#einstein tile

[thingsihavecrochetandknit]

Finished my einstein tile quilt!!! I wanted to have the braid go all the way around but I was 2 feet short 🥲

Luckily I'm still really happy with how it turned out

[makereadgrow]

English paper pieced Aperiodic Monotile wall hanging is complete!

This block is based on the Smith, Myers, Kaplan, and Goodman-Strauss's aperiodic monotile known as the "hat" (explainer here https://amp.cnn.com/cnn/2023/04/06/world/the-hat-einstein-shape-tile-discovery-scn/index.html and the original publication https://arxiv.org/abs/2303.10798 )

In order to make this I broke the shape down to its most basic form - the 30-60-90 triangle. I drafted my own triangles on cardstock and glue basted the fabric to the forms. 

 From there I built up the shapes in shades of grey with a pop of orange. I wanted colors that both hid the complexity of the blocks and revealed it upon closer inspection. Ultimately I want the viewer to find new details as they look closer and longer at the peice. 

Midway through making blocks I came to the realization (probably missed when I read the articles) that some of the shapes are mirrored in the tiling. I had already made my orange block but I elected to partially disassemble it and make that my central mirrored shape. 

Initially I had no plan for how many blocks I would make. I essentially madr blocks until I was bored of making them. Because of the somewhat fluid nature of all the seams assembly of the blocks together was far simpler than I expected. I could fold in essentially any direction without creasing the triangles. I used a diagram from the Smith et al paper as my guide to assembly. 

Once I had it all together it was time to quilt. Honestly the quilting pattern I chose was something of an impulse but initial tests were nothing short of delightful. While my local store carries only a few colors thicker hand thread I was able to find a soft grey that stood out on every fabric in this quilt, but didn't have such a harsh contrast that you can't look past the stitching. My design are simply 3" squares that overlap in the corners and were measured on the fly. Their irregularities are accidental but still a feature. 

Finally I came to binding. I realized I had 42 corners to get around. I used a 1" bias strip to bias face the peice, folding out the seam allowances on the outer edge to secure the binding by hand. The only machine work on this quilt is in the seams connecting the binding strips. In hindsight I should have cut my binding strips at 1.25" but I managed to get it all turned and stitched down. This was most certainly the most challenging part of the entire peice. 

And now it hangs on my bare office wall, enticing me to stare at more than just a blank space. 

[guy60660]

Einstein Tile | Science News

[idontknowknit]

The hat: Mathematicians invent 'einstein' tile that never repeats | CNN

[forgottenbones]

A Hobbyist Just Solved a 50-Year-Old Math Problem (Einstein Tile)

[biglisbonnews]

"Einstein Tile" mystery solved: amateur mathematician discovers unique 13-sided "hat" Mathematicians have long wondered if there was an "einstein tile" – a tile that could be used only to make a non-repeating pattern on an infinite surface. An amateur mathematician named David Smith recently developed a 13-sided tile, nicknamed "the hat," that fits the bill. — Read the rest https://boingboing.net/2023/03/31/einstein-tile-mystery-solved-amateur-mathematician-discovers-unique-13-sided-hat.html

[feamir]

I made art of the newly discovered aperiodic monotiling!!

If you don’t follow math news, this turtle-like shape is the solution to a long-standing open problem in mathematics that goes as follows: Let’s say that you want to completely cover a plane with tiles (i.e. tessellate a plane) in such a way that the tiles never create a repeating pattern (i.e. the tiling is aperiodic). What is the fewest number of tile shapes you need to do that?

For a long time, mathematicians had only been able to find a two-shape tiling that never repeated a pattern. This was called a Penrose Tiling. But just last month (March 2023) a paper came out proving that the above shape can aperiodically tile the plane by itself!*

This is really cool and has lots of mathematicians and scientists super excited, not just because it’s an elegant solution to a decades-old problem, but also because we might be able to create new materials with unusual properties using this tiling as a base for molecular crystal structures (just like scientists were able to find for the Penrose tiling)!

If you want to learn more about the discovery, the NYTimes has a really good article here, and you can read the original paper (or just look at more pretty pictures of the tiling) here!

* As long as you’re allowed to occasionally flip the tile over. I colored the flipped tiles purple in my art to emphasize them.

