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Alexandre MuñizThere are 18 hexominoes that can be traversed with orthogonal moves without revisiting cells. This tiling has a closed tour, where all of the cells in each hexomino are visited in an uninterrupted sequence. (I have a blog post in the works about this stuff, but it's not quite done, and Tuesday very nearly is.)<a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TilingTuesday</a>

RasmusEnneagonal infinite tiling <a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TilingTuesday</a> (1/3)

TimemiTUltraFractal6 IFSBarnsley for <a href="https://mastodon.scot/tags/tilingtuesday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#tilingtuesday</a>

n-gonsSierpinski Pyramid Tiling for <a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TilingTuesday</a> This kind of pyramid is a quarter of a cube.<a href="https://mathstodon.xyz/tags/Voxel" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Voxel</a> <a href="https://mathstodon.xyz/tags/Geometry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Geometry</a> <a href="https://mathstodon.xyz/tags/Tiling" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Tiling</a> <a href="https://mathstodon.xyz/tags/Fractal" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Fractal</a> <a href="https://mathstodon.xyz/tags/MathArt" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#MathArt</a>

Heribert SchützDear <a href="https://mastodon.social/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TilingTuesday</a> community,A while ago I implemented a graphical web app folding certain flat shapes to polyhedra: <a href="https://hcschuetz.github.io/polyhedron-star/dist/" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://hcschuetz.github.io/polyhedron-star/dist/</a>A few tilings are included, but I'd like to add more and ask you for contributions.A compatible tiling should fit with a triangular or a quad grid. I'm particularly (but not only) interested in tilings that are *not* invariant to reflections.

C. KnodelHappy <a href="https://mastodon.de/tags/tilingtuesday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#tilingtuesday</a> everybody!This is made with <a href="https://mastodon.de/tags/openprocessing" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#openprocessing</a> and may be enhanced in the future.<a href="https://mastodon.de/tags/processing" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#processing</a> <a href="https://mastodon.de/tags/CreativeCoding" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#CreativeCoding</a> <a href="https://mastodon.de/tags/genart" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#genart</a>

꧁ᐊ𰻞ᵕ̣̣̣̣̣̣́́♛ᵕ̣̣̣̣̣̣́́𰻞ᐅ꧂⭕'དཔལ་བེའུ།*16 🥨 (I'm like 90% sure ðe orange bit forms a single loop)<a href="https://mastodon.gamedev.place/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TilingTuesday</a> <a href="https://mastodon.gamedev.place/tags/knots" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#knots</a> <a href="https://mastodon.gamedev.place/tags/tiling" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#tiling</a> <a href="https://mastodon.gamedev.place/tags/mathart" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mathart</a> <a href="https://mastodon.gamedev.place/tags/pixelart" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#pixelart</a> <a href="https://mastodon.gamedev.place/tags/abstract" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#abstract</a>

foldworksStreet decoration featuring eight-pointed stars, Buôn Ma Thuột, Vietnam <a href="https://mathstodon.xyz/tags/Tiling" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Tiling</a> <a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TilingTuesday</a> <a href="https://mathstodon.xyz/tags/Pattern" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Pattern</a> <a href="https://mathstodon.xyz/tags/Geometry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Geometry</a> <a href="https://mathstodon.xyz/tags/MathArt" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#MathArt</a> <a href="https://mathstodon.xyz/tags/MathsArt" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#MathsArt</a>

Bojidar MarinovI've always enjoyed toying around with "knight polygons" - polygons whose every edge is a chess knight's move. So, it was only natural to use them for a floral pattern (a truncated square tiling), for a lily flower origami.<a href="https://mastodon.social/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TilingTuesday</a> <a href="https://mastodon.social/tags/origami" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#origami</a> <a href="https://mastodon.social/tags/flowers" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#flowers</a>

Malwen<a href="https://toot.wales/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TilingTuesday</a> Created in <a href="https://toot.wales/tags/OneLab" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#OneLab</a> for Android

