Infinite monohedral tiling made up of nonagons. (1/2) #TilingTuesday
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#tilingtuesday
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For #tilingtuesday .. UF6 Rootfinding Anatida for 1/(2*(z+1))-2*log(z+1)-c=0 in OM coulored with simple traps enhanced 2.
lls,
```
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 
)
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.
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
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!)
Hexagonal tiling with stars, squares and assymmetric kites for #TilingTuesday
maybe ðere's a reason pentagonal dungeon crawlers haven't been invented yet 
This week, for #TilingTuesday, I present to you this non-periodic #KnightPolygons tiling
As usual, Knight polygons are polygons traced by chess knight moves. The tiling here is created by an iterative "place a random tile at the point closest to the center" process -- which is similar to how I've drawn knight polygon tilings by hand in the past.
Tessellation with cairo pentagons and hexagons (regular and lengthened). All pentagons have the same shape, the ones joining as in cairo tessellations have different colour than the ones which not.
#tilingtuesday #tiling #Mathematics #Mathart
