Tommaths (he/him) · @TeaKayB
524 followers · 1739 posts · Server mathstodon.xyz

Today I acquired an known as the 'hat', rendered in foam. The squiggles on it are signatures of David Smith, the 'hobbyist' who discovered the shape, and Chaim Goodman-Strauss, who worked with Smith on the proof confirming that it is definitely an aperiodic monotile (the first one to be discovered!)

#mathematician #monotile #aperiodic

Last updated 1 year ago

JP · @byjp
100 followers · 422 posts · Server hachyderm.io

I've been playing about with the aperiodic recently. I'm thinking of making them into fired & glazed tiles for a wall piece somewhere and, to prepare for that, I've been thinking about whether there are lines I could draw between the sides that'd look pretty (similar to the boardgame "Tantrix")

I built a little app to make an of a tiling, so I could experiment — I'm still not 100% happy with the edge pairings, but you might enjoy looking at my work so far!

#spectre #monotile #ceramic #ruby #svg

Last updated 1 year ago

· @Kosovircek
15 followers · 19 posts · Server toot.si

A school of spectre tile fish.

Spectre tile == chiral aperiodic monotile.

Tiles created with: Kosovircek/SpectreTileMaker: A web app for deforming edges of spectre tiles. (github.com)

Inpainting with stable diffusion: AUTOMATIC1111/stable-diffusion-webui: Stable Diffusion web UI (github.com)

Using model AnythingV5Ink_ink: 万象熔炉 | Anything V5/Ink - ink | Stable Diffusion Checkpoint | Civitai

Prompt: a fish

#math #spectre #monotile #einstein #art #maths #mathematics

Last updated 1 year ago

mathBlock · @mathBlock
12 followers · 36 posts · Server mathstodon.xyz

Here is a possible new set of metatiles for the Hat , as shown composed of hats. I don't really know how to test this, though.

#monotile #aperiodic

Last updated 1 year ago

mathBlock · @mathBlock
8 followers · 35 posts · Server mathstodon.xyz

Based on polyiamonds emulating H7/H8 metatiles of the Hat (mathstodon.xyz/@mathBlock/1106), I place 4th and 5th generation iterations on top of each other.

#monotile #aperiodic

Last updated 1 year ago

mathBlock · @mathBlock
1 followers · 3 posts · Server mathstodon.xyz

This is a repost of a twitter thread where I explain the concept of drainage for tilings of the Hat . Might change a few bits, but this will mostly just be a copy job.

#monotile #aperiodic

Last updated 1 year ago

· @vmagnin
63 followers · 126 posts · Server floss.social

"A chiral aperiodic monotile"
David Smith, Joseph Samuel Myers, Craig S. Kaplan, Chaim Goodman-Strauss
Submitted on 28 May 2023
arxiv.org/abs/2305.17743

#chiral #aperiodic #monotile

Last updated 1 year ago

Fractal Kitty · @fractalkitty
838 followers · 446 posts · Server mathstodon.xyz
4sphere · @4sphere
401 followers · 1180 posts · Server mathstodon.xyz

Making some cookies with a cutter my sister got me.

#monotile

Last updated 1 year ago

· @bazzargh
97 followers · 382 posts · Server hachyderm.io

The @bbcmicrobot isn't picking up but last post generates patches of the with a toots worth of bbc basic. Just.

#spectre #monotile

Last updated 1 year ago

· @bazzargh
97 followers · 380 posts · Server hachyderm.io

Inevitably, I had to do the L-system for turtle-drawing patches of @csk 's new . trinket.io/python/108e28ab75 as before, this ends up redrawing many edges many times, and as before the one tile where the substitution doesn't apply becomes a hole (the top tile of the 'Mystic'). I've left in the hat generator code for comparison.

