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
<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>
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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.__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__.
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.__. .__. .__. .__. . .__. . .__. .__. .__. .__. . .__. . .__. .__. .__. .__.
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. .__.__. .__.__. . .__. .__. . .__.__. .__.__. . .__. .__. . .__.__. .__.__. .
| | | | | |
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.__. .__.__.__. .__. .__. .__. . .__.__. .__.__. . .__. .__. .__. .__.__.__. .__.
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.__. .__. .__. .__. . .__. . .__. .__. .__. .__. . .__. . .__. .__. .__. .__.
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. .__. . . .__. . .__. .__. .__. .__. .__. .__. .__. .__. . .__. . . .__. .
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.__. .__. .__. .__. .__. .__.__. .__.__. .__.__. .__.__. .__. .__. .__. .__. .__.
| |
| |
.__. .__. .__. .__. .__. .__.__. .__.__. .__.__. .__.__. .__. .__. .__. .__. .__.
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. .__. . . .__. . .__. .__. .__. .__. .__. .__. .__. .__. . .__. . . .__. .
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.__. .__. .__. .__. . .__. . .__. .__. .__. .__. . .__. . .__. .__. .__. .__.
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.__. .__.__.__. .__. .__. .__. . .__.__. .__.__. . .__. .__. .__. .__.__.__. .__.
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. .__.__. .__.__. . .__. .__. . .__.__. .__.__. . .__. .__. . .__.__. .__.__. .
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.__. .__. .__. .__. . .__. . .__. .__. .__. .__. . .__. . .__. .__. .__. .__.
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.__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__.
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. .__.__. .__.__. .__.__. .__.__. .__.__. .__.__. .__.__. .__.__. .__.__. .__.__. .
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.__. .__.__. .__.__. .__.__. .__.__. .__.__.__. .__.__. .__.__. .__.__. .__.__. .__.
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.__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__.
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. .__. . .__. .__. .__. .__. . .__. . . .__. . .__. .__. .__. .__. . .__. .
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.__. .__. . .__.__. .__.__. . .__. .__. .__. .__. . .__.__. .__.__. . .__. .__.
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.__. .__. . .__.__. .__.__. . .__. .__. .__. .__. . .__.__. .__.__. . .__. .__.
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. .__. . .__. .__. .__. .__. . .__. . . .__. . .__. .__. .__. .__. . .__. .
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.__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__.
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.__. .__.__. .__.__. .__.__. .__.__. .__. .__. .__.__. .__.__. .__.__. .__.__. .__.
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. .__.__. .__.__. .__. .__.__. .__.__. . . .__.__. .__.__. .__. .__.__. .__.__. .
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.__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__.
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.__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__.
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. .__.__. .__.__. . . .__.__. .__.__. . . .__.__. .__.__. . . .__.__. .__.__. .
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.__. .__.__.__. .__. .__. .__.__.__. .__. .__. .__.__.__. .__. .__. .__.__.__. .__.
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.__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__.
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. .__. . . .__. . . .__. . . .__. . . .__. . . .__. . . .__. . . .__. .
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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.
