# Hilbert curve

Hilbert curve
You are encouraged to solve this task according to the task description, using any language you may know.

Produce a graphical or ASCII-art representation of a Hilbert curve of at least order 3.

## ALGOL 68

This generates the curve following the L-System rules described in the Wikipedia article.

 L-System rule A B F + - Procedure a b forward right left
BEGIN
INT level = 4; # <-- change this #

INT side = 2**level * 2 - 2;
[-side:1, 0:side]STRING grid;
INT x := 0, y := 0, dir := 0;
INT old dir := -1;
INT e=0, n=1, w=2, s=3;

FOR i FROM 1 LWB grid TO 1 UPB grid DO
FOR j FROM 2 LWB grid TO 2 UPB grid DO grid[i,j] := " "
OD OD;

PROC left = VOID: dir := (dir + 1) MOD 4;
PROC right = VOID: dir := (dir - 1) MOD 4;
PROC move = VOID: (
CASE dir + 1 IN
# e: # x +:= 1, # n: # y -:= 1, # w: # x -:= 1, # s: # y +:= 1
ESAC
);
PROC forward = VOID: (
# draw corner #
grid[y, x] := CASE old dir + 1 IN
# e # CASE dir + 1 IN "──", "─╯", " ?", "─╮" ESAC,
# n # CASE dir + 1 IN " ╭", " │", "─╮", " ?" ESAC,
# w # CASE dir + 1 IN " ?", " ╰", "──", " ╭" ESAC,
# s # CASE dir + 1 IN " ╰", " ?", "─╯", " │" ESAC
OUT " "
ESAC;
move;
# draw segment #
grid[y, x] := IF dir = n OR dir = s THEN " │" ELSE "──" FI;
# advance to next corner #
move;
old dir := dir
);

PROC a = (INT level)VOID:
IF level > 0 THEN
left; b(level-1); forward; right; a(level-1); forward;
a(level-1); right; forward; b(level-1); left
FI,
b = (INT level)VOID:
IF level > 0 THEN
right; a(level-1); forward; left; b(level-1); forward;
b(level-1); left; forward; a(level-1); right
FI;

# draw #
a(level);

# print #
FOR row FROM 1 LWB grid TO 1 UPB grid DO
print((grid[row,], new line))
OD
END

Output:
╭───╮   ╭───╮   ╭───╮   ╭───╮   ╭───╮   ╭───╮   ╭───╮   ╭───╮
│   │   │   │   │   │   │   │   │   │   │   │   │   │   │   │
│   ╰───╯   │   │   ╰───╯   │   │   ╰───╯   │   │   ╰───╯   │
│           │   │           │   │           │   │           │
╰───╮   ╭───╯   ╰───╮   ╭───╯   ╰───╮   ╭───╯   ╰───╮   ╭───╯
│   │           │   │           │   │           │   │
╭───╯   ╰───────────╯   ╰───╮   ╭───╯   ╰───────────╯   ╰───╮
│                           │   │                           │
│   ╭───────╮   ╭───────╮   │   │   ╭───────╮   ╭───────╮   │
│   │       │   │       │   │   │   │       │   │       │   │
╰───╯   ╭───╯   ╰───╮   ╰───╯   ╰───╯   ╭───╯   ╰───╮   ╰───╯
│           │                   │           │
╭───╮   ╰───╮   ╭───╯   ╭───╮   ╭───╮   ╰───╮   ╭───╯   ╭───╮
│   │       │   │       │   │   │   │       │   │       │   │
│   ╰───────╯   ╰───────╯   ╰───╯   ╰───────╯   ╰───────╯   │
│                                                           │
╰───╮   ╭───────╮   ╭───────╮   ╭───────╮   ╭───────╮   ╭───╯
│   │       │   │       │   │       │   │       │   │
╭───╯   ╰───╮   ╰───╯   ╭───╯   ╰───╮   ╰───╯   ╭───╯   ╰───╮
│           │           │           │           │           │
│   ╭───╮   │   ╭───╮   ╰───╮   ╭───╯   ╭───╮   │   ╭───╮   │
│   │   │   │   │   │       │   │       │   │   │   │   │   │
╰───╯   ╰───╯   │   ╰───────╯   ╰───────╯   │   ╰───╯   ╰───╯
│                           │
╭───╮   ╭───╮   │   ╭───────╮   ╭───────╮   │   ╭───╮   ╭───╮
│   │   │   │   │   │       │   │       │   │   │   │   │   │
│   ╰───╯   │   ╰───╯   ╭───╯   ╰───╮   ╰───╯   │   ╰───╯   │
│           │           │           │           │           │
╰───╮   ╭───╯   ╭───╮   ╰───╮   ╭───╯   ╭───╮   ╰───╮   ╭───╯
│   │       │   │       │   │       │   │       │   │
───╯   ╰───────╯   ╰───────╯   ╰───────╯   ╰───────╯   ╰──

## C

Translation of: Kotlin
#include <stdio.h>

#define N 32
#define K 3
#define MAX N * K

typedef struct { int x; int y; } point;

void rot(int n, point *p, int rx, int ry) {
int t;
if (!ry) {
if (rx == 1) {
p->x = n - 1 - p->x;
p->y = n - 1 - p->y;
}
t = p->x;
p->x = p->y;
p->y = t;
}
}

void d2pt(int n, int d, point *p) {
int s = 1, t = d, rx, ry;
p->x = 0;
p->y = 0;
while (s < n) {
rx = 1 & (t / 2);
ry = 1 & (t ^ rx);
rot(s, p, rx, ry);
p->x += s * rx;
p->y += s * ry;
t /= 4;
s *= 2;
}
}

int main() {
int d, x, y, cx, cy, px, py;
char pts[MAX][MAX];
point curr, prev;
for (x = 0; x < MAX; ++x)
for (y = 0; y < MAX; ++y) pts[x][y] = ' ';
prev.x = prev.y = 0;
pts[0][0] = '.';
for (d = 1; d < N * N; ++d) {
d2pt(N, d, &curr);
cx = curr.x * K;
cy = curr.y * K;
px = prev.x * K;
py = prev.y * K;
pts[cx][cy] = '.';
if (cx == px ) {
if (py < cy)
for (y = py + 1; y < cy; ++y) pts[cx][y] = '|';
else
for (y = cy + 1; y < py; ++y) pts[cx][y] = '|';
}
else {
if (px < cx)
for (x = px + 1; x < cx; ++x) pts[x][cy] = '_';
else
for (x = cx + 1; x < px; ++x) pts[x][cy] = '_';
}
prev = curr;
}
for (x = 0; x < MAX; ++x) {
for (y = 0; y < MAX; ++y) printf("%c", pts[y][x]);
printf("\n");
}
return 0;
}
Output:
Same as Kotlin entry.

## Go

Library: Go Graphics

The following is based on the recursive algorithm and C code in this paper. The image produced is similar to the one linked to in the zkl example.

package main

import "github.com/fogleman/gg"

var points []gg.Point

const width = 64

func hilbert(x, y, lg, i1, i2 int) {
if lg == 1 {
px := float64(width-x) * 10
py := float64(width-y) * 10
points = append(points, gg.Point{px, py})
return
}
lg >>= 1
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)
}

func main() {
hilbert(0, 0, width, 0, 0)
dc := gg.NewContext(650, 650)
dc.SetRGB(0, 0, 0) // Black background
dc.Clear()
for _, p := range points {
dc.LineTo(p.X, p.Y)
}
dc.SetHexColor("#90EE90") // Light green curve
dc.SetLineWidth(1)
dc.Stroke()
dc.SavePNG("hilbert.png")
}

Translation of: Python
Translation of: JavaScript

Defines an SVG string which can be rendered in a browser. A Hilbert tree is defined in terms of a production rule, and folded to a list of points in a square of given size.

import Data.Bool (bool)
import Data.Tree

rule :: Char -> String
rule c =
case c of
'a' -> "daab"
'b' -> "cbba"
'c' -> "bccd"
_ -> []

vectors :: Char -> [(Int, Int)]
vectors c =
case c of
'a' -> [(-1, 1), (-1, -1), (1, -1), (1, 1)]
'b' -> [(1, -1), (-1, -1), (-1, 1), (1, 1)]
'c' -> [(1, -1), (1, 1), (-1, 1), (-1, -1)]
'd' -> [(-1, 1), (1, 1), (1, -1), (-1, -1)]
_ -> []

main :: IO ()
main = do
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
svgFromPoints w xys =
let sw = show w
points =
(unwords . fmap (((++) . show . fst) <*> ((' ' :) . show . snd))) xys
in unlines
[ "<svg xmlns=\"http://www.w3.org/2000/svg\""
, unwords ["width=\"512\" height=\"512\" viewBox=\"5 5", sw, sw, "\"> "]
, "<path d=\"M" ++ points ++ "\" "
, "stroke-width=\"2\" stroke=\"red\" fill=\"transparent\"/>"
, "</svg>"
]

