Hilbert curve: Difference between revisions

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(Hilbert curve en FreeBASIC)
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{{output}}
{{output}}
<pre>Same as Kotlin entry.</pre>
<pre>Same as Kotlin entry.</pre>

=={{header|D}}==
{{trans|Java}}
<lang d>import std.stdio;

void main() {
foreach (order; 1..6) {
int n = 1 << order;
auto points = getPointsForCurve(n);
writeln("Hilbert curve, order=", order);
auto lines = drawCurve(points, n);
foreach (line; lines) {
writeln(line);
}
writeln;
}
}

struct Point {
int x, y;

//rotate/flip a quadrant appropriately
void rot(int n, bool rx, bool ry) {
if (!ry) {
if (rx) {
x = (n - 1) - x;
y = (n - 1) - y;
}

import std.algorithm.mutation;
swap(x, y);
}
}

int calcD(int n) {
bool rx, ry;
int d;
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;
}

void toString(scope void delegate(const(char)[]) sink) const {
import std.format : formattedWrite;

sink("(");
sink.formattedWrite!"%d"(x);
sink(", ");
sink.formattedWrite!"%d"(y);
sink(")");
}
}

auto fromD(int n, int d) {
Point p;
bool 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;
}

auto getPointsForCurve(int n) {
Point[] points;
for (int d; d < n * n; ++d) {
points ~= fromD(n, d);
}
return points;
}

auto drawCurve(Point[] points, int n) {
import std.algorithm.comparison : min, max;
import std.array : uninitializedArray;
import std.exception : enforce;

auto canvas = uninitializedArray!(char[][])(n, n * 3 - 2);
foreach (line; canvas) {
line[] = ' ';
}

for (int i = 1; i < points.length; ++i) {
auto lastPoint = points[i - 1];
auto curPoint = points[i];
int deltaX = curPoint.x - lastPoint.x;
int deltaY = curPoint.y - lastPoint.y;
if (deltaX == 0) {
enforce(deltaY != 0, "Duplicate point");
// vertical line
int row = max(curPoint.y, lastPoint.y);
int col = curPoint.x * 3;
canvas[row][col] = '|';
} else {
enforce(deltaY == 0, "Diagonal line");
// horizontal line
int row = curPoint.y;
int col = min(curPoint.x, lastPoint.x) * 3 + 1;
canvas[row][col] = '_';
canvas[row][col + 1] = '_';
}
}

string[] lines;
foreach (row; canvas) {
lines ~= row.idup;
}

return lines;
}</lang>
{{out}}
<pre>Hilbert curve, order=1

|__|

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

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

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

Hilbert curve, order=5
__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __
|__| __| |__ |__| __| |__ |__| __| |__ |__| __| |__ |__| __| |__ |__|
__ |__ __| __ | __ | __ |__ __| __ | __ | __ |__ __| __
| |__ __| |__ __| | |__| |__| | |__ __| |__ __| | |__| |__| | |__ __| |__ __| |
|__ __ __ __ __| __ __ | __ __ __ __ | __ __ |__ __ __ __ __|
__| |__ __| |__ | |__| | |__| __| |__ |__| | |__| | __| |__ __| |__
| __ | | __ | |__ __| __ |__ __| __ |__ __| | __ | | __ |
|__| |__| |__| |__| __| |__ __| |__ __| |__ __| |__ __| |__ |__| |__| |__| |__|
__ __ __ __ |__ __ __ __ __ __ __ __ __ __| __ __ __ __
| |__| | | |__| | __| |__ |__| __| |__ |__| __| |__ | |__| | | |__| |
|__ __| |__ __| | __ | __ |__ __| __ | __ | |__ __| |__ __|
__| |__ __ __| |__ |__| |__| | |__ __| |__ __| | |__| |__| __| |__ __ __| |__
| __ __ __ __ | __ __ | __ __ __ __ | __ __ | __ __ __ __ |
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| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |
|__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __|
__| |__ |__| __| |__ |__| __| |__ __| |__ |__| __| |__ |__| __| |__
| __ | __ |__ __| __ | __ | | __ | __ |__ __| __ | __ |
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=={{header|FreeBASIC}}==
=={{header|FreeBASIC}}==

Revision as of 00:23, 27 July 2019

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


Task

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

<lang algol68>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 </lang>

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

C

Translation of: Kotlin

<lang c>#include <stdio.h>

  1. define N 32
  2. define K 3
  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;

}</lang>

Output:
Same as Kotlin entry.

