Rosetta Code

Hilbert curve: Difference between revisions

Page Discussion

Hilbert curve (view source)

Revision as of 17:56, 13 April 2024

3,909 bytes added ,  1 month ago
→‎{{header|Fōrmulæ}}: Added L-system solution
(→‎{{header|Fōrmulæ}}: Added L-system solution)
(15 intermediate revisions by 8 users not shown)
Line 472:
ExitApp
Return</syntaxhighlight>
 
=={{header|Binary Lambda Calculus}}==
 
As shown in https://www.ioccc.org/2012/tromp/hint.html, the 142+3 byte BLC program
 
<pre>0000000 18 18 18 18 11 11 54 68 06 04 15 5f f0 41 9d f9
0000020 de 16 ff fe 5f 3f ef f6 15 ff 94 68 40 58 11 7e
0000040 05 cb fe bc bf ee 86 cb 94 68 16 00 5c 0b fa cb
0000060 fb f7 1a 85 e0 5c f4 14 d5 fe 08 18 0b 04 8d 08
0000100 00 e0 78 01 64 45 ff e5 ff 7f ff fe 5f ff 2f c0
0000120 ee d9 7f 5b ff ff fb ff fc aa ff f7 81 7f fa df
0000140 76 69 54 68 06 01 57 f7 e1 60 5c 13 fe 80 b2 2c
0000160 18 58 1b fe 5c 10 42 ff 80 5d ee c0 6c 2c 0c 06
0000200 08 19 1a 00 16 7f bc bc fd f6 5f 7c 0a 20 31 32
0000220 33</pre>
 
(consisting of the 142 byte binary prefix https://github.com/tromp/AIT/blob/master/hilbert followed by "123") outputs the 3rd order Hilbert curve
 
<pre> _ _ _ _
| |_| | | |_| |
|_ _| |_ _|
_| |_____| |_
| ___ ___ |
|_| _| |_ |_|
_ |_ _| _
| |___| |___| |</pre>
 
=={{header|BQN}}==
Line 1,280 ⟶ 1,306:
 
</pre>
 
=={{header|EasyLang}}==
 
{{trans|FutureBasic}}
 
[https://easylang.dev/show/#cod=jVBLDoIwEN33FG9JMSCtxp2HUajSpAFTUeH2zlAKRDa2TTPz5n2atr4yHmecjsLZxnxs1dU4aOzR8kQ8y4szNFdFETFkU5eENg2wFA/flqituxrfoccAd4dVsBo5cgHA3hgiM25ocWJ0ydBLsgp5MzbM2CTxpnv5hpvRcbSjq7JvaAaW+B1npzwcVnV4kiJru+XrhZ8EilyrtorAUvJXp/7S6ZUuZtMJDqzKRRQVtMOfUCW+ Run it]
 
<syntaxhighlight lang="easylang">
order = 64
linewidth 32 / order
scale = 100 / order - 100 / (order * order)
proc hilbert x y lg i1 i2 . .
if lg = 1
line (order - x) * scale (order - y) * scale
return
.
lg = lg div 2
hilbert x + i1 * lg y + i1 * lg lg i1 1 - i2
hilbert x + i2 * lg y + (1 - i2) * lg lg i1 i2
hilbert x + (1 - i1) * lg y + (1 - i1) * lg lg i1 i2
hilbert x + (1 - i2) * lg y + i2 * lg lg 1 - i1 i2
.
hilbert 0 0 order 0 0
</syntaxhighlight>
 
=={{header|F_Sharp|F#}}==
<syntaxhighlight lang="fsharp">
// Hilbert curve. Nigel Galloway: September 18th., 2023
type C= |At|Cl|Ab|Cr
type D= |Z|U|D|L|R
let fD=function Z->0,0 |U->0,1 |D->0,-1 |L-> -1,0 |R->1,0
let fC=function At->[fD D;fD R;fD U] |Cl->[fD R;fD D;fD L] |Ab->[fD U;fD L;fD D] |Cr->[fD L;fD U;fD R]
let order(n,g)=match g with At->[n,Cl;D,At;R,At;U,Cr]
|Cl->[n,At;R,Cl;D,Cl;L,Ab]
|Ab->[n,Cr;U,Ab;L,Ab;D,Cl]
|Cr->[n,Ab;L,Cr;U,Cr;R,At]
let hilbert=Seq.unfold(fun n->Some(n,n|>List.collect order))[Z,At]
hilbert|>Seq.take 7|>Seq.iteri(fun n g->Chart.Line(g|>Seq.collect(fun(n,g)->(fD n)::(fC g))|>Seq.scan(fun(x,y)(n,g)->(x+n,y+g))(0,0))|>Chart.withTitle(sprintf "Hilbert order %d" n)|>Chart.show)
</syntaxhighlight>
{{out}}
[[File:Hilbert0.png]]
[[File:Hilbert1.png]]
[[File:Hilbert2.png]]
[[File:Hilbert3.png]]
[[File:Hilbert4.png]]
[[File:Hilbert5.png]]
[[File:Hilbert6.png]]
 