## IS-BASIC

100 PROGRAM "Hilbert.bas"
110 OPTION ANGLE DEGREES
120 GRAPHICS HIRES 2
130 LET N=5:LET P=1:LET S=11*2^(6-N)
140 PLOT 940,700,ANGLE 180;
150 CALL HILBERT(S,N,P)
160 DEF HILBERT(S,N,P)
170 IF N=0 THEN EXIT DEF
180 PLOT LEFT 90*P;
190 CALL HILBERT(S,N-1,-P)
200 PLOT FORWARD S;RIGHT 90*P;
210 CALL HILBERT(S,N-1,P)
220 PLOT FORWARD S;
230 CALL HILBERT(S,N-1,P)
240 PLOT RIGHT 90*P;FORWARD S;
250 CALL HILBERT(S,N-1,-P)
260 PLOT LEFT 90*P;
270 END DEF

## Java

// Translation from https://en.wikipedia.org/wiki/Hilbert_curve

import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;

public class HilbertCurve {
public static class Point {
public int x;
public int y;

public Point(int x, int y) {
this.x = x;
this.y = y;
}

public String toString() {
return "(" + x + ", " + y + ")";
}

public void rot(int n, boolean rx, boolean ry) {
if (!ry) {
if (rx) {
x = (n - 1) - x;
y = (n - 1) - y;
}

//Swap x and y
int t = x;
x = y;
y = t;
}

return;
}

public int calcD(int n) {
boolean rx, ry;
int d = 0;
for (int s = n >>> 1; s > 0; s >>>= 1) {
rx = ((x & s) != 0);
ry = ((y & s) != 0);
d += s * s * ((rx ? 3 : 0) ^ (ry ? 1 : 0));
rot(s, rx, ry);
}

return d;
}

}

public static Point fromD(int n, int d) {
Point p = new Point(0, 0);
boolean rx, ry;
int t = d;
for (int s = 1; s < n; s <<= 1) {
rx = ((t & 2) != 0);
ry = (((t ^ (rx ? 1 : 0)) & 1) != 0);
p.rot(s, rx, ry);
p.x += (rx ? s : 0);
p.y += (ry ? s : 0);
t >>>= 2;
}
return p;
}

public static List<Point> getPointsForCurve(int n) {
List<Point> points = new ArrayList<Point>();
for (int d = 0; d < (n * n); d++) {
Point p = fromD(n, d);
}

return points;
}

public static List<String> drawCurve(List<Point> points, int n) {
char[][] canvas = new char[n][n * 3 - 2];
for (char[] line : canvas) {
Arrays.fill(line, ' ');
}
for (int i = 1; i < points.size(); i++) {
Point lastPoint = points.get(i - 1);
Point curPoint = points.get(i);
int deltaX = curPoint.x - lastPoint.x;
int deltaY = curPoint.y - lastPoint.y;
if (deltaX == 0) {
if (deltaY == 0) {
// A mistake has been made
throw new IllegalStateException("Duplicate point, deltaX=" + deltaX + ", deltaY=" + deltaY);
}
// Vertical line
int row = Math.max(curPoint.y, lastPoint.y);
int col = curPoint.x * 3;
canvas[row][col] = '|';
}
else {
if (deltaY != 0) {
// A mistake has been made
throw new IllegalStateException("Diagonal line, deltaX=" + deltaX + ", deltaY=" + deltaY);
}
// Horizontal line
int row = curPoint.y;
int col = Math.min(curPoint.x, lastPoint.x) * 3 + 1;
canvas[row][col] = '_';
canvas[row][col + 1] = '_';
}

}
List<String> lines = new ArrayList<String>();
for (char[] row : canvas) {
String line = new String(row);
}

return lines;
}

public static void main(String... args) {
for (int order = 1; order <= 5; order++) {
int n = (1 << order);
List<Point> points = getPointsForCurve(n);
System.out.println("Hilbert curve, order=" + order);
List<String> lines = drawCurve(points, n);
for (String line : lines) {
System.out.println(line);
}
System.out.println();
}
return;
}
}
Output:
Hilbert curve, order=1

|__|

Hilbert curve, order=2
__    __
__|  |__
|   __   |
|__|  |__|

Hilbert curve, order=3
__ __    __ __
|__|   __|  |__   |__|
__   |__    __|   __
|  |__ __|  |__ __|  |
|__    __ __ __    __|
__|  |__    __|  |__
|   __   |  |   __   |
|__|  |__|  |__|  |__|

Hilbert curve, order=4
__    __ __    __ __    __ __    __ __    __
__|  |__   |__|   __|  |__   |__|   __|  |__
|   __   |   __   |__    __|   __   |   __   |
|__|  |__|  |  |__ __|  |__ __|  |  |__|  |__|
__    __   |   __ __    __ __   |   __    __
|  |__|  |  |__|   __|  |__   |__|  |  |__|  |
|__    __|   __   |__    __|   __   |__    __|
__|  |__ __|  |__ __|  |__ __|  |__ __|  |__
|   __ __    __ __    __    __ __    __ __   |
|__|   __|  |__   |__|  |__|   __|  |__   |__|
__   |__    __|   __    __   |__    __|   __
|  |__ __|  |__ __|  |  |  |__ __|  |__ __|  |
|__    __ __ __    __|  |__    __ __ __    __|
__|  |__    __|  |__    __|  |__    __|  |__
|   __   |  |   __   |  |   __   |  |   __   |
|__|  |__|  |__|  |__|  |__|  |__|  |__|  |__|

Hilbert curve, order=5
__ __    __ __    __ __    __ __    __ __    __ __    __ __    __ __    __ __    __ __
|__|   __|  |__   |__|   __|  |__   |__|   __|  |__   |__|   __|  |__   |__|   __|  |__   |__|
__   |__    __|   __   |   __   |   __   |__    __|   __   |   __   |   __   |__    __|   __
|  |__ __|  |__ __|  |  |__|  |__|  |  |__ __|  |__ __|  |  |__|  |__|  |  |__ __|  |__ __|  |
|__    __ __ __    __|   __    __   |   __ __    __ __   |   __    __   |__    __ __ __    __|
__|  |__    __|  |__   |  |__|  |  |__|   __|  |__   |__|  |  |__|  |   __|  |__    __|  |__
|   __   |  |   __   |  |__    __|   __   |__    __|   __   |__    __|  |   __   |  |   __   |
|__|  |__|  |__|  |__|   __|  |__ __|  |__ __|  |__ __|  |__ __|  |__   |__|  |__|  |__|  |__|
__    __    __    __   |__    __ __    __ __    __ __    __ __    __|   __    __    __    __
|  |__|  |  |  |__|  |   __|  |__   |__|   __|  |__   |__|   __|  |__   |  |__|  |  |  |__|  |
|__    __|  |__    __|  |   __   |   __   |__    __|   __   |   __   |  |__    __|  |__    __|
__|  |__ __ __|  |__   |__|  |__|  |  |__ __|  |__ __|  |  |__|  |__|   __|  |__ __ __|  |__
|   __ __    __ __   |   __    __   |   __ __    __ __   |   __    __   |   __ __    __ __   |
|__|   __|  |__   |__|  |  |__|  |  |__|   __|  |__   |__|  |  |__|  |  |__|   __|  |__   |__|
__   |__    __|   __   |__    __|   __   |__    __|   __   |__    __|   __   |__    __|   __
|  |__ __|  |__ __|  |__ __|  |__ __|  |__ __|  |__ __|  |__ __|  |__ __|  |__ __|  |__ __|  |
|__    __ __    __ __    __ __    __ __    __ __ __    __ __    __ __    __ __    __ __    __|
__|  |__   |__|   __|  |__   |__|   __|  |__    __|  |__   |__|   __|  |__   |__|   __|  |__
|   __   |   __   |__    __|   __   |   __   |  |   __   |   __   |__    __|   __   |   __   |
|__|  |__|  |  |__ __|  |__ __|  |  |__|  |__|  |__|  |__|  |  |__ __|  |__ __|  |  |__|  |__|
__    __   |   __ __    __ __   |   __    __    __    __   |   __ __    __ __   |   __    __
|  |__|  |  |__|   __|  |__   |__|  |  |__|  |  |  |__|  |  |__|   __|  |__   |__|  |  |__|  |
|__    __|   __   |__    __|   __   |__    __|  |__    __|   __   |__    __|   __   |__    __|
__|  |__ __|  |__ __|  |__ __|  |__ __|  |__    __|  |__ __|  |__ __|  |__ __|  |__ __|  |__
|   __ __    __ __    __    __ __    __ __   |  |   __ __    __ __    __    __ __    __ __   |
|__|   __|  |__   |__|  |__|   __|  |__   |__|  |__|   __|  |__   |__|  |__|   __|  |__   |__|
__   |__    __|   __    __   |__    __|   __    __   |__    __|   __    __   |__    __|   __
|  |__ __|  |__ __|  |  |  |__ __|  |__ __|  |  |  |__ __|  |__ __|  |  |  |__ __|  |__ __|  |
|__    __ __ __    __|  |__    __ __ __    __|  |__    __ __ __    __|  |__    __ __ __    __|
__|  |__    __|  |__    __|  |__    __|  |__    __|  |__    __|  |__    __|  |__    __|  |__
|   __   |  |   __   |  |   __   |  |   __   |  |   __   |  |   __   |  |   __   |  |   __   |
|__|  |__|  |__|  |__|  |__|  |__|  |__|  |__|  |__|  |__|  |__|  |__|  |__|  |__|  |__|  |__|

