Hilbert curve: Difference between revisions
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An SVG path is serialised from the Nth application of re-write rules to a Hilbert tree structure.
(
<lang Python>from itertools import (chain, islice, starmap)
Line 1,024:
# points :: Int -> ((Int, Int), Tree Char) -> [(Int, Int)]
def points(d):
'''Size -> subtree with its center -> All subtree points'''
def go(xy, tree):
r = d // 2
Line 1,087 ⟶ 1,088:
hilbertCurve(6)
)</lang>
=={{header|Ring}}==
|
Revision as of 07:25, 26 February 2019
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
<lang c>#include <stdio.h>
- define N 32
- define K 3
- define MAX N * K
typedef struct { int x; int y; } point;
void rot(int n, point *p, int rx, int ry) {
int t; if (!ry) { if (rx == 1) { p->x = n - 1 - p->x; p->y = n - 1 - p->y; } t = p->x; p->x = p->y; p->y = t; }
}
void d2pt(int n, int d, point *p) {
int s = 1, t = d, rx, ry; p->x = 0; p->y = 0; while (s < n) { rx = 1 & (t / 2); ry = 1 & (t ^ rx); rot(s, p, rx, ry); p->x += s * rx; p->y += s * ry; t /= 4; s *= 2; }
}
int main() {
int d, x, y, cx, cy, px, py; char pts[MAX][MAX]; point curr, prev; for (x = 0; x < MAX; ++x) for (y = 0; y < MAX; ++y) pts[x][y] = ' '; prev.x = prev.y = 0; pts[0][0] = '.'; for (d = 1; d < N * N; ++d) { d2pt(N, d, &curr); cx = curr.x * K; cy = curr.y * K; px = prev.x * K; py = prev.y * K; pts[cx][cy] = '.'; if (cx == px ) { if (py < cy) for (y = py + 1; y < cy; ++y) pts[cx][y] = '|'; else for (y = cy + 1; y < py; ++y) pts[cx][y] = '|'; } else { if (px < cx) for (x = px + 1; x < cx; ++x) pts[x][cy] = '_'; else for (x = cx + 1; x < px; ++x) pts[x][cy] = '_'; } prev = curr; } for (x = 0; x < MAX; ++x) { for (y = 0; y < MAX; ++y) printf("%c", pts[y][x]); printf("\n"); } return 0;
}</lang>
- Output:
Same as Kotlin entry.
Go
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 __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ |__| __| |__ |__| __| |__ |__| __| |__ |__| __| |__ |__| __| |__ |__| __ |__ __| __ | __ | __ |__ __| __ | __ | __ |__ __| __ | |__ __| |__ __| | |__| |__| | |__ __| |__ __| | |__| |__| | |__ __| |__ __| | |__ __ __ __ __| __ __ | __ __ __ __ | __ __ |__ __ __ __ __| __| |__ __| |__ | |__| | |__| __| |__ |__| | |__| | __| |__ __| |__ | __ | | __ | |__ __| __ |__ __| __ |__ __| | __ | | __ | |__| |__| |__| |__| __| |__ __| |__ __| |__ __| |__ __| |__ |__| |__| |__| |__| __ __ __ __ |__ __ __ __ __ __ __ __ __ __| __ __ __ __ | |__| | | |__| | __| |__ |__| __| |__ |__| __| |__ | |__| | | |__| | |__ __| |__ __| | __ | __ |__ __| __ | __ | |__ __| |__ __| __| |__ __ __| |__ |__| |__| | |__ __| |__ __| | |__| |__| __| |__ __ __| |__ | __ __ __ __ | __ __ | __ __ __ __ | __ __ | __ __ __ __ | |__| __| |__ |__| | |__| | |__| __| |__ |__| | |__| | |__| __| |__ |__| __ |__ __| __ |__ __| __ |__ __| __ |__ __| __ |__ __| __ | |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| | |__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __| __| |__ |__| __| |__ |__| __| |__ __| |__ |__| __| |__ |__| __| |__ | __ | __ |__ __| __ | __ | | __ | __ |__ __| __ | __ | |__| |__| | |__ __| |__ __| | |__| |__| |__| |__| | |__ __| |__ __| | |__| |__| __ __ | __ __ __ __ | __ __ __ __ | __ __ __ __ | __ __ | |__| | |__| __| |__ |__| | |__| | | |__| | |__| __| |__ |__| | |__| | |__ __| __ |__ __| __ |__ __| |__ __| __ |__ __| __ |__ __| __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ | __ __ __ __ __ __ __ __ __ | | __ __ __ __ __ __ __ __ __ | |__| __| |__ |__| |__| __| |__ |__| |__| __| |__ |__| |__| __| |__ |__| __ |__ __| __ __ |__ __| __ __ |__ __| __ __ |__ __| __ | |__ __| |__ __| | | |__ __| |__ __| | | |__ __| |__ __| | | |__ __| |__ __| | |__ __ __ __ __| |__ __ __ __ __| |__ __ __ __ __| |__ __ __ __ __| __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ | __ | | __ | | __ | | __ | | __ | | __ | | __ | | __ | |__| |__| |__| |__| |__| |__| |__| |__| |__| |__| |__| |__| |__| |__| |__| |__|
