#tilingtuesday — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #tilingtuesday, aggregated by home.social.
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Now the other side also has a bit of a pattern. I mucked with the photo settings a bit to try to pick up the iridescence of the beads.
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I wonder if #TilingTuesday folks know of any truchet-like physical tiles that are currently manufactured - ould like something colourful and "random" for my kitchen
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Inspiré de pièces de carrelage vu "en Los Nietos" #RegiondeMurcia #LaManga #spain
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Inspiré de pièces de carrelage vu "en Los Nietos" #RegiondeMurcia #LaManga #spain
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Inspiré de pièces de carrelage vu "en Los Nietos" #RegiondeMurcia #LaManga #spain
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Inspiré de pièces de carrelage vu "en Los Nietos" #RegiondeMurcia #LaManga #spain
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Inspiré de pièces de carrelage vu "en Los Nietos" #RegiondeMurcia #LaManga #spain
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ocd particles try to keep 5/6 equally spaced neighbors dot mp4 🤔
#TilingTuesday #animation #simulation #mathart #creativecoding
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ocd particles try to keep 5/6 equally spaced neighbors dot mp4 🤔
#TilingTuesday #animation #simulation #mathart #creativecoding
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ocd particles try to keep 5/6 equally spaced neighbors dot mp4 🤔
#TilingTuesday #animation #simulation #mathart #creativecoding
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ocd particles try to keep 5/6 equally spaced neighbors dot mp4 🤔
#TilingTuesday #animation #simulation #mathart #creativecoding
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A square paving with hexagons, Yogyakarta, Java, Indonesia
The leaves and cracks almost look like small trees
#TilingTuesday #geometry #tiling #MathArt #photography #design #TravelPhotography #Yogyakarta #Java #Indonesia #OpticalIllusion
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A square paving with hexagons, Yogyakarta, Java, Indonesia
The leaves and cracks almost look like small trees
#TilingTuesday #geometry #tiling #MathArt #photography #design #TravelPhotography #Yogyakarta #Java #Indonesia #OpticalIllusion
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A square paving with hexagons, Yogyakarta, Java, Indonesia
The leaves and cracks almost look like small trees
#TilingTuesday #geometry #tiling #MathArt #photography #design #TravelPhotography #Yogyakarta #Java #Indonesia #OpticalIllusion
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A square paving with hexagons, Yogyakarta, Java, Indonesia
The leaves and cracks almost look like small trees
#TilingTuesday #geometry #tiling #MathArt #photography #design #TravelPhotography #Yogyakarta #Java #Indonesia #OpticalIllusion
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A square paving with hexagons, Yogyakarta, Java, Indonesia
The leaves and cracks almost look like small trees
#TilingTuesday #geometry #tiling #MathArt #photography #design #TravelPhotography #Yogyakarta #Java #Indonesia #OpticalIllusion
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CW: Tesela
Usando figuras gigantes para forzar la maquina. He optimizado parte del algoritmo, pero sigue habiendo latencia. No me gusta perder el efecto de pintando de la zonas interiores.
🧩 ¡He jugado al Tesela y he conseguido 10922 puntos!
