Hilbert curve: Difference between revisions

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260 PLOT LEFT 90*P;
260 PLOT LEFT 90*P;
270 END DEF</lang>
270 END DEF</lang>

=={{header|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>
{{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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| __ | | __ | | __ | | __ | | __ | | __ | | __ | | __ |
|__| |__| |__| |__| |__| |__| |__| |__| |__| |__| |__| |__| |__| |__| |__| |__|
</pre>


=={{header|Julia}}==
=={{header|Julia}}==

Revision as of 14:56, 7 February 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.

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.

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>

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
    __ __    __ __    __ __    __ __    __ __    __ __    __ __    __ __    __ __    __ __    
|__|   __|  |__   |__|   __|  |__   |__|   __|  |__   |__|   __|  |__   |__|   __|  |__   |__|
 __   |__    __|   __   |   __   |   __   |__    __|   __   |   __   |   __   |__    __|   __ 
|  |__ __|  |__ __|  |  |__|  |__|  |  |__ __|  |__ __|  |  |__|  |__|  |  |__ __|  |__ __|  |
|__    __ __ __    __|   __    __   |   __ __    __ __   |   __    __   |__    __ __ __    __|
 __|  |__    __|  |__   |  |__|  |  |__|   __|  |__   |__|  |  |__|  |   __|  |__    __|  |__ 
|   __   |  |   __   |  |__    __|   __   |__    __|   __   |__    __|  |   __   |  |   __   |
|__|  |__|  |__|  |__|   __|  |__ __|  |__ __|  |__ __|  |__ __|  |__   |__|  |__|  |__|  |__|
 __    __    __    __   |__    __ __    __ __    __ __    __ __    __|   __    __    __    __ 
|  |__|  |  |  |__|  |   __|  |__   |__|   __|  |__   |__|   __|  |__   |  |__|  |  |  |__|  |
|__    __|  |__    __|  |   __   |   __   |__    __|   __   |   __   |  |__    __|  |__    __|
 __|  |__ __ __|  |__   |__|  |__|  |  |__ __|  |__ __|  |  |__|  |__|   __|  |__ __ __|  |__ 
|   __ __    __ __   |   __    __   |   __ __    __ __   |   __    __   |   __ __    __ __   |
|__|   __|  |__   |__|  |  |__|  |  |__|   __|  |__   |__|  |  |__|  |  |__|   __|  |__   |__|
 __   |__    __|   __   |__    __|   __   |__    __|   __   |__    __|   __   |__    __|   __ 
|  |__ __|  |__ __|  |__ __|  |__ __|  |__ __|  |__ __|  |__ __|  |__ __|  |__ __|  |__ __|  |
|__    __ __    __ __    __ __    __ __    __ __ __    __ __    __ __    __ __    __ __    __|
 __|  |__   |__|   __|  |__   |__|   __|  |__    __|  |__   |__|   __|  |__   |__|   __|  |__ 
|   __   |   __   |__    __|   __   |   __   |  |   __   |   __   |__    __|   __   |   __   |
|__|  |__|  |  |__ __|  |__ __|  |  |__|  |__|  |__|  |__|  |  |__ __|  |__ __|  |  |__|  |__|
 __    __   |   __ __    __ __   |   __    __    __    __   |   __ __    __ __   |   __    __ 
|  |__|  |  |__|   __|  |__   |__|  |  |__|  |  |  |__|  |  |__|   __|  |__   |__|  |  |__|  |
|__    __|   __   |__    __|   __   |__    __|  |__    __|   __   |__    __|   __   |__    __|
 __|  |__ __|  |__ __|  |__ __|  |__ __|  |__    __|  |__ __|  |__ __|  |__ __|  |__ __|  |__ 
|   __ __    __ __    __    __ __    __ __   |  |   __ __    __ __    __    __ __    __ __   |
|__|   __|  |__   |__|  |__|   __|  |__   |__|  |__|   __|  |__   |__|  |__|   __|  |__   |__|
 __   |__    __|   __    __   |__    __|   __    __   |__    __|   __    __   |__    __|   __ 
|  |__ __|  |__ __|  |  |  |__ __|  |__ __|  |  |  |__ __|  |__ __|  |  |  |__ __|  |__ __|  |
|__    __ __ __    __|  |__    __ __ __    __|  |__    __ __ __    __|  |__    __ __ __    __|
 __|  |__    __|  |__    __|  |__    __|  |__    __|  |__    __|  |__    __|  |__    __|  |__ 
|   __   |  |   __   |  |   __   |  |   __   |  |   __   |  |   __   |  |   __   |  |   __   |
|__|  |__|  |__|  |__|  |__|  |__|  |__|  |__|  |__|  |__|  |__|  |__|  |__|  |__|  |__|  |__|

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- 

┌─────────────────────────────────────────────────────────┐
│         ┌┐┌┐┌┐┌┐┌┐┌┐┌┐┌┐       ┌┐┌┐┌┐┌┐┌┐┌┐┌┐┌┐         │
│         │└┘││└┘││└┘││└┘│       │└┘││└┘││└┘││└┘│         │
│         └┐┌┘└┐┌┘└┐┌┘└┐┌┘       └┐┌┘└┐┌┘└┐┌┘└┐┌┘         │
│         ┌┘└──┘└┐┌┘└──┘└┐       ┌┘└──┘└┐┌┘└──┘└┐         │
│         │┌─┐┌─┐││┌─┐┌─┐│       │┌─┐┌─┐││┌─┐┌─┐│         │
│         └┘┌┘└┐└┘└┘┌┘└┐└┘       └┘┌┘└┐└┘└┘┌┘└┐└┘         │
│         ┌┐└┐┌┘┌┐┌┐└┐┌┘┌┐       ┌┐└┐┌┘┌┐┌┐└┐┌┘┌┐         │
│         │└─┘└─┘└┘└─┘└─┘│       │└─┘└─┘└┘└─┘└─┘│         │
│         └┐┌─┐┌─┐┌─┐┌─┐┌┘       └┐┌─┐┌─┐┌─┐┌─┐┌┘         │
│         ┌┘└┐└┘┌┘└┐└┘┌┘└┐       ┌┘└┐└┘┌┘└┐└┘┌┘└┐         │
│         │┌┐│┌┐└┐┌┘┌┐│┌┐│       │┌┐│┌┐└┐┌┘┌┐│┌┐│         │
│         └┘└┘│└─┘└─┘│└┘└┘╷ ╷┌─┐ └┘└┘│└─┘└─┘│└┘└┘         │
│         ┌┐┌┐│┌─┐┌─┐│┌┐┌┐│ ││ │ ┌┐┌┐│┌─┐┌─┐│┌┐┌┐         │
│         │└┘│└┘┌┘└┐└┘│└┘│├─┤├─┴┐│└┘│└┘┌┘└┐└┘│└┘│         │
│         └┐┌┘┌┐└┐┌┘┌┐└┐┌┘│ ││  │└┐┌┘┌┐└┐┌┘┌┐└┐┌┘         │
└──────────┘└─┘└─┘└─┘└─┘└─┘ └┴──┴─┘└─┘└─┘└─┘└─┘└──────────┘

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

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>

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).

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>

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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