#aperiodicmonotile — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #aperiodicmonotile, aggregated by home.social.
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Peter Selinger now has an app
https://www.mathstat.dal.ca/~selinger/hat-partition/ that lets you create hat tilings using the Markov partition described in his paper with Sébastien Labbé (https://arxiv.org/abs/2604.20964). For a printable version of this, see Sébastien's blog post: http://www.slabbe.org/blogue/2026/03/a-construction-of-the-hat-tilings-by-a-markov-partition/ -
Peter Selinger now has an app
https://www.mathstat.dal.ca/~selinger/hat-partition/ that lets you create hat tilings using the Markov partition described in his paper with Sébastien Labbé (https://arxiv.org/abs/2604.20964). For a printable version of this, see Sébastien's blog post: http://www.slabbe.org/blogue/2026/03/a-construction-of-the-hat-tilings-by-a-markov-partition/ -
Peter Selinger now has an app
https://www.mathstat.dal.ca/~selinger/hat-partition/ that lets you create hat tilings using the Markov partition described in his paper with Sébastien Labbé (https://arxiv.org/abs/2604.20964). For a printable version of this, see Sébastien's blog post: http://www.slabbe.org/blogue/2026/03/a-construction-of-the-hat-tilings-by-a-markov-partition/ -
Peter Selinger now has an app
https://www.mathstat.dal.ca/~selinger/hat-partition/ that lets you create hat tilings using the Markov partition described in his paper with Sébastien Labbé (https://arxiv.org/abs/2604.20964). For a printable version of this, see Sébastien's blog post: http://www.slabbe.org/blogue/2026/03/a-construction-of-the-hat-tilings-by-a-markov-partition/ -
Peter Selinger now has an app
https://www.mathstat.dal.ca/~selinger/hat-partition/ that lets you create hat tilings using the Markov partition described in his paper with Sébastien Labbé (https://arxiv.org/abs/2604.20964). For a printable version of this, see Sébastien's blog post: http://www.slabbe.org/blogue/2026/03/a-construction-of-the-hat-tilings-by-a-markov-partition/ -
As a follow up to last week's post on Markov partitions for Hat (hat and turtle) and Spectre (hats in turtles and turtles in hats) tilings (https://mathstodon.xyz/@pieter/116484517078239617), here is a way of colouring such tilings. For each control point, we colour the tile according to its distance from the boundary of the fractal window it lies in.
The first image shows a patch of a turtle tiling using the colour map in the second. Control points that lie near the boundary of the fractal window are close to flipping between the two states of a Conway worm, so this is a nice way of highlighting subsets of tiles that are 'close' to being Conway worms.
One of the things on my to-do list is to create an animation of a patch as the triangular grid moves slowly relative to the underlying pattern, but if anyone wants to take a stab at this, please do.
[Will post a Spectre version later]
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July 2024. A terrace in Istria. Tiles half-laid, some already fixed, a template that doesn't match the floor, an unanswered voice call from Brussels. 480 limestone pieces, CNC-cut from a shape proven mathematically a few months before. One constraint: no tile can be flipped.
Three months, a long hot summer to find out if the pattern held.
https://anarchive.fo.am/silver/spectres/
#aperiodic #tiling #spectre #anarchive #aperiodicmonotile #mathematics #appliedmathematics #reimaginingtechnology #patterns -
Here is a grouping of similarly made turtle tiles.
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Some of my patterns are based on tilings with can be thought of as having overlapping parts, this overlap often consists of something that looks like a border.
An example is this sequence in which the “borders” are unclear until they resolve into borders of a snub square tiling, or its Cairo-type tiling dual.
https://mathstodon.xyz/@HypercubicPeg/109043217999286054
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Often when I do something like this, I can find an infinite class of “tiles” where the pattern along the border can be incremented in some predictable way.
A little while back, I had a go at trying to interpret the Hat tile in a similar way using edge-touching dodecagons. Here is one of the versions that I liked.
#mathart #mathsart #aperiodicMonotile #monotile #tiling #tilingTuesday
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Back in probably 2023, someone posted their monotile tile for 3D printers, for the purpose of replacing their hexagon tiles in, I think, the game Fjord.
I don't have a 3D printer, and I'm not close to anyone who does, but it doesn't matter, because The Game Crafter has them! They are listed as 53 and 43 mm across, I presume by measuring their longest and second-longest cross-sections.
#monotile #AperiodicMonotile #BoardGames
https://www.thegamecrafter.com/parts?query=infunity%20tiles%20hat
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I have a question about the aperiodic spectre tile (or the hat/turtle).
I know that the proof of aperiodicity works by showing that the tiles must fit together in a hierarchical structure that eventually repeats itself at a larger scale. But the larger units aren't literally scaled copies of the spectre. I also know that there is some freedom as to how you draw the edges of the spectre.
Is there a way you can draw the edges that allows you to literally use spectres to cover a larger copy of themselves? If so, is this way of doing it unique?
#Math #Maths #Mathematics #Spectre #Tiling #Aperiodic #AperiodicMonotile
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[Up and Atom] on the recent aperiodic monotile discoveries earlier this year
https://youtu.be/A1BhOVW8qZU
#aperiodic #monotile #AperiodicMonotile #mathstodon #mathematics #math #maths -
Monotile is the name of my heavy metal nerdcore theremin band. The songs have a time signature of π/4.
#monotile #AperiodicMonotile #HeavyMetal #nerdcore #theremin #pi #math #mathematics #mathtodon #music #musictodon
