Lmst

#TilingTuesday one of my favorite patterns

Infinite monohedral tiling made up of nonagons. (1/2) #TilingTuesday

Driveway in Highland Park, CA
#TilingTuesday

For #tilingtuesday .. UF6 Rootfinding Anatida for 1/(2*(z+1))-2*log(z+1)-c=0 in OM coulored with simple traps enhanced 2.

#TilingTuesday

So ðis is big b😳lls,

#TilingTuesday #ballpitOwO #tiling #abstract #mathart #mastoart #geometry

#TilingTuesday

```
df = data.frame(x=0, y=0, a=0, d=1)
i = 1
while (i < 1e4) {
while (1) {
pt = df[sample(i,1),]
b = sample(-1:1,1)
a = pt$a + .05*rnorm(1) + b*pi/2
xj = pt$x + cos(a)
yj = pt$y + sin(a)
d = (xj - df$x)^2 + (yj - df$y)^2
if (min(d) > .5) {
i = i+1
df[i,] = c(xj, yj, a, min(d))
break
}
}
}
with(df, {
c = hcl(1:i/9)
plot(NA, axes=F, ann=F, xlim=range(x)/2, ylim=range(y)/2)
points(x,y,cex=d,pch=16,col=c)
})
```
#rstats #generativeart #tilingtuesday

I was playing around with tilings the other week, and stumbled on this odd effect upon overlapping two copies of the same tiling at a 90º angle.

Here, I used multiplicative blending to get at least a cool colorful effect of it, since just the black borders looked a bit bland.

(Would also appreciate pointers on how to get some kind of crystallography-like diffraction out of that pattern, for extra colorful messes 😅)

#TilingTuesday #KnightPolygons

Repeating pattern of colorful shapes with an almost kaleidoscopic effect. There are some red rectangles "spilling" into smaller rectangles at their corners, across a mess of green and blue triangles. Meanwhile, large squares split into 8 sections of alternating dark yellow and dark purple repeat every so often, floating untouched on the sea of shapes.

The edge of the repeating pattern from last image takes the left half of this one. The right half is two identical rotated patterns that combine to form it; each made out of a red square a thin green rhomus and a thicker blue one.

There are 9 2- and 3-ominoes with a path connecting two cell edges on the perimeter that are separated by a single segment along the perimeter. A checkering parity issue makes a loop impossible, but there is a unique tiling with a single path reaching the border of a 5×5 square at both ends.

#TilingTuesday

#TilingTuesday
Created in #OneLab for Android

Almost-octagons in shades of brown and cream, with 8-petalled flowers at their centres. Between these tiles are crosses with pointy ends in shades of blue and purple, that look like they might be made of stained glass.

Shah-i-Zinda, Samarkand, Uzbekistan.

“The Shah-i-Zinda Ensemble includes mausoleums and other ritual buildings of 11th–15th and 19th centuries. ...meaning "The living king" … The Shah-i-Zinda complex was formed over eight (from the 11th until the 19th) centuries and now includes more than twenty buildings.” https://en.wikipedia.org/wiki/Shah-i-Zinda

#TilingTuesday #tiling #IslamicPattern #geometry #mathArt #photography #architecture #hexagon

Two sets of hexagonal tiles separated by a plain border.
The left set of tiles: interlaced white lines make hexagons and hexagrams containing yellow flowers. Red, blue and yellow polygons fill in the other areas. The hexagon tiles have a middle border of white, cyan and blue square and rectangle tiles making cross shapes.
The right set of tiles: the centre of each tile is a cyan hexagon surrounded by white equilateral triangles and blue kites.

Pentagram flowers for #TilingTuesday

#Geometry #Tiling #MathArt

Abstract mathematical art, tiling of triangles and pentagons in bright colours over a yellow blue gradient.

#tilingtuesday & #MardiPatisserie !
by @morph
https://morphnet.de/@morph/114420601198441072

A nightrider is a variant chess piece that moves like a knight but then can continue to make additional hops in the same direction. I found a pentomino tiling where all of the pentominoes could be reached by a well placed nightrider, but in my original solution, one piece was reachable in two different positions. Carl Johan Ragnarsson suggested that it might be possible to find a tiling where each pentomino could be reached in exactly one spot, and Bryce Herdt found this solution, which appears to be unique.

Note that this is a rare instance of a pentomino tiling without a balanced, strict 4-coloring. (That is, one where all colors have an equal count, and there is no position where a shape of a given color meets another shape of the same color at a vertex.) Only 19 of the 2339 pentomino tilings of a 6×10 lack such a coloring. (And only one lacks a non-strict balanced coloring!)

#TilingTuesday