=={{header|Factor}}==
Line 1,329 ⟶ 1,402:
=={{header|Forth}}==
{{trans|Yabasic}}
{{works with|4tH |v3.62}}
<syntaxhighlight lang="forth">include lib/graphics.4th
 
64 constant /width \ hilbertHilbert curve order^2
9 constant /length \ length of a line
 
Line 1,361 ⟶ 1,434:
color_image 255 whiteout blue \ paint blue on white
0 dup origin! \ set point of origin
0 dup /width over dup hilbert \ hilbertHilbert curve, order=8
s" ghilbert.ppm" save_image \ save the image
</syntaxhighlight>
Line 1,394 ⟶ 1,467:
{{FormulaeEntry|page=https://formulae.org/?script=examples/Hilbert_curve}}
 
'''Solution'''
The following function creates a graphics of the Hilbert curve of a given size and order:
 
=== Recursive ===
 
The following defines a function that creates a graphics of the Hilbert curve of a given order and size:
 
[[File:Fōrmulæ - Hilbert curve 01.png]]
 
'''Test cases'''
 
The following creates a table with Hilbert curves for orders 1 to 5:
Line 1,403 ⟶ 1,482:
 
[[File:Fōrmulæ - Hilbert curve 03.png|279px]]
 
=== L-system ===
 
There are generic functions written in Fōrmulæ to compute an L-system in the page [[L-system#Fōrmulæ | L-system]].
 
The program that creates a Hilbert curve is:
 
[[File:Fōrmulæ - L-system - Hilbert curve 01.png]]
 
[[File:Fōrmulæ - L-system - Hilbert curve 02.png]]
 
=={{header|Frink}}==
Line 1,605 ⟶ 1,694:
and folded to a list of points in a square of given size.
 
<syntaxhighlight lang="haskell">import Data.BoolTree (boolTree (..))
 
import Data.Tree
---------------------- HILBERT CURVE ---------------------
 
hilbertTree :: Int -> Tree Char
hilbertTree n
| 0 < n = iterate go seed !! pred n
| otherwise = seed
where
seed = Node 'a' []
go tree
| null xs = Node c (flip Node [] <$> rule c)
| otherwise = Node c (go <$> xs)
where
c = rootLabel tree
xs = subForest tree
 
 
hilbertPoints :: Int -> Tree Char -> [(Int, Int)]
hilbertPoints w = go r (r, r)
where
r = quot w 2
go r xy tree
| null xs = centres
| otherwise = concat $ zipWith (go d) centres xs
where
d = quot r 2
f g x = g xy + (d * g x)
centres =
((,) . f fst)
<*> f snd <$> vectors (rootLabel tree)
xs = subForest tree
 
 
--------------------- PRODUCTION RULE --------------------
 
rule :: Char -> String
Line 1,625 ⟶ 1,747:
'd' -> [(-1, 1), (1, 1), (1, -1), (-1, -1)]
_ -> []
 
 
--------------------------- TEST -------------------------
 
main :: IO ()
Line 1,630 ⟶ 1,755:
let w = 1024
putStrLn $ svgFromPoints w $ hilbertPoints w (hilbertTree 6)
 
hilbertTree :: Int -> Tree Char
hilbertTree n =
let go tree =
let c = rootLabel tree
xs = subForest tree
in Node c (bool (go <$> xs) (flip Node [] <$> rule c) (null xs))
seed = Node 'a' []
in bool seed (iterate go seed !! pred n) (0 < n)
 
hilbertPoints :: Int -> Tree Char -> [(Int, Int)]
hilbertPoints w tree =
let go r xy tree =
let d = quot r 2
f g x = g xy + (d * g x)
centres = ((,) . f fst) <*> f snd <$> vectors (rootLabel tree)
xs = subForest tree
in bool (concat $ zipWith (go d) centres xs) centres (null xs)
r = quot w 2
in go r (r, r) tree
 
