#Tiling

[szimmetria-airtemmizs]

Mathematical fun fact of the day 3:

You can tile a regular 30-gon using a pentagon and rhombus.

#math #art #geometry #symmetry #theorem #mathematics #geogebra #tiling #tessellation #mathblr

[cant-think-of-a-good-one]

the Spectres aren't just a few shapes. they're an infinite family of shapes. a family that includes this:

i'm naming this particular shape

The Fuckre

#made this in inkscape manually #gonna try to make a geometry nodes that can do this with blender #aperiodic monotile #aperiodic tiling #geometry #mathematics #math #mathblr #shapes #tiling #tesselation #spectre #spectres #the spectres #the spectre #inkscape #vector art #fuck

[graphics-cafe]

kirby dividers

#kirby #dividers #2000s nostalgia #webcore #neocities #layouts #kawaii #kawaiicore #nintendo #kirby divider #kirby dividers #my stuff #uploads #tiling #divider #kirby and the amazing mirror #kirby gba #gba #pink divider #pink #my stuff fav

[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

[sovenasark]

18 - Lizards and lizards and lizards and lizards and

#SovenasArt #Rain World #RainWorld #RW #RW Game #RW Art Month #rain world art month #RWArtMonth #Art #Digital Art #Pixel Art #RW yellow Lizard #Rain World Yellow Lizard #RW Lizard #Rain World Lizard #Tiling #Tiling Art #Pattern #Artists on Tumblr #This was fun to do. I need to do more patterns

[mathhombre]

Aperiodic Monotile

Super big news from this lot. (ArXiv)

A monotile that admits no periodic tilings, but uncountably many aperiodic tilings. WOW.

And they're calling it the Hat.

And Craig announced it with an animation!

#tessellation #research #tiling #aperiodic #hat #Youtube

[stone-cold-groove]

The modern electrified kitchen.

#vintage illustration #vintage kitchen #kitchen design #kitchen decor #vintage kitchen appliances #tile #tiling #back splashes #kitchen tiles

[oscar-out-of-a-suitcase]

Korcula, Croatia

#landscape #nature #original photographers #view #natureview #photography #travel #photographers on tumblr #mountains #sea #architectureview #architecturephotography #architecture #dawn #tiling #old city #city photography #croatia #korcula #naturephotography #landscape photoshoot

[art-of-mathematics]

DIN A2 space filled with 4 sheets of DIN A4 paper in 4 different colors.

Each DIN A4 sheet is split into pieces ranging from DIN A5 (largest) to DIN A11 (smallest). Each size from A5 to A10 exists one time per each color. A11 exists two times per each color. (I could have continued with splitting the A11 into two A12 tiles - but these would be too tiny for my clumsy hands to handle.)

I might create some mosaic patterns with this... (using some exchange algorithms... )

#space filling #tiling #DIN Ax #mosaic #tiles #math #math art #mathematics #puzzle #paper crafts #cheap puzzle

[mydaysaresmall]

Tiling cosy pigs <3

#Happy Christmas #Pigs #Art #Tiling #Wrapping paper

[brucesterling]

https://arxiv.org/pdf/2303.10798.pdf

#monotile #mathematics #tiling #nonrepeating #aperiodic

[szimmetria-airtemmizs]

Did you know that there is a way of cutting an equilateral triangle into seven similar triangles that have pairwise different sizes, and they are not right triangles? (With right triangles it is easy to cut into any number of similar pieces.)

One of the angles in each triangle is 120 degrees and the other two are roughly 40.67915375798 and 19.32084624 degrees. You can read the details in the paper:

A note on perfect dissections of an equilateral triangle by Andrzej Zak

#math #art #tiling #geogebra #dissection #theorem

[xponentialdesign]

Alignments problem is hard to solve, can it occur despite certain amount of chaos?

#pattern #vintage #alignment #retro #loop #generative #monochrome #animation #puzzle #chaos #gif art #black and white #patterns #tiling #circles #70s #seventies #geometry #visuals #trapcode #form #trapcodeForm #after effects #2d #motif #animated #nft #objktcom #tezos #tezos art

[regolo54]

#geometry #symmetry #mathart #handmade #tessellation #mc escher #regolo54 #tiling #pattern

[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.

#math #einstein #tesselation #tiling #math art #i maed dis

[raaaaaauhrawr]

⭐️⭐️star backgrounds✨⭐️✨✨⋆˙⟡♡✧˖°

dont reccomend using the flashy ones for website backgrounds.....

#graphicz #fav #eyestrain #background #repeating #repeating pattern #webcore #tiling #tiled background #kidcore #rainbow