Quite amazing what one could get from simply playing around with circles. Two hexagonal patterns of circlets, tilted with respect to one another by 90°, overlayed and then intersected: Beautifully aperiodic! #pattern #sciart #aperiodic

Today I acquired an #aperiodic #monotile known as the 'hat', rendered in foam. The squiggles on it are signatures of David Smith, the 'hobbyist' #mathematician 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!)

More #hitomezashi explorations: if you use sine curves as segments you'll obtain a chiral #aperiodic curve.. I guess I might call it a 'shuriken' hitomezashi?

The origin of the Spectre Dress
#hatfest #aperiodic #transpride #fashion #math #openuniversity

So the origin of the spectre dress is relatively mundane and silly. Following a rough period of early transition (I started in 2022) I felt like I was finally starting to hit my stride and could feel my confidence growing. I'd purchased a trans pride-themed dress from an Etsy seller earlier in the year which had been attracting a lot of positive attention, and since I consider my transition and my journey through mathematics to be intimately related, I wanted to combine the two.

Originally I wanted to contact Stefan Pautze [http://pautze.de/] and use a colour variation of one of his designs (rough version pictured), as I've always been a huge fan of his art and I'd also met him in-person at the exhibition in memory of Uwe Grimm in 2022 where we hit it off. At this point it was still just a kernel of an idea, nothing concrete. But then two things happened in a short span of time. Hatfest was announced, and the spectre tiling was discovered about two weeks later. The idea for the dress instantly crystallized, and I got in contact with the same Etsy seller who did my pride dress to ask about a custom design. (0/8)

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

Based on polyiamonds emulating H7/H8 metatiles of the Hat #aperiodic #monotile(https://mathstodon.xyz/@mathBlock/110647330990994799), I place 4th and 5th generation iterations on top of each other.

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

The filled-in prototiles(hat shapes) are based on the H7/H8 metatiles in the Hat #aperiodic tiling. Originally constructed as three subtiles. Have not confirmed they cannot tile periodically, though.

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

#chiral #aperiodic #monotile

I doodled a spectres tonight (image is here, tiles are on my blog post).

https://fractalkitty.com/2023/06/07/spectre-tiles/

#spectre #aperiodic #monotile #mathart #fresco #jellyfish #tiling #chiral #ocean #hat

This infinite tiling pattern could end a 60-year mathematical quest
https://www.nature.com/articles/d41586-023-01801-8

a shape that can cover an infinite plane, but never make a repeating pattern.

#mathematics #science #aperiodic #pattern

This repository contains #Fortran bindings for the #Cairo vector graphics library:
https://github.com/vmagnin/cairo-fortran

It is used by:
https://github.com/vmagnin/hat_polykite
which generates a SVG file including a batch of hat polykites. On March 20, 2023, David Smith and mathematicians Joseph Samuel Myers, Craig S. Kaplan and Chaim Goodman-Strauss posted a preprint on ArXiv describing that monotile with 13 sides that, used with its reflected version, admits #aperiodic tilings of the plane:
http://arxiv.org/abs/2303.10798

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

#aperiodic #monotile #mathstodon #mathart

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

https://mikkorahikka.blog/2023/05/03/jaksoton-laatoitus-oikeilla-laatoilla/ #tiling #aperiodic #mathematics

Prachtige set onderzetters van de recent ontdekte ‘einstein’, een tegel die het vlak aperiodiek vult. Gemaakt door Martijn Leisink.
#aperiodic #tiling

A new variation of Hierarchical Colouring #aperiodicmonotile / Image 3 : levels=4, Top MetaT=H, Motif : high F weight.
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Previous post description:
I built a colouring of the #aperiodic #monotile 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: https://github.com/santoleonardo/hatviz-HierCol

Here’s a fun discovery about tiling the plane: the identification of an “einstein” (“Ein Stein”) that does so aperiodically. #Mathematics #TilingThePlane #Aperiodic #EinStein https://www.sciencenews.org/article/mathematicians-discovered-einstein-tile

Just published a new #maths 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:
https://www.printables.com/model/454334-turtle-and-fish-aperiodic-monotile-puzzle

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

I built a colouring of the #aperiodic #monotile 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: https://github.com/santoleonardo/hatviz-HierCol
Hierarchical Colouring / Image 2 : levels=5, Top MetaT=P, Motif : high F weight.