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📦 Distribución y tamaño de la bolsa: Ideal
💎 Total teselas: 1125
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🎨 Colores: 2614
🖼️ Perfil: 3368
⚪ Espacios: 4940
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Juega aquí: https://tesela.netlify.app/ -
Happy #TilingTuesday with these stone tiles from the Chinese Garden in Jardin Botanique de Montreal
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#TilingTuesday but wiθ ocd particle physics 🤨🤨🤨🤨🤨🤨🤨
(ðey attract/repel based on distance & color, & bounce) -
A ceiling of hexagons (presumably inspired by a symbol of Manchester, the worker bee), Manchester Airport, England
#TilingTuesday #geometry #tiling #MathArt #photography #design #pattern #manchester
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A ceiling of hexagons (presumably inspired by a symbol of Manchester, the worker bee), Manchester Airport, England
#TilingTuesday #geometry #tiling #MathArt #photography #design #pattern #manchester
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A ceiling of hexagons (presumably inspired by a symbol of Manchester, the worker bee), Manchester Airport, England
#TilingTuesday #geometry #tiling #MathArt #photography #design #pattern #manchester
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A ceiling of hexagons (presumably inspired by a symbol of Manchester, the worker bee), Manchester Airport, England
#TilingTuesday #geometry #tiling #MathArt #photography #design #pattern #manchester
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A ceiling of hexagons (presumably inspired by a symbol of Manchester, the worker bee), Manchester Airport, England
#TilingTuesday #geometry #tiling #MathArt #photography #design #pattern #manchester
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The Topkapi Scroll: Geometry and Ornament in Islamic Architecture
by Gülru Necipoğlu (1996, 384 pages, free PDF download)https://www.getty.edu/publications/virtuallibrary/9780892363353.html
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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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Peter Selinger has come up with a great way of generating hat tilings by overlaying a triangular grid on a periodic pattern, and placing a tile at each point that is not white, with the orientation and handedness of the tile determined by the colour of the point. A more thorough explanation is given in this preprint
https://arxiv.org/pdf/2604.20964,
where he and Sébastien Labbé show that this is a Markov partition. As mentioned in the paper, I came up with a similar construction a few years ago, but it required separate steps for tiles of a given orientation modulo 120.In this series of posts, I'll attempt to explain the connection between the two constructions, and demonstrate the analogous constructions for the hats-in-turtles and turtles-in-hats versions of the Spectre tiling. The aim is to give a sense of the main ideas, rather than a rigorous proof that this works.
Before I get into the details, here is a Markov partition for turtle tilings, where control / anchor points are located on the underside of the turtle's shell.
[Edit: For more background about the paper, see Sébastien's blog post: http://www.slabbe.org/blogue/2026/03/a-construction-of-the-hat-tilings-by-a-markov-partition/ This includes some printable files that can be used to construct patches of hat tilings in practice.]
(1/n)
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Es #tilingTuesday y sigo testeando el Tesela.
Cambios:
- Corregido bug: no cargaba correctamente la configuración anterior al retomar la sesión.
- Estadísticas sin tener que finalizar la partida.
- Botón para exportar la figura generada en PNG.🧩 I played Tesela and scored 440 points!
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📦 Bag size and distribution: Ideal
💎 Total tiles: 45
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🎨 Colors: 92
🖼️ Profile: 208
⚪ Spaces: 140
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Juega aquí: https://tesela.netlify.app -
#TilingTuesday but ðe tiles are ∛(z - (|α> + |β> + |ψ>)) IFS fractals 🕷️🪷
(ðe full image is ~7x4k)#tiling #fractal #mathart #abstract #mastoart #IFS #bigshanpee
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#TilingTuesday but ðe tiles are ∛(z - (|α> + |β> + |ψ>)) IFS fractals 🕷️🪷
(ðe full image is ~7x4k)#tiling #fractal #mathart #abstract #mastoart #IFS #bigshanpee
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#TilingTuesday but ðe tiles are ∛(z - (|α> + |β> + |ψ>)) IFS fractals 🕷️🪷
(ðe full image is ~7x4k)#tiling #fractal #mathart #abstract #mastoart #IFS #bigshanpee
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#TilingTuesday but ðe tiles are ∛(z - (|α> + |β> + |ψ>)) IFS fractals 🕷️🪷
(ðe full image is ~7x4k)#tiling #fractal #mathart #abstract #mastoart #IFS #bigshanpee
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A recursive tiling for #TilingTuesday
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#TilingTuesday but ðe tiles are √(z + |α> + |β>) IFS fractals🤨🤔
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My #garden provides today’s entry for #TilingTuesday
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@christianp @JimPropp I don’t know about rules, but the tiling on the left seems to have a clear structure.