#spectre #monotile

Last updated 1 year ago

Rob Simmons · @simrob
220 followers · 672 posts · Server social.wub.site

The Aperiodic Monotile Earrings arrived! I made a Ko-fi Shop for them: ko-fi.com/s/5852007096

#aperiodic #monotile #mathstodon #mathart

Last updated 1 year ago

Bornach · @bornach
114 followers · 1067 posts · Server masto.ai

[Mostly Mental] on 2 docent ways to prove the non-periodic tiling of the newly discovered "Einstein"
youtu.be/vtpswcAfWiI

#aperiodic #monotile

Last updated 1 year ago

· @bazzargh
96 followers · 345 posts · Server hachyderm.io

@bbcmicrobot longer explanation here hachyderm.io/@bazzargh/1102935, but I came up with this as a compact representation for drawing aperiodic s, and this version is small enough to fit in a toot. The version that fills in the tiles might be a little too long

#monotile

Last updated 2 years ago

· @bazzargh
95 followers · 341 posts · Server hachyderm.io

Dropping all the stack push/pops in the rules gives a very simple set for drawing the outline of H8-based patches.

#monotile

Last updated 2 years ago

John M. Gamble · @jgamble
79 followers · 899 posts · Server fosstodon.org

In my quest for articles on making the "hat" -- the non-periodic -- I came across this YouTube video which is not only a excellent tutorial on how to draw it, but is also a great beginner's tutorial on (which I'm not fluent in, but want to be).

youtube.com/watch?v=BirP2U5l0j

#monotile #inkscape

Last updated 2 years ago

Santo Leonardo · @santoleonardo
19 followers · 18 posts · Server mathstodon.xyz

A new variation of Hierarchical Colouring / Image 3 : levels=4, Top MetaT=H, Motif : high F weight.
----------
Previous post description:
I built a colouring of the using the colour dimension as a map of the sequence of hierarchy levels of each tile (set H,T,P,F). It works recursively: each metatile inherits a value (HiCol) from its parent and transmits a modified HiCol to its children, calculated from the inherited HiCol and from a pre-set own colour. The pre-set values are a parameter vector [H,T,P,F], which can produces many Motifs.
It is an attempt to show at the same time the global and local structure of Metatiles and tiles (hats).
Built by modifying the drawing function in the hatviz SW of @csk (Copyright (c) 2023, Craig S. Kaplan), Fork SW and a page of infos here: github.com/santoleonardo/hatvi

#monotile #aperiodic #aperiodicmonotile

Last updated 2 years ago

Damien Jorrand · @damienjorrand
111 followers · 387 posts · Server mastodon.design

Just published a new toy/game. A new interpretation of the trending aperiodic monotile.
This time playing with the "turtle" tile. And it has a new companion fish to help it tile the plane aperiodically.
The files are here:
printables.com/model/454334-tu

#monotile #aperiodic #games #game #toy #printables #stem #3dprinting #science #geometry #mathematics #math #maths

Last updated 2 years ago

Santo Leonardo · @santoleonardo
17 followers · 17 posts · Server mathstodon.xyz

I built a colouring of the using the colour dimension as a map of the sequence of hierarchy levels of each tile (set H,T,P,F). It works recursively: each metatile inherits a value (HiCol) from its parent and transmits a modified HiCol to its children, calculated from the inherited HiCol and from a pre-set own colour. The pre-set values are a parameter vector [H,T,P,F], which can produces many Motifs.
It is an attempt to show at the same time the global and local structure of Metatiles and tiles (hats).
Built by modifying the drawing function in the hatviz SW of @csk (Copyright (c) 2023, Craig S. Kaplan), Fork SW and a page of infos here: github.com/santoleonardo/hatvi
Hierarchical Colouring / Image 2 : levels=5, Top MetaT=P, Motif : high F weight.

#monotile #aperiodic

Last updated 2 years ago

Santo Leonardo · @santoleonardo
17 followers · 16 posts · Server mathstodon.xyz

I built a colouring of the using the colour dimension as a map of the sequence of hierarchy levels of each tile (set H,T,P,F). It works recursively: each metatile inherits a value (HiCol) from its parent and transmits a modified HiCol to its children, calculated from the inherited HiCol and from a pre-set own colour. The pre-set values are a parameter vector [H,T,P,F], which can produces many Motifs.
It is an attempt to show at the same time the global and local structure of Metatiles and tiles (hats).
Built by modifying the drawing function in the hatviz SW of @csk (Copyright (c) 2023, Craig S. Kaplan), Fork SW and a page of infos here: github.com/santoleonardo/hatvi
Hierarchical Colouring / Image 1 : levels=4, Top MetaT=H, Motif : high H weight.

#monotile #aperiodic

Last updated 2 years ago