D

Translation of: Java

<lang d>import std.stdio;

void main() { 

   foreach (order; 1..6) {
       int n = 1 << order;
       auto points = getPointsForCurve(n);
       writeln("Hilbert curve, order=", order);
       auto lines = drawCurve(points, n);
       foreach (line; lines) {
           writeln(line);
       }
       writeln;
   }

}

struct Point { 

   int x, y;

   //rotate/flip a quadrant appropriately
   void rot(int n, bool rx, bool ry) {
       if (!ry) {
           if (rx) {
               x = (n - 1) - x;
               y = (n - 1) - y;
           }

           import std.algorithm.mutation;
           swap(x, y);
       }
   }

   int calcD(int n) {
       bool rx, ry;
       int d;
       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;
   }

   void toString(scope void delegate(const(char)[]) sink) const {
       import std.format : formattedWrite;

       sink("(");
       sink.formattedWrite!"%d"(x);
       sink(", ");
       sink.formattedWrite!"%d"(y);
       sink(")");
   }

}

auto fromD(int n, int d) { 

   Point p;
   bool 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;

}

auto getPointsForCurve(int n) { 

   Point[] points;
   for (int d; d < n * n; ++d) {
       points ~= fromD(n, d);
   }
   return points;

}

auto drawCurve(Point[] points, int n) { 

   import std.algorithm.comparison : min, max;
   import std.array : uninitializedArray;
   import std.exception : enforce;

   auto canvas = uninitializedArray!(char[][])(n, n * 3 - 2);
   foreach (line; canvas) {
       line[] =  ' ';
   }

   for (int i = 1; i < points.length; ++i) {
       auto lastPoint = points[i - 1];
       auto curPoint = points[i];
       int deltaX = curPoint.x - lastPoint.x;
       int deltaY = curPoint.y - lastPoint.y;
       if (deltaX == 0) {
           enforce(deltaY != 0, "Duplicate point");
           // vertical line
           int row = max(curPoint.y, lastPoint.y);
           int col = curPoint.x * 3;
           canvas[row][col] = '|';
       } else {
           enforce(deltaY == 0, "Diagonal line");
           // horizontal line
           int row = curPoint.y;
           int col = min(curPoint.x, lastPoint.x) * 3 + 1;
           canvas[row][col] = '_';
           canvas[row][col + 1] = '_';
       }
   }

   string[] lines;
   foreach (row; canvas) {
       lines ~= row.idup;
   }

   return lines;

}</lang>

Output:
Hilbert curve, order=1

|__|

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

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

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

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

FreeBASIC

Translation of: Yabasic

<lang freebasic> Dim Shared As Integer ancho = 64

Sub Hilbert(x As Integer, y As Integer, lg As Integer, i1 As Integer, i2 As Integer) 

   If lg = 1 Then
       Line - ((ancho-x) * 10, (ancho-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

Screenres 655, 655

Hilbert(0, 0, ancho, 0, 0) End </lang>

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. <lang go>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")

}</lang>

Haskell

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.

<lang haskell>import Data.Bool (bool) import Data.Tree

rule :: Char -> String rule c = 

 case c of
   'a' -> "daab"
   'b' -> "cbba"
   'c' -> "bccd"
   'd' -> "addc"
   _ -> []

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>"
      ]</lang>

IS-BASIC

<lang 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</lang>

Java

<lang 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 + ")";
       }
       
       //rotate/flip a quadrant appropriately
       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);
           points.add(p);
       }
       
       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);
           lines.add(line);
       }
       
       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;
   }

}</lang>

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. <lang javascript>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);</lang>

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.

<lang JavaScript>(() => { 

   '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();

})();</lang>

Julia

Color graphics version using the Gtk package. <lang julia>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) </lang>

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). <lang scala>// 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()
   }

}</lang>

Output:
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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

<lang lua>-- 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)) </lang>

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 <lang Mathematica>Graphics@HilbertCurve[4]</lang>

Perl

<lang perl>use SVG; use List::Util qw(max min);

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

  1. 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;

  1. 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;</lang> Hilbert curve (offsite image)

Perl 6

Works with: Rakudo version 2018.03

<lang perl6>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> ],
   ],

);</lang> 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. <lang perl6>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> ],
   ],

);</lang> See: Moore curve

Phix

Library: pGUI
Translation of: Go

<lang Phix>-- 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()</lang>

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

<lang Python>Hilbert curve

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


  1. 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)
       )
   )


  1. 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


  1. 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))


  1. 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)


  1. TEST ----------------------------------------------------

def main(): 

   Testing generation of the SVG for a Hilbert curve
   print(
       hilbertCurve(6)
   )


  1. GENERIC FUNCTIONS ---------------------------------------
  1. 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}


  1. 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)


  1. 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)


  1. TEST ---------------------------------------------------

if __name__ == '__main__': 

   main()</lang>

Ring

<lang ring>

  1. Project : Hilbert curve

load "guilib.ring"

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

</lang> Output image: Hilbert curve

Scala

Scala.js

<lang Scala>@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

}</lang>

Output:

Best seen running in your browser by ScalaFiddle (ES aka JavaScript, non JVM).

Seed7

<lang 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);
   readln(KEYBOARD);
 end func;</lang>

Sidef

<lang ruby>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 {
       angle.deg2rad!
       im.ReadImage('canvas:white')
   }

   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 {

       angle.deg2rad!
       turn.deg2rad!

       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)</lang>

Output:

Hilbert curve

Vala

Library: Gtk+-3.0

<lang vala>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
   var rb1 = new Gtk.RadioButton(null);
   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.add(grid);
   window.show_all();

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

   Gtk.main();
   return 0;

}</lang>

Yabasic

Translation of: Go

<lang Yabasic>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)</lang>

zkl

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

}</lang> Image at hilbert curve

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