[mossandfog]

Newly Discovered "Einstein" Shape Has Spawned Myriad of New Pattern Designs

It’s not everyday that a brand new shape is discovered. Nor one that can create an infinite plane, without every repeating itself. The so-called “Einstein” shape was discovered by scientists this year, and is somewhat of a craze amongst those that love patterns and tiles. Unique as it is, a contest by the National Museum of Mathematics in New York and the United Kingdom Mathematics Trust in…

[existentialnoodling]

So you know all those pretty penrose tilings?

Like these:

Well the reson these exist is because a dude called penrose wanted to find a fewest number of shapes you could use to tile a surface and Guarantee™ the pattern wouldn't repeat.

Now it's all math so like infinite surfaces and repeat meant the whole infinite thing could repeat. Like you couldnt slide it around and have the pattern be the same before and after.

But that's in the weeds, the cool thing is, he was the first to find a way that only required 2 of em.

Well somebody found a way to do it with only 1 shape recently, calling it a Spectre tile

Any one if these boys:

Well, there like infinite way you can tweak the basic one that work.

And it neat! And I have discovered that they make a puzzle just getting all the pieces together

because the pattern never repeats, there are also basically infinite ways to do it wrong

So just figuring out how to put the next piece is a challenge. I know this because I made ~100 of them and have spent the day getting the bits to go together and it is HARD

It's like an infinite puzzle and I like it

Thank you for coming to my Ted talk

[whateverbringsyouthroughthenight]

An aperiodic monotile never repeats a formation, no matter how long the pattern. Called ‘the hat’, the 13-sided shape can be arranged in a tile formation such that it never forms a repeating grid One of mathematics’ most intriguing visual mysteries has finally been solved – thanks to a hobbyist in England. The conundrum: is there a shape that can be arranged in a tile formation, interlocking with itself ad infinitum, without the resulting pattern repeating over and over again?

[thingsihavecrochetandknit]

I think ive figured out my layout for my next quilt! Next up- way too many y seams 😭

[makereadgrow]

First pass of the binding - 42 corners

[samantha-rae-velcher]

