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foldworksPavement tiling, Hurghada, Egypt<a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener" target="_blank">#TilingTuesday</a> <a href="https://mathstodon.xyz/tags/geometry" class="mention hashtag" rel="nofollow noopener" target="_blank">#geometry</a> <a href="https://mathstodon.xyz/tags/tiling" class="mention hashtag" rel="nofollow noopener" target="_blank">#tiling</a> <a href="https://mathstodon.xyz/tags/MathArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#MathArt</a> <a href="https://mathstodon.xyz/tags/photography" class="mention hashtag" rel="nofollow noopener" target="_blank">#photography</a> <a href="https://mathstodon.xyz/tags/design" class="mention hashtag" rel="nofollow noopener" target="_blank">#design</a> <a href="https://mathstodon.xyz/tags/TravelPhotography" class="mention hashtag" rel="nofollow noopener" target="_blank">#TravelPhotography</a>

꧁ᐊ𰻞ᵕ̣̣̣̣̣̣́́♛ᵕ̣̣̣̣̣̣́́𰻞ᐅ꧂you could probably make ðis irl by cutting some planarians & locking ðem togeðer🪱<a href="https://mastodon.gamedev.place/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener" target="_blank">#TilingTuesday</a> <a href="https://mastodon.gamedev.place/tags/%C3%A7ue" class="mention hashtag" rel="nofollow noopener" target="_blank">#çue</a> <a href="https://mastodon.gamedev.place/tags/tiling" class="mention hashtag" rel="nofollow noopener" target="_blank">#tiling</a> <a href="https://mastodon.gamedev.place/tags/mastoart" class="mention hashtag" rel="nofollow noopener" target="_blank">#mastoart</a> <a href="https://mastodon.gamedev.place/tags/mathart" class="mention hashtag" rel="nofollow noopener" target="_blank">#mathart</a> <a href="https://mastodon.gamedev.place/tags/abstract" class="mention hashtag" rel="nofollow noopener" target="_blank">#abstract</a>

Dani Laura (they/she/he)More tesselations produced by the partitions. First two related to the root of silver ratio rectangles. Third is related to the golden one, applying an algorithm to colour each rectangle depending on its ancestors sizes. Finally, and artistic rendition of the golden partition where each rectangle is shrunk before partition to produce a frame. <a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener" target="_blank">#TilingTuesday</a> <a href="https://mathstodon.xyz/tags/geometry" class="mention hashtag" rel="nofollow noopener" target="_blank">#geometry</a> <a href="https://mathstodon.xyz/tags/tiling" class="mention hashtag" rel="nofollow noopener" target="_blank">#tiling</a> <a href="https://mathstodon.xyz/tags/mathart" class="mention hashtag" rel="nofollow noopener" target="_blank">#mathart</a> <a href="https://mathstodon.xyz/tags/algorithmicArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#algorithmicArt</a>

Dani Laura (they/she/he)I have (re)discovered partitions of the rectangles defined by the square root of metallic ratios into similar rectangles. In the case of the golden ratio it was known, as can be seen in the excellent site <a href="https://tilings.math.uni-bielefeld.de/substitution/rectangulo-dorado/" rel="nofollow noopener" translate="no" target="_blank">https://tilings.math.uni-bielefeld.de/substitution/rectangulo-dorado/</a> . I think the results are novel for the next ratios, here I present the partitions for the silver and bronze ratios. More complex partitions can be deduced from them. In the fourth image there is a grid with the eight possible tesselations related to the golden ratio, depending on the orientation of the rectangles produced. All are non-periodic, but some look more regular than other. See continuation post for more. <a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener" target="_blank">#TilingTuesday</a> <a href="https://mathstodon.xyz/tags/Mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#Mathematics</a> <a href="https://mathstodon.xyz/tags/geometry" class="mention hashtag" rel="nofollow noopener" target="_blank">#geometry</a> <a href="https://mathstodon.xyz/tags/tiling" class="mention hashtag" rel="nofollow noopener" target="_blank">#tiling</a>

