I use a lot of truchet tiles in my art (https://andrewwulf.com), but I color them afterwards, which seems fairly uncommon (article from last year, https://thecodist.com/my-art-and-color-after-tiling/) outside of shaders. I focus on 2d art for print. I also use various combinations of 1x1, 1x2, 2x2, 3x3 and 4x4 tiles, sometimes all in one work.
Wow, Wikipedia is pretty minimal in giving examples. Clicking through various links in comments for more examples should be considered mandatory (though many of the 3D ones are actually "some effect on top of Truchet").
I suppose I don't normally think about how you're actually using minimal Truchet tiles when you play one of SGT's puzzle games, since it's the most boring tileset:
There are 9 square (non-identical) tiles in a set. Each edge of each tile displays half of a two-sided symbol (eg cats, dogs, flags, etc.). Goal is to arrange the tiles in a 3x3 grid so that all touching edges match with corresponding symbol halves.
Looks simple at first, but a real challenge.
Size of the entire solution space is 9! * 4^9 (billions), and brute-force solvers have been written in Python:
Kathie Gavin (designer of Scramble Squares) says the design was inspired by "ancient Egyptian tile patterns" she saw in a museum. Does anyone know more about this?
python3 -c 'import random, time, itertools; any(time.sleep(0.01) or print(random.choice("\u2571\u2572"), end="", flush=True) for x in itertools.repeat(None))'
Quite a few bytes can be golfed out of that still:
python3 -c 'while I := __import__: I("time").sleep(0.01); print(I("random").choice("\u2571\u2572"), end="", flush=1)'
My reasoning including most failures:
Whitespace is mostly trivial and not worth mentioning, except that the space between "or" and "print" can be eliminated by moving the `time.sleep` to before a string literal. Alternatively, using `!=` works almost anywhere (though not with some alternative ideas), or `;` with the `while` version.
There are several shorter ways to get an infinite loop:
itertools.repeat(None) # for reference
itertools.repeat(0)
itertools.count()
iter(lambda: 0, 1) # also removes the import, so 10 chars shorter
iter(''.upper, 1) # same length when spaces removed, shorter if not removed
iter(int.mro, 1) # spooky, but one char shorter still
range(9**99) # much longer than the age of the universe
range(9**9) # 44 days
# but it turns out we can skip it entirely
The loop itself:
any(expr for x in it) # theoretically prevents the memory leak
[expr for x in it] # wastes 800 bytes per sec, 69 MB/day, 1 GB per 14 days
while 1: expr # breaks one-liner unless longer `__import__("")` is used, but worth it since it eliminates the entire iterable, even before doing I=__import__
while I := __import__: # 2 chars shorter than doing the assignment inside the loop
I looked into alternatives to calling sleep at all, but computers are too fast (and variable in speed) nowadays. `os.sync` looked promising but is only slow the first time. Trying to pass its return value as an argument also failed.
`flush=1` is shorter than `flush=True`. Otherwise ... I tried `sys.stdout` but hardly anything was even close:
any(time.sleep(0.01) or print(random.choice("\u2571\u2572"), end="", flush=True) for it)
any(time.sleep(0.01) or print(random.choice("\u2571\u2572"), end="", flush=1) for it)
sys.stdout.writelines(time.sleep(0.1) or random.choice("\u2571\u2572")+"\0"*8191 for it) # can avoid the flush by filling the buffer manually, but requires several more chars to import sys as well
Random:
random.choice("\u2571\u2572")
# UTF-8 b"\xe2\x95\xb1" doesn't seem useful
chr(9585+random.randrange(2)) # sigh
chr(9585+(random.random()<.5)) # nope
chr(9585+(os.getrandom(1)[0]&1)) # + has tigher precedence than &
# that last would save 1 byte with normal `import` (since the identifier is repeated), but loses with `__import__`
# is there a way to eliminate parens? Is >> or | or - useful? What about *splat?
Truchet tiling is a staple of the shader community - https://www.shadertoy.com/results?query=Truchet
A particularly nice example - https://www.shadertoy.com/view/4td3zj
And a nice '3D' one - https://www.shadertoy.com/view/4lSBzm
They also come up a lot in pen plotter art.
Like the hexagonal one.
Using multi-level Carlson Truchet tiles for half-toning images: https://nedbatchelder.com/blog/202208/truchet_images.html
some truchet tiles i did for a plotter a million years ago:
hex:
https://www.instagram.com/p/B2TRmM7p1BB
https://www.instagram.com/p/B2Q130pJwum
rectangular:
https://www.instagram.com/p/BxUMO05p3Cx
https://www.instagram.com/p/BxO1H3cJ57V
Man, I've tried writing my own version of things like this, but it ended up looking like pubes on paper.