Master List Pt. 2

YouTubers

Swaggersouls

Streamers Dream - smut

Markiplier

Games of the many - smut

Joysticks and pushing buttons - smut

Sticks and stones - smut

That one look - smut

The punishment unforgotten - Violence/smut

A need for it and her - smut

The stress is real - fluff

"Im sorry, honey" - fluff

Roomies or More? (Egos) - smut

Yancy NSFW alphabet - smut

Love mistaken for hate (Wilford Warfstache) - fluff

Don't fear the reaper (Darkiplier) - smut

Dark lust (Darkiplier) - smut

Static (Darkiplier) - smut

Warp core breech Pt.1 (ISWM) - fluff

Warp core breech Pt.2 (ISWM) - fluff

Seeing Stars (ISWM) - fluff

Jacksepticeye

Blue tint and cold tiles - smut

Marvel

Me and the Devil walking side by side (Daredevil) - fluff

Sorcerer Supreme (Doctor Strange) - smut

More like Einstein (Tony Stark) - smut

Two tons of iron (Tony Stark) - smut

Green-ish (Bruce Banner) - smut

Tender Touch (Scott Lang) - smut

The speed of light (Pietro Maximoff) - fluff

Courts of Green Pt.1 (Bucky Barnes) - fluff

Courts of Green Pt.2 (Bucky Barnes) - fluff

Courts of Green Pt.3 (Bucky Barnes) - Violence/ fluff

Feathers and Swords (Clint Barton) - smut

Hawks gold (Clint Barton) - fluff

As beautiful as an angel (Yondu Udonta) - fluff

Fear makes love (Ronan the accuser) - smut

Sharp as steel (Wolverine) - smut

Blades that steel the heart (Wolverine) - fluff

Obviously not that obvious (Drax the Destroyer) - smut

DC

Tattoo Buddies (Chato Santana) - fluff

Soldier Boy (Rick Flag) - smut

Slice and dice (Captain boomerang) - smut

Scars and stripes (BOP Victor Zsasz) - smut

TWD

Guns of blazing love (Aaron) - smut

Maybe evil Maybe not But just about (Shane) - smut

Barbed Wire Pt.1 (Negan) - smut

Barbed Wire Pt.2 (Negan) - Smut

Barbed Wire Pt.3 (Negan) - Violence/fluff

Barbed Wire Pt.4 (Negan) - Violence/fluff

Barbed Wire Pt.5 (Negan) - smut

Barbed Wire Pt.6 (Negan) - Violence/fluff

Barbed Wire Pt.7 (Negan) - Violence/fluff

Barbed Wire Pt.8 (Negan) - fluff

Star Wars

The light within (Qui Gon Jinn) - fluff

The force of two (Qui Gon Jinn) - fluff

The force binds all (Obi Wan Kenobi) - smut

The intimidating side of things (Boba Fett) - smut

Orders (Poe Dameron) - angst/ fluff

Black ink (Darth Maul) - smut

The Witcher

How The Witcher men react when you cry - fluff

Bard and Bells (Jaskier) - fluff

Gotham

Gotham Villains teaching s/o to shoot a gun

Gotham Villains when s/o doesn't answer the phone

How Gotham Villains react to their s/o getting shot

Sexting with Oswald Cobblepot - smut

Gotham's King and Queen (Oswald Cobblepot) - angst

I will kill you (Oswald Cobblepot) - fluff

Emperor Penguin (Oswald Cobblepot) - smut

Smoking Roses Pt.1 (Victor Zsasz) - smut

Smoking Roses Pt.2 (Victor Zsasz)- smut

Tainted Riddle (Ed Nygma) - fluff

What am I? (Ed Nygma) - fluff/Violence

Five-O (Jim Gordon) - smut

Stalked (Jeremiah Valeska) - Violence/fluff

Fantastic Beasts

Blue fire and silver smoke (Gellert Grindelwald) - fluff

Heaven without fear (Credence Barebone) - smut

Boardwalk Empire

Gentleman with a dark side (Arnold Rothstein) - smut

[xtruss]

At Long Last, Mathematicians Have Found a Shape With a Pattern That Never Repeats

Experts have searched for decades for a polygon that only makes non-repeating patterns. But no one knew it was possible until now

— Will Sullivan | March 29, 2023 | Smithsonian

Infinitely many copies of a 13-sided shape can be arranged with no overlaps or gaps in a pattern that never repeats. David Smith, Joseph Samuel Myers, Craig S. Kaplan and Chaim Goodman-Strauss (CC BY 4.0)

From bathroom floors to honeycombs or even groups of cells, tilings surround us. These patterns cover a space without overlapping or leaving any gaps. Like a rug filled with diamond shapes, where each section looks the same as the one next to it, every tiling ever recorded has eventually repeated itself—until now.

After decades of searching for what mathematicians call an “einstein tile”—an elusive shape that would never repeat—researchers say they have finally identified one. The 13-sided figure is the first that can fill an infinite surface with a pattern that is always original.

Repeating patterns have translational symmetry, meaning you can shift one part of the pattern and it will overlap perfectly with another part, without being rotated or reflected. The shape described in a new paper does not have translational symmetry—each section of its tiling looks different from every part that comes before it.

The designs on these rugs have translational symmetry—the patterns on the rugs repeat themselves. Juli Kosolapova via Unsplash

Sarah Hart, a mathematician at Birkbeck, University of London, who didn’t contribute to the finding, tells New Scientist’s Matthew Sparkes that she had thought finding an “einstein” (named for the German words for “one stone,” or one tile) could not be done. “There are infinitely many possible candidate tiles, and even the existence of a solution feels quite counterintuitive,” she says to the publication.

“Everybody is astonished and is delighted, both,” Marjorie Senechal, a mathematician at Smith College who did not participate in the research, tells Science News’ Emily Conover. “It wasn’t even clear that such a thing could exist.”

David Smith, a retired printing technician and nonprofessional mathematician, was the first to come up with the shape that could be a solution to the long-standing “einstein problem.” He shared his ideas with scientists who took on the challenge of trying to mathematically prove his conjecture, per the New York Times’ Siobhan Roberts.

The team published a preprint paper detailing the findings on the site arXiv last week, and it has not been peer-reviewed yet. But experts say the work is expected to be supported with further investigation, per Science News.

“This appears to be a remarkable discovery,” Joshua Socolar, a physicist at Duke University who did not contribute to the finding, tells the Times. “The most significant aspect for me is that the tiling does not clearly fall into any of the familiar classes of structures that we understand.”

Each "einstein" tile has eight kite shapes inside of it. David Smith, Joseph Samuel Myers, Craig S. Kaplan and Chaim Goodman-Strauss (CC BY 4.0)

The “einstein” tile is made up of eight kites, or four-sided polygons with two pairs of adjacent, equal-length sides. Researchers call it “the hat” because of its resemblance to a fedora.

The shape is simpler than some experts expected it to be. Chaim Goodman-Strauss, a mathematician at the University of Arkansas and one of the authors of the paper, tells Science News that if he’d been asked to guess what the shape might look like before the finding, “I would’ve drawn some crazy, squiggly, nasty thing.”