n-gonsFloor, Kalmar Castle<a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener" target="_blank">#TilingTuesday</a> <a href="https://mathstodon.xyz/tags/Tiling" class="mention hashtag" rel="nofollow noopener" target="_blank">#Tiling</a>

foldworksPavement tiling, Fes, Morocco<a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener" target="_blank">#TilingTuesday</a> <a href="https://mathstodon.xyz/tags/geometry" class="mention hashtag" rel="nofollow noopener" target="_blank">#geometry</a> <a href="https://mathstodon.xyz/tags/tiling" class="mention hashtag" rel="nofollow noopener" target="_blank">#tiling</a> <a href="https://mathstodon.xyz/tags/MathArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#MathArt</a> <a href="https://mathstodon.xyz/tags/photography" class="mention hashtag" rel="nofollow noopener" target="_blank">#photography</a> <a href="https://mathstodon.xyz/tags/design" class="mention hashtag" rel="nofollow noopener" target="_blank">#design</a> <a href="https://mathstodon.xyz/tags/TravelPhotography" class="mention hashtag" rel="nofollow noopener" target="_blank">#TravelPhotography</a> <a href="https://mathstodon.xyz/tags/IslamicPattern" class="mention hashtag" rel="nofollow noopener" target="_blank">#IslamicPattern</a>

This Is My GlasgowLove these tiles from a tenement close in the Mount Florida area of Glasgow.<a href="https://mastodon.scot/tags/glasgow" class="mention hashtag" rel="nofollow noopener" target="_blank">#glasgow</a> <a href="https://mastodon.scot/tags/mountflorida" class="mention hashtag" rel="nofollow noopener" target="_blank">#mountflorida</a> <a href="https://mastodon.scot/tags/tenement" class="mention hashtag" rel="nofollow noopener" target="_blank">#tenement</a> <a href="https://mastodon.scot/tags/architecture" class="mention hashtag" rel="nofollow noopener" target="_blank">#architecture</a> <a href="https://mastodon.scot/tags/architecturephotography" class="mention hashtag" rel="nofollow noopener" target="_blank">#architecturephotography</a> <a href="https://mastodon.scot/tags/glasgowtenements" class="mention hashtag" rel="nofollow noopener" target="_blank">#glasgowtenements</a> <a href="https://mastodon.scot/tags/tiles" class="mention hashtag" rel="nofollow noopener" target="_blank">#tiles</a> <a href="https://mastodon.scot/tags/tiling" class="mention hashtag" rel="nofollow noopener" target="_blank">#tiling</a> <a href="https://mastodon.scot/tags/ceramics" class="mention hashtag" rel="nofollow noopener" target="_blank">#ceramics</a> <a href="https://mastodon.scot/tags/tenementtiles" class="mention hashtag" rel="nofollow noopener" target="_blank">#tenementtiles</a>

n-gonsLooking for tiling patterns i. Mom’s dahlias. <a href="https://mathstodon.xyz/tags/bloomscrolling" class="mention hashtag" rel="nofollow noopener" target="_blank">#bloomscrolling</a> <a href="https://mathstodon.xyz/tags/dahlia" class="mention hashtag" rel="nofollow noopener" target="_blank">#dahlia</a> <a href="https://mathstodon.xyz/tags/tiling" class="mention hashtag" rel="nofollow noopener" target="_blank">#tiling</a>

