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n-gons<a href="https://mastodon.cloud/@katherine_montalto" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@katherine_montalto</a> this is a <a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TilingTuesday</a> friendly post:)

꧁ᐊ𰻞ᵕ̣̣̣̣̣̣́́♛ᵕ̣̣̣̣̣̣́́𰻞ᐅ꧂<a href="https://mastodon.gamedev.place/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TilingTuesday</a> 2d cross-section of an 8d point arrangement in ðe hypercubic honeycomb, wiθ 1 point at ðe center of each non-vertex facet & a sphere 10^-5 times ðe radius at ðe center of each 8-cube 𓅱<a href="https://mastodon.gamedev.place/tags/geometry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#geometry</a> <a href="https://mastodon.gamedev.place/tags/cursed" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#cursed</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/art" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#art</a>

Dani Laura (they/she/he)And for <a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TilingTuesday</a> this simple <a href="https://mathstodon.xyz/tags/tiling" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#tiling</a> with ellipse arcs. <a href="https://mathstodon.xyz/tags/MathArt" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#MathArt</a> <a href="https://mathstodon.xyz/tags/Mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Mathematics</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

Alexandre MuñizThere are 12 ways to replace two of the cells of an L tetromino with diagonal bars of opposite orientations. They form a unique 6×6 square tiling with a single cycle of overlapping perpendicular bars up to the symmetries of the square and swapping the bar orientations.<a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TilingTuesday</a>

n-gonsDodecagon decomposition 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/Tiling" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Tiling</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/Art" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Art</a>

RasmusEnneagonal tiling of surface with flat growth. <a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TilingTuesday</a>

curved-rulerNet found for early <a href="https://mastodon.gamedev.place/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TilingTuesday</a> Fun way to create 2d tilings <a href="http://www.paulbourke.net/geometry/2d3dtiles/" rel="nofollow noopener noreferrer" translate="no" target="_blank">http://www.paulbourke.net/geometry/2d3dtiles/</a>

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>

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>

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>

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