<lang lua>-- any version from 5.1 to LuaJIT 2.1.0-beta3-readline 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 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 dir,turn=0,0 s=s.."F" for c in s:gmatch(".") do if c=="F" then if scr[y]==nil then scr[y]={} end scr[y][x]=char[dir+1][turn%#char[1]+1] dir = (dir+turn) % (#move) x, y = x+move[dir+1].x,y+move[dir+1].y turn=0 elseif c=="-" then turn=1 else -- "+" turn=-1 end end for i=#scr,1,-1 do print(table.concat(scr[i])) 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 5
┌┐┌┐┌┐┌┐┌┐┌┐┌┐┌┐┌┐┌┐┌┐┌┐┌┐┌┐┌┐┌┐ │└┘││└┘││└┘││└┘││└┘││└┘││└┘││└┘│ └┐┌┘└┐┌┘└┐┌┘└┐┌┘└┐┌┘└┐┌┘└┐┌┘└┐┌┘ ┌┘└──┘└┐┌┘└──┘└┐┌┘└──┘└┐┌┘└──┘└┐ │┌─┐┌─┐││┌─┐┌─┐││┌─┐┌─┐││┌─┐┌─┐│ └┘┌┘└┐└┘└┘┌┘└┐└┘└┘┌┘└┐└┘└┘┌┘└┐└┘ ┌┐└┐┌┘┌┐┌┐└┐┌┘┌┐┌┐└┐┌┘┌┐┌┐└┐┌┘┌┐ │└─┘└─┘└┘└─┘└─┘││└─┘└─┘└┘└─┘└─┘│ └┐┌─┐┌─┐┌─┐┌─┐┌┘└┐┌─┐┌─┐┌─┐┌─┐┌┘ ┌┘└┐└┘┌┘└┐└┘┌┘└┐┌┘└┐└┘┌┘└┐└┘┌┘└┐ │┌┐│┌┐└┐┌┘┌┐│┌┐││┌┐│┌┐└┐┌┘┌┐│┌┐│ └┘└┘│└─┘└─┘│└┘└┘└┘└┘│└─┘└─┘│└┘└┘ ┌┐┌┐│┌─┐┌─┐│┌┐┌┐┌┐┌┐│┌─┐┌─┐│┌┐┌┐ │└┘│└┘┌┘└┐└┘│└┘││└┘│└┘┌┘└┐└┘│└┘│ └┐┌┘┌┐└┐┌┘┌┐└┐┌┘└┐┌┘┌┐└┐┌┘┌┐└┐┌┘ ┌┘└─┘└─┘└─┘└─┘└──┘└─┘└─┘└─┘└─┘└┐ │┌─┐┌─┐┌─┐┌─┐┌─┐┌─┐┌─┐┌─┐┌─┐┌─┐│ └┘┌┘└┐└┘┌┘└┐└┘┌┘└┐└┘┌┘└┐└┘┌┘└┐└┘ ┌┐└┐┌┘┌┐│┌┐│┌┐└┐┌┘┌┐│┌┐│┌┐└┐┌┘┌┐ │└─┘└─┘│└┘└┘│└─┘└─┘│└┘└┘│└─┘└─┘│ └┐┌──┐┌┘┌┐┌┐│┌─┐┌─┐│┌┐┌┐└┐┌──┐┌┘ ┌┘└┐┌┘└┐│└┘│└┘┌┘└┐└┘│└┘│┌┘└┐┌┘└┐ │┌┐││┌┐│└┐┌┘┌┐└┐┌┘┌┐└┐┌┘│┌┐││┌┐│ └┘└┘└┘└┘┌┘└─┘└─┘└─┘└─┘└┐└┘└┘└┘└┘ ┌┐┌┐┌┐┌┐└┐┌─┐┌─┐┌─┐┌─┐┌┘┌┐┌┐┌┐┌┐ │└┘││└┘│┌┘└┐└┘┌┘└┐└┘┌┘└┐│└┘││└┘│ └┐┌┘└┐┌┘│┌┐│┌┐└┐┌┘┌┐│┌┐│└┐┌┘└┐┌┘ ┌┘└──┘└┐└┘└┘│└─┘└─┘│└┘└┘┌┘└──┘└┐ │┌─┐┌─┐│┌┐┌┐│┌─┐┌─┐│┌┐┌┐│┌─┐┌─┐│ └┘┌┘└┐└┘│└┘│└┘┌┘└┐└┘│└┘│└┘┌┘└┐└┘ ┌┐└┐┌┘┌┐└┐┌┘┌┐└┐┌┘┌┐└┐┌┘┌┐└┐┌┘┌┐ ┘└─┘└─┘└─┘└─┘└─┘└─┘└─┘└─┘└─┘└─┘└
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
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:
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