JavaScript
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>
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:
. .__.__. .__.__. .__.__. .__.__. .__.__. .__.__. .__.__. .__.__. .__.__. .__.__. . | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. | | | | | | | | | | | | | | | | | | | | .__. .__. .__. .__. . .__. . .__. .__. .__. .__. . .__. . .__. .__. .__. .__. | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | . .__.__. .__.__. . .__. .__. . .__.__. .__.__. . .__. .__. . .__.__. .__.__. . | | | | | | | | | | | | .__. .__.__.__. .__. .__. .__. . .__.__. .__.__. . .__. .__. .__. .__.__.__. .__. | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | .__. .__. .__. .__. . .__. . .__. .__. .__. .__. . .__. . .__. .__. .__. .__. | | | | | | | | | | | | | | | | | | | | | | | | | | | | . .__. . . .__. . .__. .__. .__. .__. .__. .__. .__. .__. . .__. . . .__. . | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | .__. .__. .__. .__. .__. .__.__. .__.__. .__.__. .__.__. .__. .__. .__. .__. .__. | | | | .__. .__. .__. .__. .__. .__.__. .__.__. .__.__. .__.__. .__. .__. .__. .__. .__. | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | . .__. . . .__. . .__. .__. .__. .__. .__. .__. .__. .__. . .__. . . .__. . | | | | | | | | | | | | | | | | | | | | | | | | | | | | .__. .__. .__. .__. . .__. . .__. .__. .__. .__. . .__. . .__. .__. .__. .__. | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | .__. .__.__.__. .__. .__. .__. . .__.__. .__.__. . .__. .__. .__. .__.__.__. .__. | | | | | | | | | | | | . .__.__. .__.__. . .__. .__. . .__.__. .__.__. . .__. .__. . .__.__. .__.__. . | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | .__. .__. .__. .__. . .__. . .__. .__. .__. .__. . .__. . .__. .__. .__. .__. | | | | | | | | | | | | | | | | | | | | .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | . .__.__. .__.__. .__.__. .__.__. .__.__. .__.__. .__.__. .__.__. .__.__. .__.__. . | | | | .__. .__.__. .__.__. .__.__. .__.__. .__.__.__. .__.__. .__.__. .__.__. .__.__. .__. | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. | | | | | | | | | | | | | | | | | | | | | | | | . .__. . .__. .__. .__. .__. . .__. . . .__. . .__. .__. .__. .__. . .__. . | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | .__. .__. . .__.__. .__.__. . .__. .__. .__. .__. . .__.__. .__.__. . .__. .__. | | | | | | | | .__. .__. . .__.__. .__.__. . .__. .__. .__. .__. . .__.__. .__.__. . .__. .__. | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | . .__. . .__. .__. .__. .__. . .__. . . .__. . .__. .__. .__. .__. . .__. . | | | | | | | | | | | | | | | | | | | | | | | | .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | .__. .__.__. .__.__. .__.__. .__.__. .__. .__. .__.__. .__.__. .__.__. .__.__. .__. | | | | | | | | . .__.__. .__.__. .__. .__.__. .__.__. . . .__.__. .__.__. .__. .__.__. .__.__. . | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. | | | | | | | | | | | | | | | | .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | . .__.__. .__.__. . . .__.__. .__.__. . . .__.__. .__.__. . . .__.__. .__.__. . | | | | | | | | | | | | | | | | .__. .__.__.__. .__. .__. .__.__.__. .__. .__. .__.__.__. .__. .__. .__.__.__. .__. | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | . .__. . . .__. . . .__. . . .__. . . .__. . . .__. . . .__. . . .__. . | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__.