## JavaScript

### Imperative

An implementation of GO. Prints an SVG string that can be read in a browser.

const hilbert = (width, spacing, points) => (x, y, lg, i1, i2, f) => {
if (lg === 1) {
const px = (width - x) * spacing;
const py = (width - y) * spacing;
points.push(px, py);
return;
}
lg >>= 1;
f(x + i1 * lg, y + i1 * lg, lg, i1, 1 - i2, f);
f(x + i2 * lg, y + (1 - i2) * lg, lg, i1, i2, f);
f(x + (1 - i1) * lg, y + (1 - i1) * lg, lg, i1, i2, f);
f(x + (1 - i2) * lg, y + i2 * lg, lg, 1 - i1, i2, f);
return points;
};

/**
* Draw a hilbert curve of the given order.
* Outputs a svg string. Save the string as a .svg file and open in a browser.
* @param {!Number} order
*/

const drawHilbert = order => {
if (!order || order < 1) {
throw 'You need to give a valid positive integer';
} else {
order = Math.floor(order);
}

// Curve Constants
const width = 2 ** order;
const space = 10;

// SVG Setup
const size = 500;
const stroke = 2;
const col = "red";
const fill = "transparent";

// Prep and run function
const f = hilbert(width, space, []);
const points = f(0, 0, width, 0, 0, f);
const path = points.join(' ');

console.log(
`<svg xmlns="http://www.w3.org/2000/svg"
width="\${size}"
height="\${size}"
viewBox="\${space / 2} \${space / 2} \${width * space} \${width * space}">
<path d="M\${path}" stroke-width="\${stroke}" stroke="\${col}" fill="\${fill}"/>
</svg>`);

};

drawHilbert(6);

### Functional

Translation of: Python

A composition of pure functions which defines a Hilbert tree as the Nth application of a production rule to a seedling tree.

A list of points is derived by serialization of that tree.

Like the version above, generates an SVG string for display in a browser.

(() => {
'use strict';

const main = () => {

// rule :: Dict Char [Char]
const rule = {
a: ['d', 'a', 'a', 'b'],
b: ['c', 'b', 'b', 'a'],
c: ['b', 'c', 'c', 'd'],
d: ['a', 'd', 'd', 'c']
};

// vectors :: Dict Char [(Int, Int)]
const vectors = ({
'a': [
[-1, 1],
[-1, -1],
[1, -1],
[1, 1]
],
'b': [
[1, -1],
[-1, -1],
[-1, 1],
[1, 1]
],
'c': [
[1, -1],
[1, 1],
[-1, 1],
[-1, -1]
],
'd': [
[-1, 1],
[1, 1],
[1, -1],
[-1, -1]
]
});

// hilbertCurve :: Int -> SVG string
const hilbertCurve = n => {
const w = 1024
return svgFromPoints(w)(
hilbertPoints(w)(
hilbertTree(n)
)
);
}

// hilbertTree :: Int -> Tree Char
const hilbertTree = n => {
const go = tree =>
Node(
tree.root,
0 < tree.nest.length ? (
map(go, tree.nest)
) : map(x => Node(x, []), rule[tree.root])
);
const seed = Node('a', []);
return 0 < n ? (
take(n, iterate(go, seed)).slice(-1)[0]
) : seed;
};

// hilbertPoints :: Size -> Tree Char -> [(x, y)]
// hilbertPoints :: Int -> Tree Char -> [(Int, Int)]
const hilbertPoints = w => tree => {
const go = d => (xy, tree) => {
const
r = Math.floor(d / 2),
centres = map(
v => [
xy[0] + (r * v[0]),
xy[1] + (r * v[1])
],
vectors[tree.root]
);
return 0 < tree.nest.length ? concat(
zipWith(go(r), centres, tree.nest)
) : centres;
};
const d = Math.floor(w / 2);
return go(d)([d, d], tree);
};

// svgFromPoints :: Int -> [(Int, Int)] -> String
const svgFromPoints = w => xys =>
['<svg xmlns="http://www.w3.org/2000/svg"',
`width="500" height="500" viewBox="5 5 \${w} \${w}">`,
`<path d="M\${concat(xys).join(' ')}" `,
'stroke-width="2" stroke="red" fill="transparent"/>',
'</svg>'
].join('\n');

// TEST -------------------------------------------
console.log(
hilbertCurve(6)
);
};

// GENERIC FUNCTIONS ----------------------------------

// Node :: a -> [Tree a] -> Tree a
const Node = (v, xs) => ({
type: 'Node',
root: v, // any type of value (consistent across tree)
nest: xs || []
});

// concat :: [[a]] -> [a]
// concat :: [String] -> String
const concat = xs =>
0 < xs.length ? (() => {
const unit = 'string' !== typeof xs[0] ? (
[]
) : '';
return unit.concat.apply(unit, xs);
})() : [];

// iterate :: (a -> a) -> a -> Gen [a]
function* iterate(f, x) {
let v = x;
while (true) {
yield(v);
v = f(v);
}
}

// Returns Infinity over objects without finite length.
// This enables zip and zipWith to choose the shorter
// argument when one is non-finite, like cycle, repeat etc

// length :: [a] -> Int
const length = xs =>
(Array.isArray(xs) || 'string' === typeof xs) ? (
xs.length
) : Infinity;

// map :: (a -> b) -> [a] -> [b]
const map = (f, xs) =>
(Array.isArray(xs) ? (
xs
) : xs.split('')).map(f);

// take :: Int -> [a] -> [a]
// take :: Int -> String -> String
const take = (n, xs) =>
'GeneratorFunction' !== xs.constructor.constructor.name ? (
xs.slice(0, n)
) : [].concat.apply([], Array.from({
length: n
}, () => {
const x = xs.next();
return x.done ? [] : [x.value];
}));

// Use of `take` and `length` here allows zipping with non-finite lists
// i.e. generators like cycle, repeat, iterate.

// zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
const zipWith = (f, xs, ys) => {
const
lng = Math.min(length(xs), length(ys)),
as = take(lng, xs),
bs = take(lng, ys);
return Array.from({
length: lng
}, (_, i) => f(as[i], bs[i], i));
};

// MAIN ---
return main();
})();

## Julia

Color graphics version using the Gtk package.

using Gtk, Graphics, Colors

Base.isless(p1::Vec2, p2::Vec2) = (p1.x == p2.x ? p1.y < p2.y : p1.x < p2.x)

struct Line
p1::Point
p2::Point
end

dist(p1, p2) = sqrt((p2.y - p1.y)^2 + (p2.x - p1.x)^2)
length(ln::Line) = dist(ln.p1, ln.p2)
isvertical(line) = (line.p1.x == line.p2.x)
ishorizontal(line) = (line.p1.y == line.p2.y)

const colorseq = [colorant"blue", colorant"red", colorant"green"]
const linewidth = 1
const toporder = 3

function drawline(ctx, p1, p2, color, width)
move_to(ctx, p1.x, p1.y)
set_source(ctx, color)
line_to(ctx, p2.x, p2.y)
set_line_width(ctx, width)
stroke(ctx)
end
drawline(ctx, line, color, width=linewidth) = drawline(ctx, line.p1, line.p2, color, width)

function hilbertmutateboxes(ctx, line, order, maxorder=toporder)
if line.p1 < line.p2
p1, p2 = line.p1, line.p2
else
p2, p1 = line.p1, line.p2
end
color = colorseq[order % 3 + 1]
d = dist(p1, p2) / 3
if ishorizontal(line)
pl = Point(p1.x + d, p1.y)
plu = Point(p1.x + d, p1.y - d)
pld = Point(p1.x + d, p1.y + d)
pr = Point(p2.x - d, p2.y)
pru = Point(p2.x - d, p2.y - d)
prd = Point(p2.x - d, p2.y + d)
lines = [Line(plu, pl), Line(plu, pru), Line(pru, pr),
Line(pr, prd), Line(pld, prd), Line(pld, pl)]
else # vertical
pu = Point(p1.x, p1.y + d)
pul = Point(p1.x - d, p1.y + d)
pur = Point(p1.x + d, p1.y + d)
pd = Point(p2.x, p2.y - d)
pdl = Point(p2.x - d, p2.y - d)
pdr = Point(p2.x + d, p2.y - d)
lines = [Line(pul, pu), Line(pul, pdl), Line(pdl, pd),
Line(pu, pur), Line(pur, pdr), Line(pd, pdr)]
end
for li in lines
drawline(ctx, li, color)
end
if order <= maxorder
for li in lines
hilbertmutateboxes(ctx, li, order + 1, maxorder)
end
end
end

const can = @GtkCanvas()
const win = GtkWindow(can, "Hilbert 2D", 400, 400)

@guarded draw(can) do widget
ctx = getgc(can)
h = height(can)
w = width(can)
line = Line(Point(0, h/2), Point(w, h/2))
drawline(ctx, line, colorant"black", 2)
hilbertmutateboxes(ctx, line, 0)
end

show(can)
const cond = Condition()
endit(w) = notify(cond)
signal_connect(endit, win, :destroy)
wait(cond)

## Kotlin

Terminal drawing using ASCII characters within a 96 x 96 grid - starts at top left, ends at top right.

The coordinates of the points are generated using a translation of the C code in the Wikipedia article and then scaled by a factor of 3 (n = 32).

// Version 1.2.40

data class Point(var x: Int, var y: Int)

fun d2pt(n: Int, d: Int): Point {
var x = 0
var y = 0
var t = d
var s = 1
while (s < n) {
val rx = 1 and (t / 2)
val ry = 1 and (t xor rx)
val p = Point(x, y)
rot(s, p, rx, ry)
x = p.x + s * rx
y = p.y + s * ry
t /= 4
s *= 2
}
return Point(x, y)
}

fun rot(n: Int, p: Point, rx: Int, ry: Int) {
if (ry == 0) {
if (rx == 1) {
p.x = n - 1 - p.x
p.y = n - 1 - p.y
}
val t = p.x
p.x = p.y
p.y = t
}
}

fun main(args:Array<String>) {
val n = 32
val k = 3
val pts = List(n * k) { CharArray(n * k) { ' ' } }
var prev = Point(0, 0)
pts[0][0] = '.'
for (d in 1 until n * n) {
val curr = d2pt(n, d)
val cx = curr.x * k
val cy = curr.y * k
val px = prev.x * k
val py = prev.y * k
pts[cx][cy] = '.'
if (cx == px ) {
if (py < cy)
for (y in py + 1 until cy) pts[cx][y] = '|'
else
for (y in cy + 1 until py) pts[cx][y] = '|'
}
else {
if (px < cx)
for (x in px + 1 until cx) pts[x][cy] = '_'
else
for (x in cx + 1 until px) pts[x][cy] = '_'
}
prev = curr
}
for (i in 0 until n * k) {
for (j in 0 until n * k) print(pts[j][i])
println()
}
}
Output:
.  .__.__.  .__.__.  .__.__.  .__.__.  .__.__.  .__.__.  .__.__.  .__.__.  .__.__.  .__.__.  .
|  |     |  |     |  |     |  |     |  |     |  |     |  |     |  |     |  |     |  |     |  |
|  |     |  |     |  |     |  |     |  |     |  |     |  |     |  |     |  |     |  |     |  |
.__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.
|        |        |        |        |        |        |        |        |        |
|        |        |        |        |        |        |        |        |        |
.__.  .__.  .__.  .__.  .  .__.  .  .__.  .__.  .__.  .__.  .  .__.  .  .__.  .__.  .__.  .__.
|  |     |  |     |  |  |  |  |  |  |  |     |  |     |  |  |  |  |  |  |  |     |  |     |  |
|  |     |  |     |  |  |  |  |  |  |  |     |  |     |  |  |  |  |  |  |  |     |  |     |  |
.  .__.__.  .__.__.  .  .__.  .__.  .  .__.__.  .__.__.  .  .__.  .__.  .  .__.__.  .__.__.  .
|                    |              |                    |              |                    |
|                    |              |                    |              |                    |
.__.  .__.__.__.  .__.  .__.  .__.  .  .__.__.  .__.__.  .  .__.  .__.  .__.  .__.__.__.  .__.
|  |        |  |     |  |  |  |  |  |     |  |     |  |  |  |  |  |     |  |        |  |
|  |        |  |     |  |  |  |  |  |     |  |     |  |  |  |  |  |     |  |        |  |
.__.  .__.  .__.  .__.  .  .__.  .  .__.  .__.  .__.  .__.  .  .__.  .  .__.  .__.  .__.  .__.
|        |  |        |  |        |        |        |        |        |  |        |  |        |
|        |  |        |  |        |        |        |        |        |  |        |  |        |
.  .__.  .  .  .__.  .  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .  .__.  .  .  .__.  .
|  |  |  |  |  |  |  |     |  |     |  |     |  |     |  |     |  |     |  |  |  |  |  |  |  |
|  |  |  |  |  |  |  |     |  |     |  |     |  |     |  |     |  |     |  |  |  |  |  |  |  |
.__.  .__.  .__.  .__.  .__.  .__.__.  .__.__.  .__.__.  .__.__.  .__.  .__.  .__.  .__.  .__.
|                                            |
|                                            |
.__.  .__.  .__.  .__.  .__.  .__.__.  .__.__.  .__.__.  .__.__.  .__.  .__.  .__.  .__.  .__.
|  |  |  |  |  |  |  |     |  |     |  |     |  |     |  |     |  |     |  |  |  |  |  |  |  |
|  |  |  |  |  |  |  |     |  |     |  |     |  |     |  |     |  |     |  |  |  |  |  |  |  |
.  .__.  .  .  .__.  .  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .  .__.  .  .  .__.  .
|        |  |        |  |        |        |        |        |        |  |        |  |        |
|        |  |        |  |        |        |        |        |        |  |        |  |        |
.__.  .__.  .__.  .__.  .  .__.  .  .__.  .__.  .__.  .__.  .  .__.  .  .__.  .__.  .__.  .__.
|  |        |  |     |  |  |  |  |  |     |  |     |  |  |  |  |  |     |  |        |  |
|  |        |  |     |  |  |  |  |  |     |  |     |  |  |  |  |  |     |  |        |  |
.__.  .__.__.__.  .__.  .__.  .__.  .  .__.__.  .__.__.  .  .__.  .__.  .__.  .__.__.__.  .__.
|                    |              |                    |              |                    |
|                    |              |                    |              |                    |
.  .__.__.  .__.__.  .  .__.  .__.  .  .__.__.  .__.__.  .  .__.  .__.  .  .__.__.  .__.__.  .
|  |     |  |     |  |  |  |  |  |  |  |     |  |     |  |  |  |  |  |  |  |     |  |     |  |
|  |     |  |     |  |  |  |  |  |  |  |     |  |     |  |  |  |  |  |  |  |     |  |     |  |
.__.  .__.  .__.  .__.  .  .__.  .  .__.  .__.  .__.  .__.  .  .__.  .  .__.  .__.  .__.  .__.
|        |        |        |        |        |        |        |        |        |
|        |        |        |        |        |        |        |        |        |
.__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.
|  |     |  |     |  |     |  |     |  |     |  |     |  |     |  |     |  |     |  |     |  |
|  |     |  |     |  |     |  |     |  |     |  |     |  |     |  |     |  |     |  |     |  |
.  .__.__.  .__.__.  .__.__.  .__.__.  .__.__.  .__.__.  .__.__.  .__.__.  .__.__.  .__.__.  .
|                                                                                            |
|                                                                                            |
.__.  .__.__.  .__.__.  .__.__.  .__.__.  .__.__.__.  .__.__.  .__.__.  .__.__.  .__.__.  .__.
|  |     |  |     |  |     |  |     |  |        |  |     |  |     |  |     |  |     |  |
|  |     |  |     |  |     |  |     |  |        |  |     |  |     |  |     |  |     |  |
.__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.
|        |        |        |        |        |  |        |        |        |        |        |
|        |        |        |        |        |  |        |        |        |        |        |
.  .__.  .  .__.  .__.  .__.  .__.  .  .__.  .  .  .__.  .  .__.  .__.  .__.  .__.  .  .__.  .
|  |  |  |  |  |     |  |     |  |  |  |  |  |  |  |  |  |  |  |     |  |     |  |  |  |  |  |
|  |  |  |  |  |     |  |     |  |  |  |  |  |  |  |  |  |  |  |     |  |     |  |  |  |  |  |
.__.  .__.  .  .__.__.  .__.__.  .  .__.  .__.  .__.  .__.  .  .__.__.  .__.__.  .  .__.  .__.
|                    |                          |                    |
|                    |                          |                    |
.__.  .__.  .  .__.__.  .__.__.  .  .__.  .__.  .__.  .__.  .  .__.__.  .__.__.  .  .__.  .__.
|  |  |  |  |  |     |  |     |  |  |  |  |  |  |  |  |  |  |  |     |  |     |  |  |  |  |  |
|  |  |  |  |  |     |  |     |  |  |  |  |  |  |  |  |  |  |  |     |  |     |  |  |  |  |  |
.  .__.  .  .__.  .__.  .__.  .__.  .  .__.  .  .  .__.  .  .__.  .__.  .__.  .__.  .  .__.  .
|        |        |        |        |        |  |        |        |        |        |        |
|        |        |        |        |        |  |        |        |        |        |        |
.__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.
|  |     |  |     |  |     |  |     |  |        |  |     |  |     |  |     |  |     |  |
|  |     |  |     |  |     |  |     |  |        |  |     |  |     |  |     |  |     |  |
.__.  .__.__.  .__.__.  .__.__.  .__.__.  .__.  .__.  .__.__.  .__.__.  .__.__.  .__.__.  .__.
|                                            |  |                                            |
|                                            |  |                                            |
.  .__.__.  .__.__.  .__.  .__.__.  .__.__.  .  .  .__.__.  .__.__.  .__.  .__.__.  .__.__.  .
|  |     |  |     |  |  |  |     |  |     |  |  |  |     |  |     |  |  |  |     |  |     |  |
|  |     |  |     |  |  |  |     |  |     |  |  |  |     |  |     |  |  |  |     |  |     |  |
.__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.
|        |              |        |              |        |              |        |
|        |              |        |              |        |              |        |
.__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.
|  |     |  |     |  |  |  |     |  |     |  |  |  |     |  |     |  |  |  |     |  |     |  |
|  |     |  |     |  |  |  |     |  |     |  |  |  |     |  |     |  |  |  |     |  |     |  |
.  .__.__.  .__.__.  .  .  .__.__.  .__.__.  .  .  .__.__.  .__.__.  .  .  .__.__.  .__.__.  .
|                    |  |                    |  |                    |  |                    |
|                    |  |                    |  |                    |  |                    |
.__.  .__.__.__.  .__.  .__.  .__.__.__.  .__.  .__.  .__.__.__.  .__.  .__.  .__.__.__.  .__.
|  |        |  |        |  |        |  |        |  |        |  |        |  |        |  |
|  |        |  |        |  |        |  |        |  |        |  |        |  |        |  |
.__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.
|        |  |        |  |        |  |        |  |        |  |        |  |        |  |        |
|        |  |        |  |        |  |        |  |        |  |        |  |        |  |        |
.  .__.  .  .  .__.  .  .  .__.  .  .  .__.  .  .  .__.  .  .  .__.  .  .  .__.  .  .  .__.  .
|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
.__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.  .__.