꧁ᐊ𰻞ᵕ̣̣̣̣̣̣́́♛ᵕ̣̣̣̣̣̣́́𰻞ᐅ꧂start wiθ a cubic h🐝o🐝n🐝e🐝y🐝c🐝o🐝m🐝b split each cube into 6 pyramids merge each pair ðat shares a 4gon into irregular octahedrons & u get ðe almost regular octahedral h🍯o🍯n🍯e🍯y🍯c🍯o🍯m🍯b(yes, someone made ðis a technical term, rly)<a href="https://mastodon.gamedev.place/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener" target="_blank">#TilingTuesday</a> <a href="https://mastodon.gamedev.place/tags/3d" class="mention hashtag" rel="nofollow noopener" target="_blank">#3d</a> <a href="https://mastodon.gamedev.place/tags/honeycomb" class="mention hashtag" rel="nofollow noopener" target="_blank">#honeycomb</a> <a href="https://mastodon.gamedev.place/tags/tiling" class="mention hashtag" rel="nofollow noopener" target="_blank">#tiling</a> <a href="https://mastodon.gamedev.place/tags/mathart" class="mention hashtag" rel="nofollow noopener" target="_blank">#mathart</a> <a href="https://mastodon.gamedev.place/tags/geometry" class="mention hashtag" rel="nofollow noopener" target="_blank">#geometry</a> <a href="https://mastodon.gamedev.place/tags/animation" class="mention hashtag" rel="nofollow noopener" target="_blank">#animation</a> <a href="https://mastodon.gamedev.place/tags/creativecoding" class="mention hashtag" rel="nofollow noopener" target="_blank">#creativecoding</a>

foldworksPavement tiling, Ouarzazate, Morocco <a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener" target="_blank">#TilingTuesday</a> <a href="https://mathstodon.xyz/tags/geometry" class="mention hashtag" rel="nofollow noopener" target="_blank">#geometry</a> <a href="https://mathstodon.xyz/tags/tiling" class="mention hashtag" rel="nofollow noopener" target="_blank">#tiling</a> <a href="https://mathstodon.xyz/tags/MathArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#MathArt</a> <a href="https://mathstodon.xyz/tags/photography" class="mention hashtag" rel="nofollow noopener" target="_blank">#photography</a> <a href="https://mathstodon.xyz/tags/design" class="mention hashtag" rel="nofollow noopener" target="_blank">#design</a> <a href="https://mathstodon.xyz/tags/TravelPhotography" class="mention hashtag" rel="nofollow noopener" target="_blank">#TravelPhotography</a> <a href="https://mathstodon.xyz/tags/octagon" class="mention hashtag" rel="nofollow noopener" target="_blank">#octagon</a>

This Is My GlasgowLove these decorative tiles at the entrance to the 1890s former Sanitary Chambers on Montrose Street in central Glasgow. If you zoom in, the pattern on the lower tiles does rather look, to me at any rate, like a strange crested bird with wild eyes, but there's nothing wrong with that!<a href="https://mastodon.scot/tags/glasgow" class="mention hashtag" rel="nofollow noopener" target="_blank">#glasgow</a> <a href="https://mastodon.scot/tags/architecture" class="mention hashtag" rel="nofollow noopener" target="_blank">#architecture</a> <a href="https://mastodon.scot/tags/tiles" class="mention hashtag" rel="nofollow noopener" target="_blank">#tiles</a> <a href="https://mastodon.scot/tags/tiling" class="mention hashtag" rel="nofollow noopener" target="_blank">#tiling</a> <a href="https://mastodon.scot/tags/ceramics" class="mention hashtag" rel="nofollow noopener" target="_blank">#ceramics</a> <a href="https://mastodon.scot/tags/design" class="mention hashtag" rel="nofollow noopener" target="_blank">#design</a> <a href="https://mastodon.scot/tags/designdetail" class="mention hashtag" rel="nofollow noopener" target="_blank">#designdetail</a>

RasmusModule that can be used to create the structure. (2/2)<a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener" target="_blank">#TilingTuesday</a> <a href="https://mathstodon.xyz/tags/tiling" class="mention hashtag" rel="nofollow noopener" target="_blank">#tiling</a> <a href="https://mathstodon.xyz/tags/geometry" class="mention hashtag" rel="nofollow noopener" target="_blank">#geometry</a> <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#math</a> <a href="https://mathstodon.xyz/tags/3d" class="mention hashtag" rel="nofollow noopener" target="_blank">#3d</a>

