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!)

I've been playing about with the #Spectre aperiodic #monotile recently. I'm thinking of making them into fired & glazed #ceramic 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 #ruby app to make an #SVG 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!

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

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.

"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

Making some cookies with a cutter my sister got me.

#monotile

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

Inevitably, I had to do the L-system for turtle-drawing patches of @csk 's new #spectre #monotile. https://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.

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

@bbcmicrobot longer explanation here https://hachyderm.io/@bazzargh/110293551149890811, but I came up with this as a compact representation for drawing aperiodic #monotile 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

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

In my quest for articles on making the "hat" -- the non-periodic #monotile -- 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 #Inkscape (which I'm not fluent in, but want to be).

https://www.youtube.com/watch?v=BirP2U5l0j0

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

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.

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 1 : levels=4, Top MetaT=H, Motif : high H weight.