Dani Laura (they/she/he)I have found a novel family of rep-tiles which produce aperiodic tilings. The prototile is a triangle with smallest side 1 and biggest side 2, the other side is 1 < x <= 2. The family includes one pointed isosceles triangle, the right triangle of angles 30-60-90 (half an equilateral triangle), and other scalene, obtuse or acute, triangles. The first image shows relevant members of the family, the second the substitution rule. The isosceles triangle of the family has another already known aperiodic tiling ( <a href="https://tilings.math.uni-bielefeld.de/substitution/viper/" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://tilings.math.uni-bielefeld.de/substitution/viper/</a> ) which looks the same but is different because there the tile has no reflections, whereas here some tiles are reflected (in the case of the isosceles triangle the reflection makes a difference when applying the substitution). Figure 3 shows the difference between that tessellation and the one proposed here, mine has just four slopes. Last figure shows a zoom into one big instance of the tiling for the right triangle. <a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TilingTuesday</a> <a href="https://mathstodon.xyz/tags/tiling" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#tiling</a> <a href="https://mathstodon.xyz/tags/Mathart" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Mathart</a> <a href="https://mathstodon.xyz/tags/geometry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#geometry</a> <a href="https://mathstodon.xyz/tags/Mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Mathematics</a>

RasmusGrowth steps 1 - 12 of genus 289 oriented surface made of 1152 hexagonal tiles. <a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TilingTuesday</a>

Jean-Baptiste EtienneAn other "<a href="https://mathstodon.xyz/tags/truchet" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#truchet</a>" <a href="https://mathstodon.xyz/tags/animation" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#animation</a> for <a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TilingTuesday</a>

Σ(i³) = (Σi)²<a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TilingTuesday</a>

꧁ᐊ𰻞ᵕ̣̣̣̣̣̣́́♛ᵕ̣̣̣̣̣̣́́𰻞ᐅ꧂traitoR<a href="https://mastodon.gamedev.place/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TilingTuesday</a> <a href="https://mastodon.gamedev.place/tags/vibes" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#vibes</a> <a href="https://mastodon.gamedev.place/tags/tiling" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#tiling</a> <a href="https://mastodon.gamedev.place/tags/abstract" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#abstract</a> <a href="https://mastodon.gamedev.place/tags/mathart" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mathart</a> <a href="https://mastodon.gamedev.place/tags/mastoart" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mastoart</a>

TimemiTJust spotted the <a href="https://mastodon.scot/tags/tilingtuesday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#tilingtuesday</a> tag..must have a few of them in my folders...here's a mandelbulber tiling.

foldworksWindow, County Hall, Preston, Lancashire, England <a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TilingTuesday</a> <a href="https://mathstodon.xyz/tags/geometry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#geometry</a> <a href="https://mathstodon.xyz/tags/tiling" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#tiling</a> <a href="https://mathstodon.xyz/tags/MathArt" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#MathArt</a> <a href="https://mathstodon.xyz/tags/photography" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#photography</a> <a href="https://mathstodon.xyz/tags/pattern" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#pattern</a> <a href="https://mathstodon.xyz/tags/architecture" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#architecture</a> <a href="https://mathstodon.xyz/tags/window" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#window</a>

Alexandre MuñizI've been learning how to use Jaap Scherphuis' PolySolver more effectively lately. I previously tried manually to get symmetrical markings on a tiling with the 12 internal-edge-marked pentiamonds, but had to give up just short. This time I had PolySolver's help.<a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TilingTuesday</a>

n-gonsA square decomposed into triangles, squares and crowns for <a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TilingTuesday</a><a href="https://mathstodon.xyz/tags/Geometry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Geometry</a> <a href="https://mathstodon.xyz/tags/Tiling" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Tiling</a> <a href="https://mathstodon.xyz/tags/MathArt" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#MathArt</a> <a href="https://mathstodon.xyz/tags/Art" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Art</a>

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