#monotile — Public Fediverse posts

Bad Apple!! but it's an aperiodic tiling using the hat monotile.

See also on PeerTube and YouTube:

https://makertube.net/w/fs3rbUMqJeVcZagdZQ6RfH

https://www.youtube.com/watch?v=RLZx-5ymfDU&list=RDRLZx-5ymfDU

#badapple #monotile #aperiodic #meme #tiling

Well this is, indeed, fun.
I have lots of tweaks to do to the final output, but it works.
My only challenge now is knowing when to stop, ie have I covered the rectangle I want? Slightly harder than it sounds, but I have a plan #spectre #monotile

Here is a grouping of similarly made turtle tiles.

#mathart #mathart #aperiodicMonotile #monotile #tiling

I’ve finally started playing around with the idea of spectre tiles and have noticed something that looks somewhat interesting.

I wonder if it is specific to the particular tiling that I was looking at, or if it is true in general for tilings using spectres.

I noticed that the spectre tile can be decomposed into two pieces, one a 3-fold symmetric thing involving the head part of the spectre and the other a mirrored pair of irregular 120°-120°-90°-120°-90° pentagons (like those in the Cairo tiling that is also the dual of the snub-square tiling). An image search later led me to Dave Smith’s site (https://hedraweb.wordpress.com/2023/07/16/wheel-tiling-and-the-spectre/) where he described these as the propeller and bow-tie used in the wheel tiling, and how they relate to the spectre.

Using a spectre tiling from https://cs.uwaterloo.ca/~csk/spectre/, I was trying something involving squares, triangles and equilateral-but-not-equiangular hexagons, and that ended up making me notice a lot of triangular groupings of 1, 3, and 6 hexagons showing up. I thought that it might be worth looking at how the propellers fit on that tiling instead.

I coloured the propellers such that the same colour indicates the same orientation. The parts with green showing through are from the “odd tiles” in the original picture. Each odd tile is surrounded by six triangular groupings of propellers which alternate in colour.

I do not know if this is a fluke because of particular choices made when constructing that patch of tiling.

Any ideas? Has someone tried it using a patch from a different spectre tiling?

I apologize in advance if it is something that is already well-known. I haven’t read much of the relevant literature at this point…only enough to start playing 😊.
@csk #monotile

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

————

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

What do you get when your #ADnD #Dungeon master is a #maths nerd? You get a #MathsPuzzle like this: there's a weirdly shaped hole in the wall, and a bunch of puzzle pieces on the floor looking all the same... #monotile

Note: I'm not looking for a solution, we want to figure it out in our next session!

Found the posting.

The game was Fjords, plural, and the link to the pieces is included.

#BoardGames #Monotile #Tiling

https://mastodon.social/@galaxy_map/110134343462015513

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

Math friends - I need your help:

Does anyone know a source for cookie cutters in the form of a monotile? :monotile:

Instructions to 3D print one would be fine, too.

#math #cookies #monotile #einstein :monotile:

Hats on a soccer ball by @jonpaulsballs #BridgesMathArt #aperiodic #monotile #tiling #geometry

Hats on a soccer ball by @jonpaulsballs #BridgesMathArt #aperiodic #monotile #tiling #geometry

When it comes to debugging, I have a bad habit of sometimes guessing parameters when I think that all that prevents me getting the output I expect is something simple, like an incorrect sign. Invariably I end up wasting far too much time making increasingly complicated guesses, when a few minutes thought and some pen and paper would have revealed the bug. I don't recommend this habit to anyone, but in one instance it led me to discover a series of tilings that I probably wouldn't have found otherwise.

Take a tiling of turtle tiles (a version of the chiral aperiodic monotile), throw away the tiles with less frequent handedness, and flip the other tiles about the axis shown in the first image. This doesn't produce a new tiling, since there will be overlaps. However, the tiles can be grouped in roughly triangular clusters of 1, 3 or 6 tiles, all with the same orientation modulo \(120^\circ\), and the tiles in each cluster don't overlap after flipping. In addition, the clusters of flipped tiles can be translated in a consistent manner to avoid overlaps, leaving a partial tiling whose gaps all have the same shape - the 'rooster'.

(1/n)
#tilingTuesday #aperiodic #monotile #tiling

When it comes to debugging, I have a bad habit of sometimes guessing parameters when I think that all that prevents me getting the output I expect is something simple, like an incorrect sign. Invariably I end up wasting far too much time making increasingly complicated guesses, when a few minutes thought and some pen and paper would have revealed the bug. I don't recommend this habit to anyone, but in one instance it led me to discover a series of tilings that I probably wouldn't have found otherwise.

Take a tiling of turtle tiles (a version of the chiral aperiodic monotile), throw away the tiles with less frequent handedness, and flip the other tiles about the axis shown in the first image. This doesn't produce a new tiling, since there will be overlaps. However, the tiles can be grouped in roughly triangular clusters of 1, 3 or 6 tiles, all with the same orientation modulo \(120^\circ\), and the tiles in each cluster don't overlap after flipping. In addition, the clusters of flipped tiles can be translated in a consistent manner to avoid overlaps, leaving a partial tiling whose gaps all have the same shape - the 'rooster'.

(1/n)
#tilingTuesday #aperiodic #monotile #tiling

Our first attempt to aperiodically tile with the Spectre piece resulted in... Switzerland. Who knew?

