you could probably make ðis irl by cutting some planarians & locking ðem togeðer

I have (re)discovered partitions of the rectangles defined by the square root of metallic ratios into similar rectangles. In the case of the golden ratio it was known, as can be seen in the excellent site https://tilings.math.uni-bielefeld.de/substitution/rectangulo-dorado/ .
I think the results are novel for the next ratios, here I present the partitions for the silver and bronze ratios. More complex partitions can be deduced from them.
In the fourth image there is a grid with the eight possible tesselations related to the golden ratio, depending on the orientation of the rectangles produced. All are non-periodic, but some look more regular than other. See continuation post for more.
#TilingTuesday #Mathematics #geometry #tiling

One of the things which frustrates me no end, is that every single #Tiling #WindowManager I've ever seen on #Linux is designed with the assumption that "simple" and "pretty" are mutually exclusive.

The closest I've come to "pretty" is XMonad, because at least that allows you to have colour schemes, and to change the width of the (flat) window borders. Most of the others don't even allow that much.

But maybe things have changed since I last looked? Do any of you know of a tiling window manager which is actually PRETTY? Like, 3-dimensional window borders and other things one can customise the look of?

A decorative Art Nouveau tile peeking out from behind a modern intercom system at the entrance to a traditional sandstone Glasgow tenement in the Mount Florida area of Glasgow.

Floor, Kalmar Castle

Pavement tiling, Fes, Morocco

Love these tiles from a tenement close in the Mount Florida area of Glasgow.

wow! now i can try all those and see what my first first #tiling window manager was... http://www.tribblix.org/Use/5.desktop.html ...before #xmonad

Looking for tiling patterns i. Mom’s dahlias.

start wiθ a cubic honeycomb
split each cube into 6 pyramids
merge each pair ðat shares a 4gon into irregular octahedrons
& u get ðe almost regular octahedral honeycomb

(yes, someone made ðis a technical term, rly)

Pavement tiling, Ouarzazate, Morocco
#TilingTuesday #geometry #tiling #MathArt #photography #design #TravelPhotography #octagon

Love these decorative tiles at the entrance to the 1890s former Sanitary Chambers on Montrose Street in central Glasgow. If you zoom in, the pattern on the lower tiles does rather look, to me at any rate, like a strange crested bird with wild eyes, but there's nothing wrong with that!

Monohedral triangle tiling of the gyroid, which is the dual tessellation of a partial Cayley surface complex of the group:

```
G = ⟨ f₁,t₁ | f₁², t₁⁶, (f₁t₁)⁴, (f₁t₁f₁t₁⁻¹f₁t₁²)² ⟩
```

Ball of radius 21. (1/2)

Weiss eins wie emnsch ein A0 PDF in A4 aufsplitten kann (mit etwas Rand zum kleben) auf einem Mac (keine Drucker installiert)? #sewing #pattern #patterndesing #fedihelp #schnittmuster #tiling #pdftiling #postertiling Danke im Voraus

Base of a Celtic cross (c. 1890), Glasnevin Cemetery (Irish: Reilig Ghlas Naíon), Dublin, Ireland

Monohedral hexagonal tiling which is the dual tessellation of a partial Cayley surface complex of the group:
\[
G =
\left\langle t_1,\, t_2,\, t_3 \,\right|\,
\begin{array}[t]{l}
&t_1 t_2^{-1} t_3 t_2 \\
&(t_1 t_3)^2 \\
&t_2^3 \\
&t_1 t_2^{-1} t_3 t_2 \\
&(t_1 t_3)^2 \\
&t_1^2 t_3^{-2} t_2^{-1} \rangle
\end{array}
\]

Orthographic view of an embedded ball of radius 15. (1/2)