Christian Lawson-Perfect @christianp

14 posts10 participants0 posts today

**Σ(i³) = (Σi)²** @SvenGeier · 1d

Σ(i³) = (Σi)² @SvenGeier

Done in multiple layers, but not layers that are recognizably stacked on top of each other... #TilingTuesday

**n-gons** @ngons · 1d

n-gons @ngons

#Tiling of Icosahedra and excavated dodecahedra for today's #TilingTuesday

GIF

#Geometry #MathArt

**curved-ruler** @curved_ruler@mastodon.gamedev.place · 1d

curved-ruler @curved_ruler@mastodon.gamedev.place

And one for #TilingTuesday

**sɹɐʎA xɘlA** @loosenut@genart.social · 1d

sɹɐʎA xɘlA @loosenut@genart.social

#TilingTuesday? In this economy? YOLO

GIF

**Non-Euclidean Dreamer** @noneuclideandreamer · 1d *

1d *

Non-Euclidean Dreamer @noneuclideandreamer

Now we project a six-dimensional grid onto 3-d space in a way that gives us Icosahedral symmetry.

GIF

#TilingTuesday

**Bojidar Marinov** @bojidar_bg@mastodon.social · 1d

Bojidar Marinov @bojidar_bg@mastodon.social

#TilingTuesday - Randomly browsing Wikipedia got me to the article on the 8-fold-symmetric Ammann-Beenker tiling... which seemed like just the perfect thing to recreate with #KnightPolygons !
..Unlike the previous nonperiodic knight polygon tiling in https://mastodon.social/@bojidar_bg/114381818097729168, it is a lot harder to see the fractal structure in this one
(Also, I have two sets of replacements for each of the square half tiles. I didn't quite figure out the color rules for those—but I know there are some.)

Tiling of rhomboids (green going vertical, orange going diagonal) and squares (two shades of blue). There are florets every now and then, with no clear structure to them

Description: Replacement rules for various tiles in a knight polygon ammann-beenker tiling.
Alternate: A table of tiles; the first and third column hold individual tiles: thick (green) and thin (orange) rhomboids, as well as squares split in half; the second and fourth columns hold the corresponding replacements; each of the original tiles made out of 5-7 smaller tiles.
The split-in-half square tiles are listed twice: once with thick rhomboids, and once with this ones.

Description: 2nd order replacement tiles.
Alternative: An M and a V (plus some extra rhomboids above the M) made out of a mosaic of tiles.

**foldworks** @foldworks · 1d *

1d *

foldworks @foldworks

Multi-level Cairo tiling outside Deichman Library, Oslo, Norway: something strange going on between the medium and big hexagons?

“...opened to the public on 18 June 2020. Deichman Bjørvika has won several awards, including the International Federation of Library Associations and Institutions / Systematic Public Library of the Year award” https://en.wikipedia.org/wiki/Oslo_Public_Library

Edit: deleting and redrafting so that post is public, and should have been threaded with https://mathstodon.xyz/@foldworks/114500543669491352
#TilingTuesday #geometry #MathArt #photography #architecture #pentagon #hexagon #library

Photograph of grey street paving that consists of symmetrical pentagons in in symmetrical hexagons. The middle has medium-sized hexagons; the left has pentagons inside the hexagons; the right has bigger hexagons with pentagons inside.

**foldworks** @foldworks · 1d *

1d *

foldworks @foldworks

A more conventional Cairo tiling inside the building.
Edit: should have been threaded from https://mathstodon.xyz/@foldworks/114500546387557561
#TilingTuesday #geometry #MathArt #photography #architecture #pentagon #hexagon #library

A photograph of the interior of a building. At the bottom are escalators going up: a slightly blurred person is going down. At the top is the ceiling with a Cairo tiling of symmetrical pentagons. In the middle one can see similar ceilings of higher floors.
The composition is dominated by diagonal lines. The ceilings are brown-grey but the escalator is blue-white.

**Dani Laura (they/she/he)** @DaniLaura · 1d

Dani Laura (they/she/he) @DaniLaura

$A subfractal tiling made with kites arranged in groups of 6 forming a hexagonal structure.$

#TilingTuesday #tiling #geometry

**Malwen** @Malwen@toot.wales · 1d

Malwen @Malwen@toot.wales

For this week's #TilingTuesday I'm reviewing the app "Azul Tiles Game" https://play.google.com/store/apps/details?id=com.Owapps.Tiles&gl=UK&utm_source=emea_OO, which is based on the board game Azul https://en.wikipedia.org/wiki/Azul_(board_game) I don't think it is an official app by the makers of the board game, but I could be wrong.
The instructions appeared as white text on a pale beige background, which made them very hard to read. It took me several games to get the hang of how to play as I'd never played the board game.

screen shot showing an almost completed game of Azul. There are lots of small square tiles coloured yellow, blue, purple, green and red. Some of the tiles are stacked in columns of the same colour. Other tiles are arranged in a 5x5 square where tiles along a diagonal have the same colour. There is one red tile at the top of the board which is yet to be placed.

**Alexandre Muñiz** @two_star · 1d

Alexandre Muñiz @two_star

Using the set of 3- and 4-iamonds with a single marked edge, we can tile a hexagon with sides of alternating lengths. We require marked edges to match.

Tiling this shape without additional restrictions is fairly easy to do manually. Shown are (top left) a tiling where all of the marked edges have the same orientation, (top right) a tiling where no two pieces with the same shape touch, and (bottom) a tiling, found by Bryce Herdt, where tiles of the same shape are clumped into groups.

Small polyominoes with marked edges have been explored by Peter Esser: http://polyforms.eu/notchedpolyominoes/start.html

#TilingTuesday