki. The Northern Lights shine above them.

On clear days I can see those mountains all the way from Nairn to Fraserburgh, and as you say 180 Deg the Northern lights. I love living here.

 

Looks fantastic by the way 👏

[ProDave]

5 hours ago, saveasteading said:

I was involved, I'll have you know!

Hundreds of swatches, reduced to the final 20. 

Mostly I just agreed with the final decision.

I'll admit that the purple features weren't my choice but it's inspired.

 

That view, if it wasn't for a mountain in the way, would be all the way to @ProDave and @Jenki. The Northern Lights shine above them.

We are in an east / west glen.  We can't actually see that far, the mountains to the west are the most distant we can see which is no more than 10 miles, that is looking down the glen to the west.  North and south we can't see far at all, can't even see the Black Isle.  And looking north we are looking up hill out of the glen.  So we don't see the northern lights very often, it has to be a spectacular show to get high enough to be seen over the hills to the north.  I think it's only 3 times I have seen them.

[SteamyTea]

12 hours ago, saveasteading said:

It bothers me if I see repeats in a quasi natural product, especially if they line up.

Mathematicians discover shape that can tile a wall and never repeat

Aperiodic tiling, in which shapes can fit together to create infinite patterns that never repeat, has fascinated mathematicians for decades, but until now no one knew if it could be done with just one shape

By Matthew Sparkes

21 March 2023

 

 

 

 

This single shape produces a pattern that never repeats

David Smith, Joseph Myers, Chaim Goodman-Strauss and Craig S. Kaplan

 

Mathematicians have discovered a single shape that can be used to cover a surface completely without ever creating a repeating pattern. The long-sought shape is surprisingly simple but has taken decades to uncover – and could find uses in everything from material science to decorating.

Simple shapes such as squares and equilateral triangles can tile, or snugly cover a surface without gaps, in a repeating pattern that will be familiar to anyone who has stared at a bathroom wall. Mathematicians are interested in a more complex version of tiling, known as aperiodic tiling, which involves using shapes that don’t ever form a repeating pattern.

The most famous aperiodic tiles were created by mathematician Roger Penrose, who in the 1970s discovered that two shapes could be combined to create an infinite, never-repeating tiling. Now, Chaim Goodman-Strauss at the University of Arkansas and his colleagues have found a single tile shape – which they have called “the hat” – that does the same job.

Goodman-Strauss says that both finding and proving the tile to be aperiodic involved the use of powerful computers and human ingenuity. The team used computers to eliminate large numbers of options, then applied their experience to finding a shape and developing a proof.

“You’re literally looking for like a one in a million thing. You filter out the 999,999 of the boring ones, then you’ve got something that’s weird, and then that’s worth further exploration,” he says Goodman-Strauss. “And then by hand you start examining them and try to understand them, and start to pull out the structure. That’s where a computer would be worthless as a human had to be involved in constructing a proof that a human could understand.”

Until now, it wasn’t even clear whether such a single shape, known as an einstein (from the German “ein stein” or “one stone”), could even exist. Sarah Hart at Birkbeck, University of London, who wasn’t involved with the research, says that until now she thought it would be impossible. “There are infinitely many possible candidate tiles, and even the existence of a solution feels quite counterintuitive,” she says.

Despite evading mathematicians for decades, the newly discovered einstein isn’t a convoluted or complex shape. It features just 13 sides. The shape also retains its aperiodic qualities when varying the lengths of the sides, meaning that the solution is actually a continuum of similar shapes.

Much of the difficulty in finding an einstein is proving that it really can tile aperiodically, without throwing up unusual counterexamples. The team discovered two proofs for the tile, with one being based on computer code that has been publicly released.

Hart says that knowledge of aperiodic tile shapes could help us design materials that are stronger or have other useful properties. Repeating patterns like tiles are also seen in crystal structures, where they can lead to fault lines along which material tends to break.

 

 

Another example of “the hat”

David Smith, Joseph Samuel Myers, Craig S. Kaplan, and Chaim Goodman-Strauss

 

“Certain strange and wonderful types of crystalline structures called quasicrystals exhibit aperiodicity,” she says. “It may be that this new tiling may have applications to our understanding of the possible structures in quasicrystals.”

Colin Adams at Williams College in Massachusetts says he was shocked at the simplicity of the solution, and that this was a problem that “does not easily yield to brute force” computation. He is also keen to put it to practical use.

“You’re going to see people putting these in a bathroom because it’s just cool. I would put it in my bathroom if I were tiling it right now,” he says.