## Lua

Solved by using the Lindenmayer path, printed with Unicode, which does not show perfectly on web, but is quite nice on console. Should work with all Lua versions, used nothing special. Should work up to Hilbert(12) if your console is big enough for that.

Implemented a full line-drawing Unicode/ASCII drawing and added for the example my signature to the default axiom "A" for fun and a second Hilbert "A" at the end, because it's looking better in the display like that. The implementation of repeated commands was just an additional line of code, so why not?

Lindenmayer:

• A,B are Lindenmayer AXIOMS

Line drawing:

• +,- turn right, left
• F draw line forward
• <num> repeat the following draw command <num> times
• <any> move on canvas without drawing
-- any version from LuaJIT 2.0/5.1, Lua 5.2, Lua 5.3 to LuaJIT 2.1.0-beta3-readline
local bit=bit32 or bit -- Lua 5.2/5.3 compatibilty
-- Hilbert curve implemented by Lindenmayer system
function string.hilbert(s, n)
for i=1,n do
s=s:gsub("[AB]",function(c)
if c=="A" then
c="-BF+AFA+FB-"
else
c="+AF-BFB-FA+"
end
return c
end)
end
s=s:gsub("[AB]",""):gsub("%+%-",""):gsub("%-%+","")
return s
end
-- Or the characters for ASCII line drawing
function charor(c1, c2)
local bits={
[" "]=0x0, ["╷"]=0x1, ["╶"]=0x2, ["┌"]=0x3, ["╵"]=0x4, ["│"]=0x5, ["└"]=0x6, ["├"]=0x7,
["╴"]=0x8, ["┐"]=0x9, ["─"]=0xa, ["┬"]=0xb, ["┘"]=0xc, ["┤"]=0xd, ["┴"]=0xe, ["┼"]=0xf,}
local char={" ", "╷", "╶", "┌", "╵", "│", "└", "├", "╴", "┐", "─", "┬", "┘", "┤", "┴", "┼",}
local b1,b2=bits[c1] or 0,bits[c2] or 0
return char[bit.bor(b1,b2)+1]
end
-- ASCII line drawing routine
function draw(s)
local char={
{"─","┘","╴","┐",}, -- r
{"│","┐","╷","┌",}, -- up
{"─","┌","╶","└",}, -- l
{"│","└","╵","┘",}, -- down
}
local scr={}
local move={{x=1,y=0},{x=0,y=1},{x=-1,y=0},{x=0,y=-1}}
local x,y=1,1
local minx,maxx,miny,maxy=1,1,1,1
local dir,turn=0,0
s=s.."F"
local rep=0
for c in s:gmatch(".") do
if c=="F" then
repeat
if scr[y]==nil then scr[y]={} end
scr[y][x]=charor(char[dir+1][turn%#char[1]+1],scr[y][x] or " ")
dir = (dir+turn) % #move
x, y = x+move[dir+1].x,y+move[dir+1].y
maxx,maxy=math.max(maxx,x),math.max(maxy,y)
minx,miny=math.min(minx,x),math.min(miny,y)
turn=0
rep=rep>1 and rep-1 or 0
until rep==0
elseif c=="-" then
repeat
turn=turn+1
rep=rep>1 and rep-1 or 0
until rep==0
elseif c=="+" then
repeat
turn=turn-1
rep=rep>1 and rep-1 or 0
until rep==0
elseif c:match("%d") then -- allow repeated commands
rep=rep*10+tonumber(c)
else
repeat
x, y = x+move[dir+1].x,y+move[dir+1].y
maxx,maxy=math.max(maxx,x),math.max(maxy,y)
minx,miny=math.min(minx,x),math.min(miny,y)
rep=rep>1 and rep-1 or 0
until rep==0
end
end
for i=maxy,miny,-1 do
local oneline={}
for x=minx,maxx do
oneline[1+x-minx]=scr[i] and scr[i][x] or " "
end
local line=table.concat(oneline)
io.write(line, "\n")
end
end
-- MAIN --
local n=arg[1] and tonumber(arg[1]) or 3
local str=arg[2] or "A"
draw(str:hilbert(n))