RasmusMonohedral triangle tiling of the gyroid, which is the dual tessellation of a partial Cayley surface complex of the group: ``` G = ⟨ f₁,t₁ | f₁², t₁⁶, (f₁t₁)⁴, (f₁t₁f₁t₁⁻¹f₁t₁²)² ⟩ ```Ball of radius 21. (1/2)<a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener" target="_blank">#TilingTuesday</a> <a href="https://mathstodon.xyz/tags/tiling" class="mention hashtag" rel="nofollow noopener" target="_blank">#tiling</a> <a href="https://mathstodon.xyz/tags/geometry" class="mention hashtag" rel="nofollow noopener" target="_blank">#geometry</a> <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#math</a> <a href="https://mathstodon.xyz/tags/3d" class="mention hashtag" rel="nofollow noopener" target="_blank">#3d</a>

foldworksBase of a Celtic cross (c. 1890), Glasnevin Cemetery (Irish: Reilig Ghlas Naíon), Dublin, Ireland<a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener" target="_blank">#TilingTuesday</a> <a href="https://mathstodon.xyz/tags/geometry" class="mention hashtag" rel="nofollow noopener" target="_blank">#geometry</a> <a href="https://mathstodon.xyz/tags/tiling" class="mention hashtag" rel="nofollow noopener" target="_blank">#tiling</a> <a href="https://mathstodon.xyz/tags/MathArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#MathArt</a> <a href="https://mathstodon.xyz/tags/photography" class="mention hashtag" rel="nofollow noopener" target="_blank">#photography</a> <a href="https://mathstodon.xyz/tags/design" class="mention hashtag" rel="nofollow noopener" target="_blank">#design</a> <a href="https://mathstodon.xyz/tags/celtic" class="mention hashtag" rel="nofollow noopener" target="_blank">#celtic</a> <a href="https://mathstodon.xyz/tags/CelticCross" class="mention hashtag" rel="nofollow noopener" target="_blank">#CelticCross</a> <a href="https://mathstodon.xyz/tags/triskelion" class="mention hashtag" rel="nofollow noopener" target="_blank">#triskelion</a> <a href="https://mathstodon.xyz/tags/spiral" class="mention hashtag" rel="nofollow noopener" target="_blank">#spiral</a>

GNOME🪟 "Unlock Modern Window Management in GNOME with Tiling Shell" with Domenico Ferraro at <a href="https://floss.social/tags/GUADEC2025" class="mention hashtag" rel="nofollow noopener" target="_blank">#GUADEC2025</a> 📅 25 July 🕒 15:15 CEST 📍 Brescia🧭 Layout editor, Snap Assistant & more—Domenico shows how Tiling Shell transforms GNOME window management.🔗 <a href="https://events.gnome.org/event/259/contributions/1241/" rel="nofollow noopener" translate="no" target="_blank">https://events.gnome.org/event/259/contributions/1241/</a><a href="https://floss.social/tags/GNOME" class="mention hashtag" rel="nofollow noopener" target="_blank">#GNOME</a> <a href="https://floss.social/tags/Tiling" class="mention hashtag" rel="nofollow noopener" target="_blank">#Tiling</a> <a href="https://floss.social/tags/Linux" class="mention hashtag" rel="nofollow noopener" target="_blank">#Linux</a> <a href="https://floss.social/tags/FOSS" class="mention hashtag" rel="nofollow noopener" target="_blank">#FOSS</a> <a href="https://floss.social/tags/Productivity" class="mention hashtag" rel="nofollow noopener" target="_blank">#Productivity</a>