@nervous_jessica @nervous_jesse #monotile #spectre #puzzles

This week at Café Scientifique in Seven Arts, Leeds, my colleague Alastair Rucklidge talked about the recently discovered aperiodic monotile :monotile: :monotile_spectre: I was there and it was amazing to see the very humble David Smith, who made the discovery 😍 . There was a good audience and lively questions and discussions at the end, so well done Alastair and thanks to the organizers.

#Leeds #CafeScientifique #monotile #tiling

Inside the Hat: Kites, Triangles & Hexagons #monotile #kickstarter #infunitytiles https://www.kickstarter.com/projects/atlasgames/infunity-tiles/posts/3938757

OK. I have not worked this through yet. But the kites that form a Hat aperiodic #monotile imply an overlay of triangles, like so:

[Up and Atom] on the recent aperiodic monotile discoveries earlier this year
https://youtu.be/A1BhOVW8qZU
#aperiodic #monotile #AperiodicMonotile #mathstodon #mathematics #math #maths

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!

I think I have found an original simple proof the the Turtle #aperiodic #monotile cannot tile periodically. https://mathblock8128.wordpress.com/2023/07/15/the-turtle-prototile-is-not-periodic-a-simple-proof/

Hey #STEM and #nonbinary folx!
🦇​
Do you need a full sized Journal with Date/Day of Week.Time at top with dots in place of lines on the page?
What if it had 200 pages?
:flag_nonbinary:​
I think you might like this #monotile #specter design in a hardcover (soft cover coming soon)
🖤​
So come on and show your #PRIDE and get a nice journal that was designed by a lovely #spacecat that also happens to be incredibly sexy.

CLICK BELOW!

https://a.co/d/ieNqUWD

Hey #STEM and #nonbinary folx!
🦇​
Do you need a full sized Journal with Date/Day of Week.Time at top with dots in place of lines on the page?
What if it had 200 pages?
:flag_nonbinary:​
I think you might like this #monotile #specter design in a hardcover (soft cover coming soon)
🖤​
So come on and show your #PRIDE and get a nice journal that was designed by a lovely #spacecat that also happens to be incredibly sexy.

CLICK BELOW!

https://a.co/d/ieNqUWD

Hey #STEM and #nonbinary folx!
🦇​
Do you need a full sized Journal with Date/Day of Week.Time at top with dots in place of lines on the page?
What if it had 200 pages?
:flag_nonbinary:​
I think you might like this #monotile #specter design in a hardcover (soft cover coming soon)
🖤​
So come on and show your #PRIDE and get a nice journal that was designed by a lovely #spacecat that also happens to be incredibly sexy.

CLICK BELOW!

https://a.co/d/ieNqUWD

Hey #STEM and #nonbinary folx!
🦇​
Do you need a full sized Journal with Date/Day of Week.Time at top with dots in place of lines on the page?
What if it had 200 pages?
:flag_nonbinary:​
I think you might like this #monotile #specter design in a hardcover (soft cover coming soon)
🖤​
So come on and show your #PRIDE and get a nice journal that was designed by a lovely #spacecat that also happens to be incredibly sexy.

CLICK BELOW!

https://a.co/d/ieNqUWD

A school of spectre tile fish.

Spectre tile == chiral aperiodic monotile.

The tile: https://hedraweb.wordpress.com/
Tiles created with: https://github.com/Kosovircek/SpectreTileMaker
Inpainting with stable diffusion: https://github.com/AUTOMATIC1111/stable-diffusion-webui
Using model AnythingV5Ink_ink: https://civitai.com/models/9409/or-anything-v5ink
Prompt: a fish

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

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.

Oi, maths people (‘cos I’m not one):

Can there be such a thing as a Voronoi aperiodic monotile?

#maths #voronoi #aperiodic #monotile

I guess that #aperiodic #monotile tiled floors could be annoying to #OCD people. Sometimes I find myself avoiding the gaps between tiles, but not compulsively or obsessively.
#NumberPhile

https://youtu.be/ArADlJx7SlU?list=TLPQMjUwNjIwMjNvFmKlxUoq-g

Journal I designed is now up for sale! #STEM Folx that like #aperiodic monotile stuff check it out!

#monotile #journal #hardback #pride #nonbinary

Non-Binary Specter Journal https://a.co/d/22rlUMl

Just got the #PROOF copy of #journal I designed. The art will be used on other things as well but I really wanted to have a useful item for #PRIDE related reasons. Has taken much longer than expected to get proof and such. Better late than never I suppose.
🦇​
You #STEM kids should love the series as I finish them.
:flag_nonbinary:​
#monotile #hat #nailsthatglow #art

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

@alexlomas printed me some of @carlos_lunamota’s version of the Smith, Myers, and Goodman-Strauss aperiodic monotile (https://www.printables.com/model/448090-aperiodic-monotile-pipes) So cool 😍

#Aperiodic #Tesselation #Monotile #3Dprinting #Einstein

A new variation of Hierarchical Colouring #aperiodicmonotile / Image 3 : levels=4, Top MetaT=H, Motif : high F weight.
----------
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

@jchyip
Great!
"[...] a pattern that never repeats".
"The einstein sits in a weird purgatory between #order and #disorder."
An aperiodic #monotile.

Before: periodic monotiles.

My guess:
the #Triangle (prime number 3) is the key element to order (in terms of 'arrange') such an asymetric existence.

#Thx4sharing, @gerritbeine !

https://www.architonic.com/es/product/valence-design-monotile-concrete-light-grey/1501310

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