Output:
luajit hilbert.lua 4 1M9FAF-4F2+2F-2F-2F++4F-F-4F+2F+2F+2F++3F+2F+3F--4FA10F-16F-58F-16F-
┌─────────────────────────────────────────────────────────┐
│         ┌┐┌┐┌┐┌┐┌┐┌┐┌┐┌┐       ┌┐┌┐┌┐┌┐┌┐┌┐┌┐┌┐         │
│         │└┘││└┘││└┘││└┘│       │└┘││└┘││└┘││└┘│         │
│         └┐┌┘└┐┌┘└┐┌┘└┐┌┘       └┐┌┘└┐┌┘└┐┌┘└┐┌┘         │
│         ┌┘└──┘└┐┌┘└──┘└┐       ┌┘└──┘└┐┌┘└──┘└┐         │
│         │┌─┐┌─┐││┌─┐┌─┐│       │┌─┐┌─┐││┌─┐┌─┐│         │
│         └┘┌┘└┐└┘└┘┌┘└┐└┘       └┘┌┘└┐└┘└┘┌┘└┐└┘         │
│         ┌┐└┐┌┘┌┐┌┐└┐┌┘┌┐       ┌┐└┐┌┘┌┐┌┐└┐┌┘┌┐         │
│         │└─┘└─┘└┘└─┘└─┘│       │└─┘└─┘└┘└─┘└─┘│         │
│         └┐┌─┐┌─┐┌─┐┌─┐┌┘       └┐┌─┐┌─┐┌─┐┌─┐┌┘         │
│         ┌┘└┐└┘┌┘└┐└┘┌┘└┐       ┌┘└┐└┘┌┘└┐└┘┌┘└┐         │
│         │┌┐│┌┐└┐┌┘┌┐│┌┐│       │┌┐│┌┐└┐┌┘┌┐│┌┐│         │
│         └┘└┘│└─┘└─┘│└┘└┘╷ ╷┌─┐ └┘└┘│└─┘└─┘│└┘└┘         │
│         ┌┐┌┐│┌─┐┌─┐│┌┐┌┐│ ││ │ ┌┐┌┐│┌─┐┌─┐│┌┐┌┐         │
│         │└┘│└┘┌┘└┐└┘│└┘│├─┤├─┴┐│└┘│└┘┌┘└┐└┘│└┘│         │
│         └┐┌┘┌┐└┐┌┘┌┐└┐┌┘│ ││  │└┐┌┘┌┐└┐┌┘┌┐└┐┌┘         │
└──────────┘└─┘└─┘└─┘└─┘└─┘ └┴──┴─┘└─┘└─┘└─┘└─┘└──────────┘

## Mathematica

Works with: Mathematica 11

[email protected][4]

## Perl

use SVG;
use List::Util qw(max min);

use constant pi => 2 * atan2(1, 0);

# Compute the curve with a Lindemayer-system
%rules = (
A => '-BF+AFA+FB-',
B => '+AF-BFB-FA+'
);
\$hilbert = 'A';
\$hilbert =~ s/([AB])/\$rules{\$1}/eg for 1..6;

# Draw the curve in SVG
(\$x, \$y) = (0, 0);
\$theta = pi/2;
\$r = 5;

for (split //, \$hilbert) {
if (/F/) {
push @X, sprintf "%.0f", \$x;
push @Y, sprintf "%.0f", \$y;
\$x += \$r * cos(\$theta);
\$y += \$r * sin(\$theta);
}
elsif (/\+/) { \$theta += pi/2; }
elsif (/\-/) { \$theta -= pi/2; }
}

\$max = max(@X,@Y);
\$xt = -min(@X)+10;
\$yt = -min(@Y)+10;
\$svg = SVG->new(width=>\$max+20, height=>\$max+20);
\$points = \$svg->get_path(x=>\@X, y=>\@Y, -type=>'polyline');
\$svg->rect(width=>"100%", height=>"100%", style=>{'fill'=>'black'});
\$svg->polyline(%\$points, style=>{'stroke'=>'orange', 'stroke-width'=>1}, transform=>"translate(\$xt,\$yt)");

open \$fh, '>', 'hilbert_curve.svg';
print \$fh \$svg->xmlify(-namespace=>'svg');
close \$fh;

Hilbert curve (offsite image)

## Perl 6

Works with: Rakudo version 2018.03
use SVG;

role Lindenmayer {
has %.rules;
method succ {
self.comb.map( { %!rules{\$^c} // \$c } ).join but Lindenmayer(%!rules)
}
}

my \$hilbert = 'A' but Lindenmayer( { A => '-BF+AFA+FB-', B => '+AF-BFB-FA+' } );

\$hilbert++ xx 7;
my @points = (647, 13);

for \$hilbert.comb {
state (\$x, \$y) = @points[0,1];
state \$d = -5 - 0i;
when 'F' { @points.append: (\$x += \$d.re).round(1), (\$y += \$d.im).round(1) }
when /< + - >/ { \$d *= "{\$_}1i" }
default { }
}

say SVG.serialize(
svg => [
:660width, :660height, :style<stroke:blue>,
:rect[:width<100%>, :height<100%>, :fill<white>],
:polyline[ :points(@points.join: ','), :fill<white> ],
],
);

See: Hilbert curve

There is a variation of a Hilbert curve known as a Moore curve which is essentially 4 Hilbert curves joined together in a loop.

use SVG;

role Lindenmayer {
has %.rules;
method succ {
self.comb.map( { %!rules{\$^c} // \$c } ).join but Lindenmayer(%!rules)
}
}

my \$moore = 'AFA+F+AFA' but Lindenmayer( { A => '-BF+AFA+FB-', B => '+AF-BFB-FA+' } );

\$moore++ xx 6;
my @points = (327, 647);

for \$moore.comb {
state (\$x, \$y) = @points[0,1];
state \$d = 0 - 5i;
when 'F' { @points.append: (\$x += \$d.re).round(1), (\$y += \$d.im).round(1) }
when /< + - >/ { \$d *= "{\$_}1i" }
default { }
}

say SVG.serialize(
svg => [
:660width, :660height, :style<stroke:darkviolet>,
:rect[:width<100%>, :height<100%>, :fill<white>],
:polyline[ :points(@points.join: ','), :fill<white> ],
],
);

See: Moore curve

## Phix

Library: pGUI
Translation of: Go
-- demo\rosetta\hilbert_curve.exw
include pGUI.e

Ihandle dlg, canvas
cdCanvas cddbuffer, cdcanvas

constant width = 64

sequence points = {}

procedure hilbert(integer x, y, lg, i1, i2)
if lg=1 then
integer px := (width-x) * 10,
py := (width-y) * 10
points = append(points, {px, py})
return
end if
lg /= 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)
end procedure

function redraw_cb(Ihandle /*ih*/, integer /*posx*/, integer /*posy*/)
cdCanvasActivate(cddbuffer)
cdCanvasBegin(cddbuffer, CD_OPEN_LINES)
for i=1 to length(points) do
integer {x,y} = points[i]
cdCanvasVertex(cddbuffer, x, y)
end for
cdCanvasEnd(cddbuffer)
cdCanvasFlush(cddbuffer)
return IUP_DEFAULT
end function

function map_cb(Ihandle ih)
cdcanvas = cdCreateCanvas(CD_IUP, ih)
cddbuffer = cdCreateCanvas(CD_DBUFFER, cdcanvas)
cdCanvasSetBackground(cddbuffer, CD_WHITE)
cdCanvasSetForeground(cddbuffer, CD_MAGENTA)
return IUP_DEFAULT
end function

procedure main()
hilbert(0, 0, width, 0, 0)
IupOpen()
canvas = IupCanvas(NULL)
IupSetAttribute(canvas, "RASTERSIZE", "655x655")
IupSetCallback(canvas, "MAP_CB", Icallback("map_cb"))
dlg = IupDialog(canvas)
IupSetAttribute(dlg, "TITLE", "Hilbert Curve")
IupSetAttribute(dlg, "DIALOGFRAME", "YES") -- no resize here
IupCloseOnEscape(dlg)
IupSetCallback(canvas, "ACTION", Icallback("redraw_cb"))
IupMap(dlg)
IupShowXY(dlg,IUP_CENTER,IUP_CENTER)
IupMainLoop()
IupClose()
end procedure
main()

## Python

### Functional

Composition of pure functions, with type comments for the reader rather than the compiler.

An SVG path is serialised from the Nth application of re-write rules to a Hilbert tree structure.

(To view the Hilbert curve, save the output SVG text in a file with an appropriate extension (e.g. .svg), and open it with a browser).

