🮘🮙 Truchet tilings

[afiaith]

🖽 Truchet tiles are cool. The simplest of forms can yield interesting patterns. Here are some patterns I find aesthetically pleasing; if you have any suggestions for other tilesets, I’d be happy to hear

Such tiles are also used in the package Babel for redacting text.

For more truchet tilings, see the tags #truchet and #truchettiles on Mathstodon.

#import "@preview/suiji:0.3.0": *

#set page(width: auto, height: auto, margin: 0pt)
#set text(font: "Iosevka")
#set block(spacing: 0.5em)

#let maze(width: 50, height: 20, leading: 0.50em, tiles) = {
  let rng = gen-rng(0)
  par(
    leading: leading,
    for y in range(height) {
      for x in range(width) {
        let tile
        (rng, tile) = choice(rng, tiles)
        tile
      }
      linebreak()
    }
  )
}

#for tileset in (
  ("╱", "╲"),
  ("🮘", "🮙"),
  ("🮤", "🮥","🮦", "🮧", "🮨", "🮩", "🮪", "🮫", "🮬", "🮭"),
  ("│", "─", "┤", "├", "┴", "┬", "┼", "╯", "╮", " ", "╰", "╭"),
  ("╭","╮", "╯", "╰"),
  ("🮨", "🮩"),
  ("🭋",  "🭀",  "🭈", "🭘", "🭛", "🭣", "🭦"),
  ("╯╭","╮╰"),
  ("╯╭","╮╰", "│", "─"),
) {
  maze(tileset)
  pagebreak(weak: true)
}

Zoom in to see the details of the more intricate patterns (such as (“🮘”, “🮙”), which might make one a bit dizzy ).

[Mc-Zen]

This is actually super cool.

[afiaith]

Thanks! ^_^

My favourite set is these two quarter-circles, which create this wavy maze-like pattern. They are equivalent to ("🮨", "🮩"), but unfortunately I couldn’t find any fitting Unicode characters to represent the quarter-circles. The set ("╯╭","╮╰") is an approximation, but it’s misaligned: it creates an interesting pattern (the second to last here), but the lines don’t always connect.

[Mc-Zen]

I did a little modification to make it work with arbitrary content

#import "@preview/suiji:0.3.0": *

#set page(width: auto, height: auto, margin: 0pt)
#set text(font: "Iosevka")
#set block(spacing: 0.5em)



#let maze(width: 50, height: 20, tiles) = {
  let cells = ()
  let rng = gen-rng(0)
  for y in range(height) {
    for x in range(width) {
      let tile
      (rng, tile) = choice(rng, tiles)
      cells.push(tile)
    }
  }
  grid(
    columns: width,
    ..cells
  )
}

#let tile = box(width: 1em, height: 1em, {
  place(path(((0.5em, 0em), (0em, -.25em)), ((0em, .5em), (.25em, 0em))))
  place(path(((0.5em, 1em), (0em, .25em)), ((1em, .5em), (-.25em, 0em))))
})
#let tile2 = (rotate(90deg, tile))

#maze((tile, tile2))

[Mc-Zen]

I also like this one:

Here, the tile

#let tile1 = box(width: 1em, height: 1em, {
  place(path((.5em, 0em), (.5em, 1em)))
  place(path((0em, .5em), (1em, .5em)))
})

is added.

[afiaith]

@Mc-Zen

I did a little modification to make it work with arbitrary content

Cool!

BTW, you don’t have to push the cells into an array, only to be spread later. The function can be refactored like this:

#let maze(width: 50, height: 20, tiles) = {
  let rng = gen-rng(0)
  grid(
    columns: width,
    ..for y in range(height) {
      for x in range(width) {
        let tile
        (rng, tile) = choice(rng, tiles)
        (tile,)
      }
    }
  )
}

[afiaith]

And since we don’t do anything different with the two axes, the function can be refactored yet again to be even shorter, like this:

#let maze(width: 50, height: 20, tiles) = {
  let rng = gen-rng(0)
  grid(
    columns: width,
    ..for i in range(width * height) {
      let tile
      (rng, tile) = choice(rng, tiles)
      (tile,)
    }
  )
}

[Mc-Zen]

Good call, this is indeed more elegant!

it’s fascinating how this still works with updating the RNG (as compared to range(width * height).map(...) which would disallow changing the value of rng as it is outside the lambda scope).

[SillyFreak]

@Mc-Zen

it’s fascinating how this still works with updating the RNG (as compared to range(width * height).map(...) which would disallow changing the value of rng as it is outside the lambda scope).

fyi, that would be what fold is basically for. I didn’t check this for errors, but roughly the following should work:

    ..range(width * height).fold((rng, ()), ((rng, arr), i) => {
      let tile
      (rng, tile) = choice(rng, tiles)
      arr.push(tile)
      (rng, arr)
    }).last()

(I still prefer the loop in this case, but just so you know )