jaz :twt: :wales_flag:
boosted
#TilingTuesday
Created in #OneLab
Most hashtags are pretty obvious, you just put # in front of a topic. For example if a post is about coffee it might have the tag #Coffee
However, many popular hashtags have difficult-to-guess names, so I've started a list to help people discover them:
➡️ https://fedi.tips/fun-and-useful-hashtags-to-follow-on-mastodon-and-the-wider-fediverse
Copy-paste a hashtag into the search box in Mastodon if you want to browse or follow it.
If you have suggestions for non-obvious hashtags that should be added to the list, let me know in the replies 🙂
#TilingTuesday for pics of cool tilings
#MakanApaToday for pics of South-East Asian food
#Catstodon and #MastoCats for cats when it's not Saturday
#PhDLife and #PhDone for (very recently ex-)PhD students
Jason
boosted
Tilings and tessellations are such an interesting area of mathematics. They seem so simple that everything should have been discovered already, and yet new fundamental questions are raised every year!
In this case, researchers wondered about "soft" tilings, i.e. tilings with as few corners as possible and are entirely "rounded" elsewhere. It turns out they are everywhere in nature, both in 2D and 3D. And you can have tilings of three-dimensional spaces that have no corners at all!
https://www.reviewertoo.com/tessellation-revelation/
#TilingTuesday
Tilings and tessellations are such an interesting area of mathematics. They seem so simple that everything should have been discovered already, and yet new fundamental questions are raised every year!
In this case, researchers wondered about "soft" tilings, i.e. tilings with as few corners as possible and are entirely "rounded" elsewhere. It turns out they are everywhere in nature, both in 2D and 3D. And you can have tilings of three-dimensional spaces that have no corners at all!
https://www.reviewertoo.com/tessellation-revelation/
#TilingTuesday
Mre. Dartigen [maker mode]
boosted
Zellij floor tiles, Bahia Palace, Marrakesh, Morocco.
#TilingTuesday #geometry #tiling #MathArt #photography #design #IslamicPattern #IslamicArt
Zellij floor tiles, Bahia Palace, Marrakesh, Morocco.
#TilingTuesday #geometry #tiling #MathArt #photography #design #IslamicPattern #IslamicArt
Andrew Wooldridge 🎆
boosted
Fragmentarium2.5 based on
Hyperbolic-Honeycombs by neozhaoliang
#tilingtuesday
Fragmentarium2.5 based on
Hyperbolic-Honeycombs by neozhaoliang
#tilingtuesday
Travis F W
boosted
Advent of Tilings - Day 23.1
Almost at the end we see the light through diamond and hexagon shaped tunnels of an infinite surface, again monohedrally tiled.
#math #geometry #3d #combinatorics #tiling #AdventOfTilings #TilingTuesday
Advent of Tilings - Day 23.1
Almost at the end we see the light through diamond and hexagon shaped tunnels of an infinite surface, again monohedrally tiled.
#math #geometry #3d #combinatorics #tiling #AdventOfTilings #TilingTuesday
halcy :icosahedron:
boosted
Meet Taubin smoothing. It is a nice smoothing method that is great for smoothing voxel based meshes. So for smoothing stepped "Lego-like" meshes.
The left here shows a raw voxelised (thresholded) voxel boundary surface. On the right is the Taubin smoothed result.
Taubin smoothing works by first doing an aggressive Laplacian smoothing step (a bit like a blurring), which removes bumps etc, but which unfortunately can distort the shape too (e.g. unwanted shrinkage/growth). Next it uses an "inverse smooth" (a bit like a sharpening operation) to attempt to push back the shape a bit to avoid distortion. With the right parameter choices it can perform really well.
This animation is for a thresholded 3D image. The colors are the original voxel intensities. The resulting shape presents as a central sphere like blob contained in a dodecahedron "cage".
See also: https://doi.org/10.1145/218380.218473
#GeometryProcessing #JuliaLang #Makie #Meshing #TilingTuesday
Advent of Tilings - Day 17.1
A heftier caliber construction of 2304 tiles forming a genus 289 surface, intended for a sturdier branch. This would also have been a worthy contribution to #TilingTuesday which unfortunately was forgotten.
Meet Taubin smoothing. It is a nice smoothing method that is great for smoothing voxel based meshes. So for smoothing stepped "Lego-like" meshes.
The left here shows a raw voxelised (thresholded) voxel boundary surface. On the right is the Taubin smoothed result.
Taubin smoothing works by first doing an aggressive Laplacian smoothing step (a bit like a blurring), which removes bumps etc, but which unfortunately can distort the shape too (e.g. unwanted shrinkage/growth). Next it uses an "inverse smooth" (a bit like a sharpening operation) to attempt to push back the shape a bit to avoid distortion. With the right parameter choices it can perform really well.
This animation is for a thresholded 3D image. The colors are the original voxel intensities. The resulting shape presents as a central sphere like blob contained in a dodecahedron "cage".
See also: https://doi.org/10.1145/218380.218473
#GeometryProcessing #JuliaLang #Makie #Meshing #TilingTuesday
Yogthos
boosted
New maths blog post! The fifth in my series about handling aperiodic tilings combinatorially with string-processing algorithms:
https://www.chiark.greenend.org.uk/~sgtatham/quasiblog/aperiodic-refine/
In this instalment I've automated the process of converting a tiling substitution system into one for which you can build a deterministic transducer, if the starting system didn't already admit one. I discuss the algorithm, its limitations, and a particular success in which it found a more economical substitution system for the hat tiling than any I already knew of.
4 media
STOP OCCUPATION 🍉 S. Costa
boosted
Animated Wythoff tiling construction on a hexagonal grid on an infinite ribbon.
made with #p5js
Animated Wythoff tiling construction on a hexagonal grid on an infinite ribbon.
made with #p5js
Anke
and 1 other
boosted
Autumnal tiling for #TilingTuesday
Each cephalopod's chromatophore organ comprises an elastic sac containing pigment of different colors with a set of obliquely striated radial muscles. When excited, the muscles contract, expanding the chromatophore, enhancing that color [📹 SaltyFlyTying] #globalmuseum #cephalopod
@globalmuseum Most appropriate for a #TilingTuesday.