Nice.
It's a shame that regular octagons do not tile the plane. Octagons + squares might work I suppose.
You can use the monotile! See my links below.
Ah perfect! I went away at lunch and tried to work it out, including for the spectre tile (monotile), although I took a different approach.
Reminds me of this, created by one of the tailwind guys: https://heropatterns.com/
These are really useful for subtle background patterns on footers etc.
I use a lot of truchet tiles in my art (https://andrewwulf.com), but I color them afterwards, which seems fairly uncommon (article from last year, https://thecodist.com/my-art-and-color-after-tiling/) outside of shaders. I focus on 2d art for print. I also use various combinations of 1x1, 1x2, 2x2, 3x3 and 4x4 tiles, sometimes all in one work.
We have this card-tiling game based on this idea.
https://www.ravensburger.us/en-US/products/games/thinkfun/iz...
It's not a great game, but it's fun enough. The box is small, so we keep it around even if we don't play it much.
Wow, Wikipedia is pretty minimal in giving examples. Clicking through various links in comments for more examples should be considered mandatory (though many of the 3D ones are actually "some effect on top of Truchet").
I suppose I don't normally think about how you're actually using minimal Truchet tiles when you play one of SGT's puzzle games, since it's the most boring tileset:
https://www.chiark.greenend.org.uk/~sgtatham/puzzles/js/slan...
"Scramble Squares" is a card-tiling puzzle which looks like a specialized form of Truchet Tiling.
https://scramblesquares.com
There are 9 square (non-identical) tiles in a set. Each edge of each tile displays half of a two-sided symbol (eg cats, dogs, flags, etc.). Goal is to arrange the tiles in a 3x3 grid so that all touching edges match with corresponding symbol halves.
Looks simple at first, but a real challenge.
Size of the entire solution space is 9! * 4^9 (billions), and brute-force solvers have been written in Python:
https://github.com/roadfoodr/scramble-squares-solver
What are the combinatorial rule(s) used to construct these tiles ?? Some clues: https://www.reddit.com/r/puzzles/comments/1e09up6/help_how_t...
Kathie Gavin (designer of Scramble Squares) says the design was inspired by "ancient Egyptian tile patterns" she saw in a museum. Does anyone know more about this?
These are also good to avoid tiling textures having a https://en.wikipedia.org/wiki/Moir%C3%A9_pattern. Just do a randomized labyrinth per square and voila.
oh! moiré and the double slit experiment are related things, TIL
I need some of these mathematical tiles to be available as physical ceramic tiles for nerdy backsplashes and bathrooms.
8-Bit Show and Tell recently did a video about Truchet Tiles on PETSCII. Fun watch:
https://www.youtube.com/watch?v=MVQJykMJSH0
not sure why this is on top of the feed but i appreciate it ! Is there a website where you can draw on the truchet tiles live ? would be cool
Not exactly what you are requesting, but I added truchet patterns to a monotile renderer a while back. See here https://www.johansivertsen.com/post/monotile/ The drawing tool is here: https://www.johansivertsen.com/customhatviz/app.html Press 'build supertiles' a few times and enable the truchet overlay.
10 PRINT CHR$(205.5+RND(1)); : GOTO 10
https://github.com/the-real-tokai/macuahuitl/blob/master/tem...
(how about this fancy version with SVG output? :D No longer a single line though.)
Quite a few bytes can be golfed out of that still:
My reasoning including most failures:Whitespace is mostly trivial and not worth mentioning, except that the space between "or" and "print" can be eliminated by moving the `time.sleep` to before a string literal. Alternatively, using `!=` works almost anywhere (though not with some alternative ideas), or `;` with the `while` version.
There are several shorter ways to get an infinite loop:
The loop itself: I looked into alternatives to calling sleep at all, but computers are too fast (and variable in speed) nowadays. `os.sync` looked promising but is only slow the first time. Trying to pass its return value as an argument also failed.`flush=1` is shorter than `flush=True`. Otherwise ... I tried `sys.stdout` but hardly anything was even close:
Random:I used to do this on my VIC-20 a million years ago. Just looking at this line brought back the visual image like it was yesterday.
https://thewoodenwagon.com/woodentoy/CAF3064.html
did anyone have wooden truchet tiles of various colors as a kid that you would place on a board and flip them around to make various designs
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