This Is My GlasgowA rather beautiful bit of tiling from a tenement close in the Garnethill area of Glasgow.<a href="https://mastodon.scot/tags/glasgow" class="mention hashtag" rel="nofollow noopener" target="_blank">#glasgow</a> <a href="https://mastodon.scot/tags/tile" class="mention hashtag" rel="nofollow noopener" target="_blank">#tile</a> <a href="https://mastodon.scot/tags/tiling" class="mention hashtag" rel="nofollow noopener" target="_blank">#tiling</a> <a href="https://mastodon.scot/tags/ceramics" class="mention hashtag" rel="nofollow noopener" target="_blank">#ceramics</a> <a href="https://mastodon.scot/tags/tenementtiles" class="mention hashtag" rel="nofollow noopener" target="_blank">#tenementtiles</a> <a href="https://mastodon.scot/tags/tenement" class="mention hashtag" rel="nofollow noopener" target="_blank">#tenement</a> <a href="https://mastodon.scot/tags/glasgowtenements" class="mention hashtag" rel="nofollow noopener" target="_blank">#glasgowtenements</a> <a href="https://mastodon.scot/tags/garnethill" class="mention hashtag" rel="nofollow noopener" target="_blank">#garnethill</a> <a href="https://mastodon.scot/tags/architecture" class="mention hashtag" rel="nofollow noopener" target="_blank">#architecture</a> <a href="https://mastodon.scot/tags/architecturephotography" class="mention hashtag" rel="nofollow noopener" target="_blank">#architecturephotography</a>

꧁ᐊ𰻞ᵕ̣̣̣̣̣̣́́♛ᵕ̣̣̣̣̣̣́́𰻞ᐅ꧂4d shapes 9d colors 😳<a href="https://mastodon.gamedev.place/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener" target="_blank">#TilingTuesday</a> <a href="https://mastodon.gamedev.place/tags/4d" class="mention hashtag" rel="nofollow noopener" target="_blank">#4d</a> <a href="https://mastodon.gamedev.place/tags/mathart" class="mention hashtag" rel="nofollow noopener" target="_blank">#mathart</a> <a href="https://mastodon.gamedev.place/tags/animation" class="mention hashtag" rel="nofollow noopener" target="_blank">#animation</a> <a href="https://mastodon.gamedev.place/tags/abstract" class="mention hashtag" rel="nofollow noopener" target="_blank">#abstract</a> <a href="https://mastodon.gamedev.place/tags/tiling" class="mention hashtag" rel="nofollow noopener" target="_blank">#tiling</a> <a href="https://mastodon.gamedev.place/tags/mastoart" class="mention hashtag" rel="nofollow noopener" target="_blank">#mastoart</a>

RasmusThe hexagonal tile is of course slightly skewed. (2/3) <a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener" target="_blank">#TilingTuesday</a> <a href="https://mathstodon.xyz/tags/tiling" class="mention hashtag" rel="nofollow noopener" target="_blank">#tiling</a> <a href="https://mathstodon.xyz/tags/geometry" class="mention hashtag" rel="nofollow noopener" target="_blank">#geometry</a> <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#math</a>

RasmusThe tiling can be divided down into different modules of higher genus. One can be seen below. (2/3) <a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener" target="_blank">#TilingTuesday</a> <a href="https://mathstodon.xyz/tags/tiling" class="mention hashtag" rel="nofollow noopener" target="_blank">#tiling</a> <a href="https://mathstodon.xyz/tags/geometry" class="mention hashtag" rel="nofollow noopener" target="_blank">#geometry</a> <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#math</a>

RasmusMonohedral Hexagonal Tiling of infinite stacked surface with triangular, hexagonal and rhombic channels. (1/3) <a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener" target="_blank">#TilingTuesday</a> <a href="https://mathstodon.xyz/tags/tiling" class="mention hashtag" rel="nofollow noopener" target="_blank">#tiling</a> <a href="https://mathstodon.xyz/tags/geometry" class="mention hashtag" rel="nofollow noopener" target="_blank">#geometry</a> <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#math</a>

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