Works with: Python version 3.7
'''Hilbert curve'''

from itertools import (chain, islice, starmap)
from inspect import signature

# hilbertCurve :: Int -> SVG String
def hilbertCurve(n):
'''An SVG string representing a
Hilbert curve of degree n.
'''

w = 1024
return svgFromPoints(w)(
hilbertPoints(w)(
hilbertTree(n)
)
)

# hilbertTree :: Int -> Tree Char
def hilbertTree(n):
'''Nth application of a rule to a seedling tree.'''

# rule :: Dict Char [Char]
rule = {
'a': ['d', 'a', 'a', 'b'],
'b': ['c', 'b', 'b', 'a'],
'c': ['b', 'c', 'c', 'd'],
'd': ['a', 'd', 'd', 'c']
}

# go :: Tree Char -> Tree Char
def go(tree):
c = tree['root']
xs = tree['nest']
return Node(c)(
map(go, xs) if xs else map(
flip(Node)([]),
rule[c]
)
)
seed = Node('a')([])
return list(islice(
iterate(go)(seed), n
))[-1] if 0 < n else seed

# hilbertPoints :: Int -> Tree Char -> [(Int, Int)]
def hilbertPoints(w):
'''Serialization of a tree to a list of points
bounded by a square of side w.
'''

# vectors :: Dict Char [(Int, Int)]
vectors = {
'a': [(-1, 1), (-1, -1), (1, -1), (1, 1)],
'b': [(1, -1), (-1, -1), (-1, 1), (1, 1)],
'c': [(1, -1), (1, 1), (-1, 1), (-1, -1)],
'd': [(-1, 1), (1, 1), (1, -1), (-1, -1)]
}

# points :: Int -> ((Int, Int), Tree Char) -> [(Int, Int)]
def points(d):
'''Size -> Centre of a Hilbert subtree -> All subtree points
'''

def go(xy, tree):
r = d // 2
centres = map(
lambda v: (
xy[0] + (r * v[0]),
xy[1] + (r * v[1])
),
vectors[tree['root']]
)
return chain.from_iterable(
starmap(points(r), zip(centres, tree['nest']))
) if tree['nest'] else centres
return lambda xy, tree: go(xy, tree)

d = w // 2
return lambda tree: list(points(d)((d, d), tree))

# svgFromPoints :: Int -> [(Int, Int)] -> SVG String
def svgFromPoints(w):
'''Width of square canvas -> Point list -> SVG string'''

def go(w, xys):
xs = ' '.join(map(
lambda xy: str(xy[0]) + ' ' + str(xy[1]),
xys
))
return '\n'.join(
['<svg xmlns="http://www.w3.org/2000/svg"',
f'width="512" height="512" viewBox="5 5 {w} {w}">',
f'<path d="M{xs}" ',
'stroke-width="2" stroke="red" fill="transparent"/>',
'</svg>'
]
)
return lambda xys: go(w, xys)

# TEST ----------------------------------------------------
def main():
'''Testing generation of the SVG for a Hilbert curve'''
print(
hilbertCurve(6)
)

# GENERIC FUNCTIONS ---------------------------------------

# Node :: a -> [Tree a] -> Tree a
def Node(v):
'''Contructor for a Tree node which connects a
value of some kind to a list of zero or
more child trees.'''

return lambda xs: {'type': 'Node', 'root': v, 'nest': xs}

# flip :: (a -> b -> c) -> b -> a -> c
def flip(f):
'''The (curried or uncurried) function f with its
arguments reversed.'''

if 1 < len(signature(f).parameters):
return lambda a, b: f(b, a)
else:
return lambda a: lambda b: f(b)(a)

# iterate :: (a -> a) -> a -> Gen [a]
def iterate(f):
'''An infinite list of repeated
applications of f to x.
'''

def go(x):
v = x
while True:
yield v
v = f(v)
return lambda x: go(x)

# TEST ---------------------------------------------------
if __name__ == '__main__':
main()

## Ring

# Project : Hilbert curve

paint = null
x1 = 0
y1 = 0

new qapp
{
win1 = new qwidget() {
setwindowtitle("Hilbert curve")
setgeometry(100,100,400,500)
label1 = new qlabel(win1) {
setgeometry(10,10,400,400)
settext("")
}
new qpushbutton(win1) {
setgeometry(150,400,100,30)
settext("draw")
setclickevent("draw()")
}
show()
}
exec()
}

func draw
p1 = new qpicture()
color = new qcolor() {
setrgb(0,0,255,255)
}
pen = new qpen() {
setcolor(color)
setwidth(1)
}
paint = new qpainter() {
begin(p1)
setpen(pen)

x1 = 0.5
y1 = 0.5
hilbert(0, 0, 200, 0, 0, 200, 4)

endpaint()
}
label1 { setpicture(p1) show() }

func hilbert (x, y, xi, xj, yi, yj, n)
cur = new QCursor() {
setpos(100, 100)
}

if (n <= 0)
drawtoline(x + (xi + yi)/2, y + (xj + yj)/2)
else
hilbert(x, y, yi/2, yj/2, xi/2, xj/2, n-1)
hilbert(x+xi/2, y+xj/2 , xi/2, xj/2, yi/2, yj/2, n-1)
hilbert(x+xi/2+yi/2, y+xj/2+yj/2, xi/2, xj/2, yi/2, yj/2, n-1);
hilbert(x+xi/2+yi, y+xj/2+yj, -yi/2,-yj/2, -xi/2, -xj/2, n-1)
ok

func drawtoline x2, y2
paint.drawline(x1, y1, x2, y2)
x1 = x2
y1 = y2

Output image: Hilbert curve

## Scala

### Scala.js

@js.annotation.JSExportTopLevel("ScalaFiddle")
object ScalaFiddle {
// \$FiddleStart
import scala.util.Random

case class Point(x: Int, y: Int)

def xy2d(order: Int, d: Int): Point = {
def rot(order: Int, p: Point, rx: Int, ry: Int): Point = {
val np = if (rx == 1) Point(order - 1 - p.x, order - 1 - p.y) else p
if (ry == 0) Point(np.y, np.x) else p
}

@scala.annotation.tailrec
def iter(rx: Int, ry: Int, s: Int, t: Int, p: Point): Point = {
if (s < order) {
val _rx = 1 & (t / 2)
val _ry = 1 & (t ^ _rx)
val temp = rot(s, p, _rx, _ry)
iter(_rx, _ry, s * 2, t / 4, Point(temp.x + s * _rx, temp.y + s * _ry))
} else p
}

iter(0, 0, 1, d, Point(0, 0))
}

def randomColor =
s"rgb(\${Random.nextInt(240)}, \${Random.nextInt(240)}, \${Random.nextInt(240)})"

val order = 64
val factor = math.min(Fiddle.canvas.height, Fiddle.canvas.width) / order.toDouble
val maxD = order * order
var d = 0
Fiddle.draw.strokeStyle = randomColor
Fiddle.draw.lineWidth = 2
Fiddle.draw.lineCap = "square"

Fiddle.schedule(10) {
val h = xy2d(order, d)
Fiddle.draw.lineTo(h.x * factor, h.y * factor)
Fiddle.draw.stroke
if ({d += 1; d >= maxD})
{d = 1; Fiddle.draw.strokeStyle = randomColor}
Fiddle.draw.beginPath
Fiddle.draw.moveTo(h.x * factor, h.y * factor)
}
// \$FiddleEnd
}
Output:
Best seen running in your browser by ScalaFiddle (ES aka JavaScript, non JVM).

## Seed7

\$ include "seed7_05.s7i";
include "draw.s7i";
include "keybd.s7i";

const integer: delta is 8;

const proc: drawDown (inout integer: x, inout integer: y, in integer: n) is forward;
const proc: drawUp (inout integer: x, inout integer: y, in integer: n) is forward;

const proc: drawRight (inout integer: x, inout integer: y, in integer: n) is func
begin
if n > 0 then
drawDown(x, y, pred(n));
line(x, y, 0, delta, white);
y +:= delta;
drawRight(x, y, pred(n));
line(x, y, delta, 0, white);
x +:= delta;
drawRight(x, y, pred(n));
line(x, y, 0, -delta, white);
y -:= delta;
drawUp(x, y, pred(n));
end if;
end func;

const proc: drawLeft (inout integer: x, inout integer: y, in integer: n) is func
begin
if n > 0 then
drawUp(x, y, pred(n));
line(x, y, 0, -delta, white);
y -:= delta;
drawLeft(x, y, pred(n));
line(x, y, -delta, 0, white);
x -:= delta;
drawLeft(x, y, pred(n));
line(x, y, 0, delta, white);
y +:= delta;
drawDown(x, y, pred(n));
end if;
end func;

const proc: drawDown (inout integer: x, inout integer: y, in integer: n) is func
begin
if n > 0 then
drawRight(x, y, pred(n));
line(x, y, delta, 0, white);
x +:= delta;
drawDown(x, y, pred(n));
line(x, y, 0, delta, white);
y +:= delta;
drawDown(x, y, pred(n));
line(x, y, -delta, 0, white);
x -:= delta;
drawLeft(x, y, pred(n));
end if;
end func;

const proc: drawUp (inout integer: x, inout integer: y, in integer: n) is func
begin
if n > 0 then
drawLeft(x, y, pred(n));
line(x, y, -delta, 0, white);
x -:= delta;
drawUp(x, y, pred(n));
line(x, y, 0, -delta, white);
y -:= delta;
drawUp(x, y, pred(n));
line(x, y, delta, 0, white);
x +:= delta;
drawRight(x, y, pred(n));
end if;
end func;

const proc: main is func
local
var integer: x is 11;
var integer: y is 11;
begin
screen(526, 526);
KEYBOARD := GRAPH_KEYBOARD;
drawRight(x, y, 6);
end func;