svgFromPoints :: Int -> [(Int, Int)] -> String
Line 1,655 ⟶ 1,760:
let sw = show w
points =
(unwords . fmap (((++<>) . show . fst) <*> ((' ' :) . show . snd))) xys
in unlines
[ "<svg xmlns=\"http://www.w3.org/2000/svg\"",
unwords
, unwords ["width=\"512\" height=\"512\" viewBox=\"5 5", sw, sw, "\"> "]
, ["width=\"512\"<path dheight=\"M512\" ++viewBox=\"5 points5", ++sw, sw, "\"> "],
, "stroke-width<path d=\"2\M" stroke=\++ points ++ "red\" fill=\"transparent\"/>",
"stroke-width=\"2\" stroke=\"red\" fill=\"transparent\"/>",
, "</svg>"
] "</syntaxhighlightsvg>"
]</syntaxhighlight>
 
=={{header|IS-BASIC}}==
Line 2,013 ⟶ 2,119:
 
// hilbertCurve :: Dict Char [(Int, Int)] ->
// Dict Char [Char] -> Int -> Int -> SVG string
const hilbertCurve = dictVector =>
dictRule => nwidth => {compose(
const w = 1024;svgFromPoints(width),
hilbertPoints(dictVector)(width),
 
return svgFromPointshilbertTree(wdictRule)(
);
hilbertPoints(dictVector)(w)(
hilbertTree(dictRule)(n)
)
);
};
 
 
// hilbertTree :: Dict Char [Char] -> Int -> Tree Char
const hilbertTree = rule => n => {
const go = treen => {
const xsgo = tree.nest; => {
const xs = tree.nest;
 
return Node(tree.root)(
Boolean( 0 < xs.length) ? (
? xs.map(go)
) : rule[tree.root].map(
flip(Node)([])
)
);
};
const seed = Node("a")([]);
 
return 0 < n
? take(n)(
iterate(go)(seed)
)
.slice(-1);[0]
: seed;
};
const seed = Node("a")([]);
 
return Boolean(n) ? (
take(n)(iterate(go)(seed))
.slice(-1)[0]
) : seed;
};
 
 
Line 2,061 ⟶ 2,166:
]);
 
return Boolean(0 < t.nest.length) ? (
? zipWith(go(r))(centres)(t.nest)
.flat go(r)
) : )(centres;)(t.nest).flat()
: centres;
};
const d = Math.floor(w / 2);
Line 2,115 ⟶ 2,221:
c: ["b", "c", "c", "d"],
d: ["a", "d", "d", "c"]
})(1024)(6);
 
 
Line 2,130 ⟶ 2,236:
nest: xs || []
});
 
 
// compose (<<<) :: (b -> c) -> (a -> b) -> a -> c
const compose = (...fs) =>
// A function defined by the right-to-left
// composition of all the functions in fs.
fs.reduce(
(f, g) => x => f(g(x)),
x => x
);
 
 
// flip :: (a -> b -> c) -> b -> a -> c
const flip = op =>
// The binary function op with
// its arguments reversed.
1 !== op.length ? (
? (a, b) => op(b, a)
) : (a => b => op(b)(a));
 
 
Line 2,163 ⟶ 2,279:
"GeneratorFunction" !== xs.constructor
.constructor.name ? (
xs.length
) : Infinity;
 
 
Line 2,174 ⟶ 2,290:
xs => "GeneratorFunction" !== xs
.constructor.constructor.name ? (
xs.slice(0, n)
) : Array.from({
length: n
}, () => {
const x = xs.next();
 
return x.done ? [] : [x.value];
}).flat();
 
 
Line 2,196 ⟶ 2,312:
}, (_, i) => f(as[i], bs[i]));
};
 
 
// MAIN ---
Line 4,435 ⟶ 4,552:
{{trans|Go}}
{{libheader|DOME}}
<syntaxhighlight lang="ecmascriptwren">import "graphics" for Canvas, Color, Point
import "dome" for Window
 
Line 4,473 ⟶ 4,590:
static draw(dt) {}
}</syntaxhighlight>
 
{{out}}
[[File:Wren-Hilbert_curve.png|400px]]
 
=={{header|XPL0}}==
Laurence
2,120

edits

Retrieved from "https://rosettacode.org/wiki/Special:MobileDiff/345320...363554"