In the 1970s, mathematician Roger Penrose discovered that two shapes could form a non-repeating tiling pattern together, prompting hopes that a single shape may be found to do this one day. Researchers have been able to make other non-repeating patterns in the past, but the challenge has been finding a shape that can only make a non-repeating pattern, Goodman-Strauss tells the Times.

The shape of “the hat” can also be morphed to form additional tile shapes that make non-repeating patterns, as shown in the video above.

This new finding could lead to materials science investigations—for example, shapes that form non-repeating tilings could help design stronger materials, Hart tells New Scientist. The elusive shape might also spark creative inspiration for new decorative designs or art.

[cerastes]

I picked up Qiubai from the current banner and know absolutely nothing about her. She worth leveling and if so is there anything I should know about her skills/talents and how best to use them?

Qiubai is one of those units whose banner was very untimely, smack between Lin and Chongyue's limited banner, and the Monster Hunter collab limited banner (not to mention that afterwards, there was Absolute Beast Ines to account for, and a bit farther down the road, fan favorite Muelsyse and Ho'olheyak), so a lot of people decided to skip her, making her one of the rarer Operators.

But I am not a lot of people, and my main reason is "She's Fucking Cool, Your Honor".

I think she's a damn good Operator worth investing in. The main criticism levied against her, besides the unfortunate timing of her banner, is that she's Not Thorns, which is like looking at a successful and highly skilled physicist and saying that he's shit because he's not Albert Einstein. The actual criticism I would levy against her, as someone that uses her all the time, is that she does require a bit of presence of mind to use her due to the nature of her Talents requiring procs if she's not supported appropriately, and her S3 having a rather long downtime.

So, Talents (E2 no pots): First is whenever she attacks enemies affected by Slow or Bind, she deals 40% of her Attack as extra Arts damage. This is a good extra bit of juice you can squeeze out of every attack, as well as a means to deal with high Defense powerhouses. Second is that attacks have a 20% chance to Bind for 1.5 seconds. Attacks that proc this 20% apply Bind first and then count the attack, meaning that every time she procs her Second talent, her first Talent is also activated. This is true, to my knowledge, to all Operators with similar effects (such as enemies receiving extra damage when Stunned in her range; the Stunning hit benefits from this extra damage instead of having to follow up to start benefiting). Her attack interval is 1.3, meaning that whenever she procs Talent 2, she'll usually get two free Talent 1 procs in, "usually" because sometimes the enemy is actually at the edge of her range or just wandered off, and the projectile doesn't land in time.

S1 is your least used Skill, probably, but it's not useless: It's Bind centric, and Binds the enemy for 2.5 (3 M3; M3 numbers in parenthesis from hereon) seconds, followed by a small AoE explosion of 240% (300%) Arts damage once it expires. It is Automatic and Attack Charged on a low limit of 5 SP (4 SP) so it reliably gets fired off. It's honestly not a bad skill, it's just that her S2 and S3 exist.

S2 changes her range into a single file 4 tiles forward and immediately slashes all these tiles to deal 240% (300%) Arts damage and enemies in this slashed ground are Slowed throughout the duration, 5 seconds. QB gets an steroid of +90% (+140%) Attack for these 5 seconds, and when the skill expired, the initial slash explodes once again for 240% (300%) Physical damage. The slash itself CANNOT hit air units, but QB's regular attack can, be wary of this. This Skill is your go-to for general use when you just need to kill regular enemies and elites, since it gives her phenomenal true AoE capabilities, a strong steroid, and since enemies are Slowed in the slashed area, she will proc Talent 1 every time while Skill is active (against ground units, that is). All of this on a very good timer of 12 SP (10 SP), making this skill's strength its ability to reliable, consistently use it: It's ALWAYS ready when you need it, and on longer fights against very strong enemies that you need to stall for a bit, you can use it several times.

S3 changes her range to one extra side tile forward, changes damage type entirely to Arts, Talent 1 is augmented by 1.5x (2x), gives QB +45% (+55%) Attack, Lord ranged attack penalty is negated, QB attacks 2 extra targets, so 3 total per attack, and each attack animation she does gives her 13+ ASPD for the duration of the skill, stacking up to 6 (8) times. This is QB's burst skill to deal with numerous strong enemies or even just one strong enemy, to be honest. She'll become a machine gun of Arts damage, and since she's attacking so fast, she'll likely keep proccing Talent 2 repeatedly, meaning, even more damage from Talent 1, which in itself also gets augmented. The sole weakness of this skill is that it exists on a 55 SP charge, unlike her very fast S1 and S2. It lasts 30 seconds. I recommend Mastering this skill first because its gains are actually very good, due to the Attack bonus and the Talent 1 augmentation coming into play for a very drastic increase in damage.