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);
- Compute the curve with a Lindemayer-system
%rules = (
A => '-BF+AFA+FB-', B => '+AF-BFB-FA+'
); $hilbert = 'A'; $hilbert =~ s/([AB])/$rules{$1}/eg for 1..6;
- Draw the curve in SVG
($x, $y) = (0, 0); $theta = pi/2; $r = 5;
for (split //, $hilbert) {
if (/F/) { push @X, sprintf "%.0f", $x; push @Y, sprintf "%.0f", $y; $x += $r * cos($theta); $y += $r * sin($theta); } elsif (/\+/) { $theta += pi/2; } elsif (/\-/) { $theta -= pi/2; }
}
$max = max(@X,@Y); $xt = -min(@X)+10; $yt = -min(@Y)+10; $svg = SVG->new(width=>$max+20, height=>$max+20); $points = $svg->get_path(x=>\@X, y=>\@Y, -type=>'polyline'); $svg->rect(width=>"100%", height=>"100%", style=>{'fill'=>'black'}); $svg->polyline(%$points, style=>{'stroke'=>'orange', 'stroke-width'=>1}, transform=>"translate($xt,$yt)");
open $fh, '>', 'hilbert_curve.svg'; print $fh $svg->xmlify(-namespace=>'svg'); close $fh;</lang> Hilbert curve (offsite image)
Perl 6
<lang perl6>use SVG;
role Lindenmayer {
has %.rules; method succ { self.comb.map( { %!rules{$^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
<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, and open it with a browser).
<lang Python>from itertools import (chain, islice, starmap)
- 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']
}
- 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)]
}
- hilbertCurve :: Int -> SVG String
def hilbertCurve(n):
w = 1024 return svgFromPoints(w)( hilbertPoints(w)( hilbertTree(n) ) )
- hilbertTree :: Int -> Tree Char
def hilbertTree(n):
Nth application of a rule to a tree seedling
# go :: Tree Char -> Tree Char def go(tree): c = tree['root'] xs = tree['nest'] return Node(c)( map(go, xs) if xs else map( lambda x: Node(x)([]), rule[c] ) ) seed = Node('a')([]) return list(islice( iterate(go)(seed), n ))[-1] if 0 < n else seed
- hilbertPoints :: Int -> Tree Char -> [(Int, Int)]
def hilbertPoints(w):
Serialization of a tree to a list of points in a square of side w
# points :: Int -> ((Int, Int), Tree Char) -> [(Int, Int)] def points(d): Size -> subtree with its center -> All subtree points def go(xy, tree): r = d // 2 centres = map( lambda tpl: ( xy[0] + (r * tpl[0]), xy[1] + (r * tpl[1]) ), vectors[tree['root']] ) return chain.from_iterable( starmap(points(r), zip(centres, tree['nest'])) ) if tree['nest'] else centres return lambda xy, tree: go(xy, tree)
d = w // 2 return lambda tree: list(points(d)((d, d), tree))
- svgFromPoints :: Int -> [(Int, Int)] -> SVG String
def svgFromPoints(w):
Width of square canvas -> Point list -> SVG string
def go(w, xys): xs = ' '.join(map( lambda xy: str(xy[0]) + ' ' + str(xy[1]), xys )) return '\n'.join( ['<svg xmlns="http://www.w3.org/2000/svg"', f'width="512" height="512" viewBox="5 5 {w} {w}">', f'<path d="M{xs}" ', 'stroke-width="2" stroke="red" fill="transparent"/>', '</svg>' ] ) return lambda xys: go(w, xys)
- GENERIC FUNCTIONS ---------------------------------------
- Node :: a -> [Tree a] -> Tree a
def Node(v):
return lambda xs: { 'type': 'Node', 'root': v, 'nest': xs }
- iterate :: (a -> a) -> a -> Gen [a]
def iterate(f):
def go(x): v = x while True: yield(v) v = f(v) return lambda x: go(x)
- TEST ---------------------------------------------------
if __name__ == '__main__':
print ( hilbertCurve(6) )</lang>
Ring
<lang ring>
- 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:
Vala
<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