Le Pouls Du Monde

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

n-gonsDodecagon decomposition for <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/MathArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#MathArt</a> <a href="https://mathstodon.xyz/tags/Art" class="mention hashtag" rel="nofollow noopener" target="_blank">#Art</a>

n-gonsRhombicosidodecahedronFace to face tiling 240 equilateral polyhedra.<a href="https://mathstodon.xyz/tags/Hedron" class="mention hashtag" rel="nofollow noopener" target="_blank">#Hedron</a> <a href="https://mathstodon.xyz/tags/Geometry" class="mention hashtag" rel="nofollow noopener" target="_blank">#Geometry</a> <a href="https://mathstodon.xyz/tags/3D" class="mention hashtag" rel="nofollow noopener" target="_blank">#3D</a> <a href="https://mathstodon.xyz/tags/MathArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#MathArt</a> <a href="https://mathstodon.xyz/tags/Tiling" class="mention hashtag" rel="nofollow noopener" target="_blank">#Tiling</a>

This Is My GlasgowLove this beautiful Art Nouveau style tenement tile pattern, featuring Scottish Bluebells. It's from a tenement close in the Pollokshields 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/architecture" class="mention hashtag" rel="nofollow noopener" target="_blank">#architecture</a> <a href="https://mastodon.scot/tags/scottishbluebells" class="mention hashtag" rel="nofollow noopener" target="_blank">#scottishbluebells</a> <a href="https://mastodon.scot/tags/tiles" class="mention hashtag" rel="nofollow noopener" target="_blank">#tiles</a> <a href="https://mastodon.scot/tags/tenementtiles" class="mention hashtag" rel="nofollow noopener" target="_blank">#tenementtiles</a> <a href="https://mastodon.scot/tags/ceramics" class="mention hashtag" rel="nofollow noopener" target="_blank">#ceramics</a> <a href="https://mastodon.scot/tags/tiling" class="mention hashtag" rel="nofollow noopener" target="_blank">#tiling</a> <a href="https://mastodon.scot/tags/artnouveau" class="mention hashtag" rel="nofollow noopener" target="_blank">#artnouveau</a> <a href="https://mastodon.scot/tags/bluebells" class="mention hashtag" rel="nofollow noopener" target="_blank">#bluebells</a>

n-gonsSierpinski Pyramid Tiling for <a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener" 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" target="_blank">#Voxel</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/Fractal" class="mention hashtag" rel="nofollow noopener" target="_blank">#Fractal</a> <a href="https://mathstodon.xyz/tags/MathArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#MathArt</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" target="_blank">#TilingTuesday</a> <a href="https://mastodon.gamedev.place/tags/knots" class="mention hashtag" rel="nofollow noopener" target="_blank">#knots</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/pixelart" class="mention hashtag" rel="nofollow noopener" target="_blank">#pixelart</a> <a href="https://mastodon.gamedev.place/tags/abstract" class="mention hashtag" rel="nofollow noopener" 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" target="_blank">#Tiling</a> <a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener" target="_blank">#TilingTuesday</a> <a href="https://mathstodon.xyz/tags/Pattern" class="mention hashtag" rel="nofollow noopener" target="_blank">#Pattern</a> <a href="https://mathstodon.xyz/tags/Geometry" class="mention hashtag" rel="nofollow noopener" target="_blank">#Geometry</a> <a href="https://mathstodon.xyz/tags/MathArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#MathArt</a> <a href="https://mathstodon.xyz/tags/MathsArt" class="mention hashtag" rel="nofollow noopener" 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" 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" 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/Mathart" class="mention hashtag" rel="nofollow noopener" target="_blank">#Mathart</a> <a href="https://mathstodon.xyz/tags/geometry" class="mention hashtag" rel="nofollow noopener" target="_blank">#geometry</a> <a href="https://mathstodon.xyz/tags/Mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#Mathematics</a>

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