S2 is true AoE so you use it to deal with many enemies, S3 is Arts burst so you use it to delete strong enemies. You want to pair QB up with people that can Slow or Bind enemies so you can constantly enjoy Talent 1 bonuses instead of relying on Talent 2 procs. Her Best Match is Suzuran S3 for QB's S3, since that'll just make her become absurdly devastating, but for less bursty options (Suzuran's S3 also has long downtime), you can use Angelina S2, Podenco S2, Ethan, Dorothy S2, and other such Decel Binders and Operators with consistent ability to Slow or Bind. KEEP IN MIND: It needs to be the status effect known as Slow, capitalized, not just any slow effect! Meaning, Ch'en the Holungday, for example, who spreads movement speed slowing areas with her Skills, DOES NOT combo with QB for Talent 1 purposes. It needs to be the status known as Slow (which reduces enemy movement speed by 80%).

QB's main strengths are the ability to vary damage types, synergize well with support units to hose out great damage, have reliable true AoE that can be spammed, and good burst when that is necessary, further improved by synergizing well with a popular and strong Operator (Suzuran). QB's main drawbacks are that her S3 exists on rather long downtime, and that against highly Resistant enemies, her Skills will not fare particularly well, as they all have an Arts damage component to them (you'll mainly want to use S2 here, since her steroid affects her Phys damage output and the expiration explosion is Phys).

Overall, a very fun and strong Operator! I recommend investing in her, yeah.

[raccoonspooky]

Reasons why diff slashers are out there doing ~All That~

Michael Myers:

He’s got something stuck in his teeth and no matter wtf he does he cant get it. Someone take peepaw to the dentist please. He’s got an inner thigh rash from them nasty ass coveralls and probably needs some aveeno.

Honestly please wash those or get him new ones because the reason he sits up the way he does is because the fabric doesnt crease any more so he just has to very straight leggedly stand up every time hes knocked down.

Billy Loomis:

He’s abstained from jerking off for too many months, the anti nut mindset has rewritten his brain chemistry and now all he can do is ~mansplain manipulate manslaughter~ dude’s backed up so bad he can see shrimp colors.

Bo Sinclair:

The entire events of the movie happen because he was staring at himself in the bathroom mirror like a bird flirting with his own reflection. He slipped on the tile and gave himself a REALLY bad concussion. He can see sounds and taste lights. He wears a baseball hat at night and leaves his keys in the ignition, if he takes off the hat all the blood swelling in his brain is dispersed way too fast and he’ll sputter out like a de-inflating balloon.

Vincent Sinclair:

He listened to evanescence one time.

Billy Lenz:

Dude has straight up rabies. And like some weird bacterial disease that you can get from being bitten by a bat. Its actually a medical anomaly that he’s on two feet at all? Yknow that post that says that like 60% of bacteria found on NYC subways has no known origin? Basically Billy Lenz is the canadian equivalent of that.

Jason Voohees:

He’s actually a meat puppet for thousands of single celled organisms found in the lake. Imagine if your spore creation gained sentience and then it evolved itself into a giant buff guy, like ur spore creation would immediately go on a rampage duh. Dude is a macro-biome habitat of millions of critters all playing QWOP with his arms and legs.

Brahms Heelshire:

His mother was really into those baby mozart and baby einstein VHS tapes. Dude’s been weird since the WOMB. He’s also got a critical vitamin D deficiency and is likely anemic. No, he wont eat his spinach to help with the iron issue. But he will hide it in the walls and then huff and whine that something smells funny and that you should maybe go clean it up. Give him a flinstone vitamin gummy pls.

Alternatively: He’s like that because he’s bri-ish, you eat enough mushy peas in your lifetime and this bullshit just sorta becomes you. Sure, whatever! Eat beans on toast, put on a mask, live in the walls!

Any of the texas chainsaws:

Tapeworm. Why? Because its funny. Hungry ass tapeworm infested ass cannibals. Gotta eat up to appease ur worm!

OG big boy is really into that QVC old lady channel and every time the women are talking about lipsticks or lotions or whatever he’s seething in jealousy. Therefore he must kill.