#penrose tiling

[andmaybegayer]

Penrose quilt is officially finished! 2022-07-30 to 2023-04-02, all hand sewn by me and my mother.

It would figure that the Einstein would be found like a month before I finished this! Honestly probably for the best, the Einstein has too many concave angles.

We'll embroider patches for it soon but for now we're calling it, it still needs its first wash and I'll probably have to patch up some quilting after that.

#penrose quilt #textiles #sewing #quilting #penrose tiling #aperiodic tiling

[proteus-thrmanfish]

#penrose tiling #pattern #art #digital art #artists on tumblr #my art

[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

#nerdshit #penrose #penrose tiling #einstein tiling #vampire tile #spectre tile #infinite puzzles

[koravelliumavast]

Penrose tiles are so cool. its an aperiodic pattern that does not repeat itself at all ever.

LOOK AT IT

#i just learned about them. #penrose tiles

[polyphonetic]

NEW SHAPE DROPPED

Spectre

As a refresher on tiling:

The above image is an example of penrose tiling. It lacks translational symmetry, but it does have reflection and fivefold rotational symmetry. It's very cool but note that it has two different "shapes", two rhombi.

Below us is Hat!

Hat is a tile that is especially cool because you only need itself and a reflection of itself to make a provably aperiodic tiling!

It is kind of a whole wiggly range of similar shapes (like if you tweak the edges a little it can still repeat) BUT it requires a reflection of itself, which is kind of using *two* shapes. Spectre, however, only needs itself:

You can read about Spectre here!

Like Hat, it also can exist as a range of slightly similar shapes! For example, here's doggy : )

#math #tiling #geometry #penrose #hat #spectre #kassandra rambles #polygons #aperiodic tiling

[szimmetria-airtemmizs]

In the math camp I also received a marvelous gift. A large set of Penrose tiles made from wood!

#math #camp #art #penrose #tiles #tilling #aperiodic

[bakingmoomins]

i am now known as the spiral girl by my professors

#talked to my new thesis advisor about what i wanna do and he was like oh Thank God it's not another penrose thesis #and then he was like it's also nice that it's not about the hat bc that's gonna be the next penrose and everyone is gonna be doing #a thesis and projects about it. :~) glad you're doing something more neglected like the spiral tilings :) #and today i was talking to my diff eq prof and she was like oooh so you're [advisor]'s name spiral girl! nice!! #🐌

[hychlorions]

pov you’re my friend and it’s just another 12am on a monday

#.docx #you get it. #speaking of math do u guys wanna hear about how the penrose theatre is such a good name. #it's named after the penrose triangle!! popularized by lionel and roger penrose in the 1950s #roger penrose some 20 years later will come up with something called penrose tiling #it's a type of aperiodic tiling and other ways needed 100+ shapes to tile aperiodically #which in simple terms is like. you can't copy-paste a given pattern and have it fit without having to rotate it. smthn like that #they got to whittle that number down to 6 overtime. roger penrose got it down to two #interesting stuff but that's unimportant #now. a previous version of roger penrose's aperiodic tiling had a shape called a justice cap #it looks like a little paper boat. that's also unimportant #now penrose theatre appears in the magical turnabout #and you know who the lead defense attorney is there? Mr justice himself B) #anyway these are all probably just little coincidences and i sound a lil insane rn #but in a boring way #did i make this post just to ramble in the tags bc this penrose thing has been on my mind since last year? maybe #so i'm sorry if u read through this and thought i was leading up to something big lmao

[tactfulsaboteur]

(ancestral blood memory urge to remodel a bathroom)

#i NEED a house #i'm going to put in a walk in shower and do everything in penrose tiles

[thisgodwontforgiveyou]

the cube in the artifact ending just being a shitty plastic extremely euclidean trinket is so funnnnnnyyyyyy fuuuuuuck

#i looked up other depictions of penrose cubes out of curiosity and seeing people struggle to convey it without just using tiles is awesome

[dracomaton-integration]

Did you guys know that there are 'patterns' that never repeat??

There are tiles that neatly fit together and can cover an infinitely wide surface but they don't form a regular pattern no matter how far you zoom out. Penrose tiles are the most famous. Here's a patch from the Tilings Encyclopedia Tilings Encyclopedia | Penrose Kite Dart (uni-bielefeld.de).

Check out this Penrose tile generator:

Penrose tilingCraft Design Online

If you know how to do Magic Eyes, you can check for repeated patterns. You'll see patches of regularity separated by intersecting, straight lines of chaos that look like the Spiderverse. Here's my sketch of the Spiderverse lines, sorry it's a little rough, it's hard to draw when your eyes are crossed.

My favourite is one of the very latest discovered: a single tile that only tiles aperiodically, without any reflections (it's called the Spectre since it has no reflection, haha). This image is part of it's proof of aperiodicy (idk if that's a word haha)

aaaand here's the link to that article, in case any math nerds like me want to read an extremely technical article. 2305.17743.pdf (arxiv.org)

Anyways, that's what I've been obsessed with for the past few weeks! I'm currently considering a textiles project involving the Spectre, stay tuned!

#penrose tiles #mathiness #math nerd #tile #Spectre #magic eye

[andmaybegayer]

Quilting complete

I bought 30g of perle to do this and this is all that's left. I used one reel and my mother used two which is pretty much exactly our relative difference in sewing speed. Lean Manufacturing Dot JPEG. Next up is binding the edge.

#penrose quilt #textiles #penrose tiling #aperiodic tiling

[reblogs-the-art]

"Why Penrose Tiles Never Repeat"

#penrose tile #beautiful geometry #Youtube

[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

#Post #David Smith #Einstein tile #mathematics #non-repeating patterns #roger penrose #tiling #Mark Frauenfelder #Boing Boing

[koravelliumavast]

Penrose tiles (at least the ones in your banner) also remind me a bit of an aerial view of the Shattered Plains

YES YES YES

Also this one doesn’t look like the one in my banner but the pattern in it is so cool

#asks #like look at these shattered plains maps and... #penrose tiles

[a-crow-with-rights-and-anxiety]

Hey so you remember this thing that everyone on mathblr got excited about recently?

This is the hat, and it's what's called an "aperiodic monotile". This means that no matter how you arrange copies of this tile, you can never get an arrangement that will repeat infinitely (think of it like the irrational numbers of tilings). This was big news in mathematics as while sets of more than one tiles have been found that are aperiodic (e.g: The Penrose Tiles), this was the first tile that's aperiodic by itself, hence "monotile". (There are some caveats to this but that's not important for understanding this post)

However.

If you look at images of the hat tiling, you may notice something.

If you look at the tiles labled 1 and 2, you'll see that one's a reflected copy of the other. In fact, any infinite arrangement with hats requires you to you mix unreflected and reflected tiles. Which raises the question: is it possible to have an aperiodic monotile that doesn't need reflections?

Presenting the Spectre, A chiral aperiodic monotile.

Using only translation and rotation, any arrangement of copies of this tile will never repeat.

Mathematically speaking, this is really fucking cool.

The paper on it is still in preprint, but hopefully I won't need to retract this post. A copy of it can be found here and a post going into some more details of how the shape was discovered is here.

#I know not a lot of people who follow me are interested in maths #It's not stopping me though. #I WILL talk about maths and you WILL hear me #Apologies if I've made any mistakes #math #maths #aperiodic monotile #spectre