```
library(tidyverse)
library(interp)
x = c(runif(500), 0,0,1,1)
y = c(runif(500), 0,1,0,1)
triangles(tri.mesh(x = x,y = y)) |>
as_tibble() |>
mutate(i=1:n()) |>
rowwise() |>
mutate(tri = list(
tibble(x=x[c(node1,node2,node3,node1)],
y=y[c(node1,node2,node3,node1)]))) |>
unnest('tri') |>
ggplot() +
geom_polygon(aes(x=x,y=y,group=i,fill=i), show.legend=FALSE) +
scale_fill_viridis_c(option='F') +
theme_void()
```
A tridecagonal (13-gon) tiling of a 3-periodic infinite surface. (1/n) #TilingTuesday
Window, North Gate, Imperial Citadel of Thăng Long, Hanoi, Vietnam https://en.wikipedia.org/wiki/Imperial_Citadel_of_Th%C4%83ng_Long#North_Gate_(C%E1%BB%ADa_B%E1%BA%AFc,_or_B%E1%BA%AFc_M%C3%B4n)
#Tiling #TilingTuesday #Pattern #Geometry #MathArt #MathsArt #photography #architecture
Diagonal 
section of ðe 4d cartesian product of 2 "I want to be a sea urchin and eat cabbage"(yes, really) tilings
kinda like ðis
Unfortunately we are still too dimensionally, perceptually, & probably intellectually challenged to even try to look at ðe full θing 
Back to #KnightPolygons (polygons formed by (2,1)-moves), here is a pair of tilings I did back c. 2020, using a knight polygon I dub the "Swan".
Two tilings of tangent circles for #TilingTuesday .
#MathArt #tiling #Mathematics
And for #TilingTuesday this simple #tiling with ellipse arcs.
#MathArt #Mathematics
There 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.
Sierpinski Pyramid Tiling for #TilingTuesday
This kind of pyramid is a quarter of a cube.
Dear #TilingTuesday community,
A while ago I implemented a graphical web app folding certain flat shapes to polyhedra: https://hcschuetz.github.io/polyhedron-star/dist/
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.
I'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.
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 ( https://tilings.math.uni-bielefeld.de/substitution/viper/ ) 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.
#TilingTuesday #tiling #Mathart #geometry #Mathematics
A square decomposed into triangles, squares and crowns for #TilingTuesday
#TilingTuesday Snub Flower Tiling Revisited
I found a beautiful egg shape hidden in my previous design.
Alos note: Today, new versions of the mac apps I use for most of my tiling designs are released!! That is @zellige, which I used for the egg, as well as @girih (for equilateral shapes), thank you Stefan!