## Sidef

require('Image::Magick')

class Turtle(
x = 500,
y = 500,
angle = 0,
scale = 1,
mirror = 1,
xoff = 0,
yoff = 0,
color = 'black',
) {

has im = %O<Image::Magick>.new(size => "#{x}x#{y}")

method init {
}

method forward(r) {
var (newx, newy) = (x + r*sin(angle), y + r*-cos(angle))

im.Draw(
primitive => 'line',
points => join(' ',
int(x * scale + xoff),
int(y * scale + yoff),
int(newx * scale + xoff),
int(newy * scale + yoff),
),
stroke => color,
strokewidth => 1,
)

(x, y) = (newx, newy)
}

method save_as(filename) {
im.Write(filename)
}

method turn(theta) {
angle += theta*mirror
}

method state {
[x, y, angle, mirror]
}

method setstate(state) {
(x, y, angle, mirror) = state...
}

method mirror {
mirror.neg!
}
}

class LSystem(
angle = 90,
scale = 1,
xoff = 0,
yoff = 0,
len = 5,
color = 'black',
width = 500,
height = 500,
turn = 0,
) {

has stack = []
has table = Hash()

has turtle = Turtle(
x: width,
y: height,
angle: turn,
scale: scale,
color: color,
xoff: xoff,
yoff: yoff,
)

method init {

table = Hash(
'+' => { turtle.turn(angle) },
'-' => { turtle.turn(-angle) },
':' => { turtle.mirror },
'[' => { stack.push(turtle.state) },
']' => { turtle.setstate(stack.pop) },
)
}

method execute(string, repetitions, filename, rules) {

repetitions.times {
string.gsub!(/(.)/, {|c| rules{c} \\ c })
}

string.each_char { |c|
if (table.contains(c)) {
table{c}.run
}
elsif (c.contains(/^[[:upper:]]\z/)) {
turtle.forward(len)
}
}

turtle.save_as(filename)
}
}

var rules = Hash(
a => '-bF+aFa+Fb-',
b => '+aF-bFb-Fa+',
)

var lsys = LSystem(
width: 600,
height: 600,

xoff: -50,
yoff: -50,

len: 8,
angle: 90,
color: 'dark green',
)

lsys.execute('a', 6, "hilbert_curve.png", rules)
Output:

## Vala

Library: Gtk+-3.0
struct Point{
int x;
int y;
Point(int px,int py){
x=px;
y=py;
}
}

public class Hilbert : Gtk.DrawingArea {

private int it = 1;
private Point[] points;
private const int WINSIZE = 300;

public Hilbert() {
set_size_request(WINSIZE, WINSIZE);
}

public void button_toggled_cb(Gtk.ToggleButton button){
if(button.get_active()){
it = int.parse(button.get_label());
redraw_canvas();
}
}

public override bool draw(Cairo.Context cr){
int border_size = 20;
int unit = (WINSIZE - 2 * border_size)/((1<<it)-1);

//adjust border_size to center the drawing
border_size = border_size + (WINSIZE - 2 * border_size - unit * ((1<<it)-1)) / 2;

//white background
cr.rectangle(0, 0, WINSIZE, WINSIZE);
cr.set_source_rgb(1, 1, 1);
cr.fill_preserve();
cr.stroke();

points = {};
hilbert(0, 0, 1<<it, 0, 0);

//magenta lines
cr.set_source_rgb(1, 0, 1);

// move to first point
Point point = translate(border_size, WINSIZE, unit*points[0].x, unit*points[0].y);
cr.move_to(point.x, point.y);

foreach(Point i in points[1:points.length]){
point = translate(border_size, WINSIZE, unit*i.x, unit*i.y);
cr.line_to(point.x, point.y);
}
cr.stroke();
return false;
}

private Point translate(int border_size, int size, int x, int y){
return Point(border_size + x,size - border_size - y);
}

private void hilbert(int x, int y, int lg, int i1, int i2) {
if (lg == 1) {
points += Point(x,y);
return;
}
lg >>= 1;
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);
}

private void redraw_canvas(){
var window = get_window();
if (window == null)return;
window.invalidate_region(window.get_clip_region(), true);
}
}

int main(string[] args){
Gtk.init (ref args);

var window = new Gtk.Window();
window.title = "Rosetta Code / Hilbert";
window.window_position = Gtk.WindowPosition.CENTER;
window.destroy.connect(Gtk.main_quit);
window.set_resizable(false);

var label = new Gtk.Label("Iterations:");

// create radio buttons to select the number of iterations
rb1.set_label("1");
var rb2 = new Gtk.RadioButton.with_label_from_widget(rb1, "2");
var rb3 = new Gtk.RadioButton.with_label_from_widget(rb1, "3");
var rb4 = new Gtk.RadioButton.with_label_from_widget(rb1, "4");
var rb5 = new Gtk.RadioButton.with_label_from_widget(rb1, "5");

var hilbert = new Hilbert();

rb1.toggled.connect(hilbert.button_toggled_cb);
rb2.toggled.connect(hilbert.button_toggled_cb);
rb3.toggled.connect(hilbert.button_toggled_cb);
rb4.toggled.connect(hilbert.button_toggled_cb);
rb5.toggled.connect(hilbert.button_toggled_cb);

var box = new Gtk.Box(Gtk.Orientation.HORIZONTAL, 0);
box.pack_start(label, false, false, 5);
box.pack_start(rb1, false, false, 0);
box.pack_start(rb2, false, false, 0);
box.pack_start(rb3, false, false, 0);
box.pack_start(rb4, false, false, 0);
box.pack_start(rb5, false, false, 0);

var grid = new Gtk.Grid();
grid.attach(box, 0, 0, 1, 1);
grid.attach(hilbert, 0, 1, 1, 1);
grid.set_border_width(5);
grid.set_row_spacing(5);

window.show_all();

//initialise the drawing with iteration = 4
rb4.set_active(true);

Gtk.main();
return 0;
}

## Yabasic

Translation of: Go
width = 64

sub hilbert(x, y, lg, i1, i2)
if lg = 1 then
line to (width-x) * 10, (width-y) * 10
return
end if
lg = lg / 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)
end sub

open window 655, 655

hilbert(0, 0, width, 0, 0)

## zkl

Uses Image Magick and the PPM class from http://rosettacode.org/wiki/Bitmap/Bresenham%27s_line_algorithm#zkl

hilbert(6) : turtle(_);

fcn hilbert(n){ // Lindenmayer system --> Data of As & Bs
var [const] A="-BF+AFA+FB-", B="+AF-BFB-FA+";
buf1,buf2 := Data(Void,"A").howza(3), Data().howza(3); // characters
do(n){
buf1.pump(buf2.clear(),fcn(c){ if(c=="A") A else if(c=="B") B else c });
t:=buf1; buf1=buf2; buf2=t; // swap buffers
}
buf1 // n=6 --> 13,651 letters
}

fcn turtle(hilbert){
const D=10;
ds,dir := T( T(D,0), T(0,-D), T(-D,0), T(0,D) ), 0; // turtle offsets
dx,dy := ds[dir];
img:=PPM(650,650); x,y:=10,10; color:=0x00ff00;
hilbert.replace("A","").replace("B",""); // A & B are no-op during drawing
foreach c in (hilbert){
switch(c){
case("F"){ img.line(x,y, (x+=dx),(y+=dy), color) } // draw forward
case("+"){ dir=(dir+1)%4; dx,dy = ds[dir] } // turn right 90*
case("-"){ dir=(dir-1)%4; dx,dy = ds[dir] } // turn left 90*
}
}
img.writeJPGFile("hilbert.zkl.jpg");
}

Image at hilbert curve