If colour is ignored, it has rotational symmetry of order 2. In fact, it’s as if the tiling on the right has been copied, split and filled with a horizontal band of two pentagons and two rhombuses.
The tiling on the right was known by Dürer https://plus.maths.org/content/trouble-five and https://mathstodon.xyz/@foldworks/112711074311119074.
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For #TilingTuesday, 4-colourings of the Penrose P2 and P3 tilings, via refinements of their substitution systems.
Penrose tilings must _admit_ proper 4-colourings, by the Four Colour Theorem and the Erdős–de Bruijn theorem. 4CT says that any finite patch of a given plane tiling must have a 4-colouring; EdB says, in that case, so does the whole plane.
But EdB doesn't provide an efficient algorithm for constructing such a colouring; it only guarantees that one exists in principle. If you wanted a large patch of 4-coloured tiling, you might have to generate a finite patch first, and then run one of the horrible algorithms from proofs of 4CT. And once you'd done it, there'd be no guarantee that _that_ 4-coloured patch would extend to a 4-colouring of the whole plane.
What you want is a refined substitution system, containing multiple types of each Penrose tile shape, each already equipped with a colour. Then you could generate tilings efficiently from that, and you'd know you had not just a finite coloured patch, but a finite patch from a whole coloured plane.
For P3 (rhombs) this is easy. Split each rhomb into a subtype for each of its 10 rotations. The adjacency graph on those 20 classes has no self-edges. There's no reason to expect that graph to be _planar_, but it turns out it can be 4-coloured anyway. So you can 4-colour a P3 tiling by assigning colours based only on tile shape and orientation.
For P2 (kites and darts), if you make the same graph, it doesn't admit a 4-colouring. But as part of my transducers research, I wrote code to refine a substitution system further, by classifying each tile based on its immediate neighbours. If I classify the P2 tiles by orientation and _then_ run a pass of that refinement algorithm, it generates 50 subtypes of kite and 40 subtypes of dart, and the adjacency graph for _those_ classes is 4-colourable. So it takes a bit more work, but it's still a substitution system that directly delivers a 4-coloured P2 tiling.
The pictures here are derived from those two refined substitution systems. In each case, the 4-colouring of the class graph was done by brute force: SageMath's first_coloring() function. So the colours aren't optimised for aesthetics!
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What are the rules for tiling with regular pentagons and the parallelogram that fits in the gaps?
Here I've got two patches of tilings.
The one on the right has fivefold rotational symmetry and it looks like it could expand forever.
The one on the left doesn't have rotational symmetry. I think the difference was that I started with one pentagon with 4 others adjacent to it, which has sort of forced everything else. At the moment I've got two pentagons of degree 4, and I think I can get another pentagon of degree 4 by building on the left-hand side.
Is there something like the Aztec diamond theorem for this tiling? @JimPropp ?
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An external tiling, Brick Lane Mosque, London
The whole tiling can light up at night (there's a photo near the end of https://bricklanejammemasjid.org.uk/gallery)
#TilingTuesday #geometry #tiling #MathArt #photography #design #TravelPhotography #IslamicPattern #IslamicArt #mosque
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An external tiling, Brick Lane Mosque, London
The whole tiling can light up at night (there's a photo near the end of https://bricklanejammemasjid.org.uk/gallery)
#TilingTuesday #geometry #tiling #MathArt #photography #design #TravelPhotography #IslamicPattern #IslamicArt #mosque
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An external tiling, Brick Lane Mosque, London
The whole tiling can light up at night (there's a photo near the end of https://bricklanejammemasjid.org.uk/gallery)
#TilingTuesday #geometry #tiling #MathArt #photography #design #TravelPhotography #IslamicPattern #IslamicArt #mosque
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An external tiling, Brick Lane Mosque, London
The whole tiling can light up at night (there's a photo near the end of https://bricklanejammemasjid.org.uk/gallery)
#TilingTuesday #geometry #tiling #MathArt #photography #design #TravelPhotography #IslamicPattern #IslamicArt #mosque
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