Peano curve

From Rosetta Code
Task
Peano 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 Peano curve of at least order 3.

C[edit]

Adaptation of the C program in the Breinholt-Schierz paper , requires the WinBGIm library.

 
/*Abhishek Ghosh, 14th September 2018*/
 
#include <graphics.h>
#include <math.h>
 
void Peano(int x, int y, int lg, int i1, int i2) {
 
if (lg == 1) {
lineto(3*x,3*y);
return;
}
 
lg = lg/3;
Peano(x+(2*i1*lg), y+(2*i1*lg), lg, i1, i2);
Peano(x+((i1-i2+1)*lg), y+((i1+i2)*lg), lg, i1, 1-i2);
Peano(x+lg, y+lg, lg, i1, 1-i2);
Peano(x+((i1+i2)*lg), y+((i1-i2+1)*lg), lg, 1-i1, 1-i2);
Peano(x+(2*i2*lg), y+(2*(1-i2)*lg), lg, i1, i2);
Peano(x+((1+i2-i1)*lg), y+((2-i1-i2)*lg), lg, i1, i2);
Peano(x+(2*(1-i1)*lg), y+(2*(1-i1)*lg), lg, i1, i2);
Peano(x+((2-i1-i2)*lg), y+((1+i2-i1)*lg), lg, 1-i1, i2);
Peano(x+(2*(1-i2)*lg), y+(2*i2*lg), lg, 1-i1, i2);
}
 
int main(void) {
 
initwindow(1000,1000,"Peano, Peano");
 
Peano(0, 0, 1000, 0, 0); /* Start Peano recursion. */
 
getch();
cleardevice();
 
return 0;
}
 

Go[edit]

Library: Go Graphics


The following is based on the recursive algorithm and C code in this paper scaled up to 81 x 81 points. The image produced is a variant known as a Peano-Meander curve (see Figure 1(b) here).

package main
 
import "github.com/fogleman/gg"
 
var points []gg.Point
 
const width = 81
 
func peano(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 /= 3
peano(x+2*i1*lg, y+2*i1*lg, lg, i1, i2)
peano(x+(i1-i2+1)*lg, y+(i1+i2)*lg, lg, i1, 1-i2)
peano(x+lg, y+lg, lg, i1, 1-i2)
peano(x+(i1+i2)*lg, y+(i1-i2+1)*lg, lg, 1-i1, 1-i2)
peano(x+2*i2*lg, y+2*(1-i2)*lg, lg, i1, i2)
peano(x+(1+i2-i1)*lg, y+(2-i1-i2)*lg, lg, i1, i2)
peano(x+2*(1-i1)*lg, y+2*(1-i1)*lg, lg, i1, i2)
peano(x+(2-i1-i2)*lg, y+(1+i2-i1)*lg, lg, 1-i1, i2)
peano(x+2*(1-i2)*lg, y+2*i2*lg, lg, 1-i1, i2)
}
 
func main() {
peano(0, 0, width, 0, 0)
dc := gg.NewContext(820, 820)
dc.SetRGB(1, 1, 1) // White background
dc.Clear()
for _, p := range points {
dc.LineTo(p.X, p.Y)
}
dc.SetRGB(1, 0, 1) // Magenta curve
dc.SetLineWidth(1)
dc.Stroke()
dc.SavePNG("peano.png")
}

IS-BASIC[edit]

100 PROGRAM "PeanoC.bas"
110 OPTION ANGLE DEGREES
120 SET VIDEO MODE 5:SET VIDEO COLOR 0:SET VIDEO X 40:SET VIDEO Y 27
130 OPEN #101:"video:"
140 DISPLAY #101:AT 1 FROM 1 TO 27
150 PLOT 280,240,ANGLE 90;
160 CALL PEANO(28,90,6)
170 DEF PEANO(D,A,LEV)
180 IF LEV=0 THEN EXIT DEF
190 PLOT RIGHT A;
200 CALL PEANO(D,-A,LEV-1)
210 PLOT FORWARD D;
220 CALL PEANO(D,A,LEV-1)
230 PLOT FORWARD D;
240 CALL PEANO(D,-A,LEV-1)
250 PLOT LEFT A;
260 END DEF

Fōrmulæ[edit]

In this page you can see the solution of this task.

Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text (more info). Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation —i.e. XML, JSON— they are intended for transportation effects more than visualization and edition.

The option to show Fōrmulæ programs and their results is showing images. Unfortunately images cannot be uploaded in Rosetta Code.

Julia[edit]

The peano function is from the C version.

using Gtk, Graphics, Colors
 
function peano(ctx, x, y, lg, i1, i2)
if lg < 3
line_to(ctx, x - 250, y - 250)
stroke(ctx)
move_to(ctx, x - 250 , y - 250)
else
lg = div(lg, 3)
peano(ctx, x + (2 * i1 * lg), y + (2 * i1 * lg), lg, i1, i2)
peano(ctx, x + ((i1 - i2 + 1) * lg), y + ((i1 + i2) * lg), lg, i1, 1 - i2)
peano(ctx, x + lg, y + lg, lg, i1, 1 - i2)
peano(ctx, x + ((i1 + i2) * lg), y + ((i1 - i2 + 1) * lg), lg, 1 - i1, 1 - i2)
peano(ctx, x + (2 * i2 * lg), y + ( 2 * (1-i2) * lg), lg, i1, i2)
peano(ctx, x + ((1 + i2 - i1) * lg), y + ((2 - i1 - i2) * lg), lg, i1, i2)
peano(ctx, x + (2 * (1 - i1) * lg), y + (2 * (1 - i1) * lg), lg, i1, i2)
peano(ctx, x + ((2 - i1 - i2) * lg), y + ((1 + i2 - i1) * lg), lg, 1 - i1, i2)
peano(ctx, x + (2 * (1 - i2) * lg), y + (2 * i2 * lg), lg, 1 - i1, i2)
end
end
 
const can = @GtkCanvas()
const win = GtkWindow(can, "Peano Curve", 500, 500)
 
@guarded draw(can) do widget
ctx = getgc(can)
h = height(can)
w = width(can)
set_source(ctx, colorant"blue")
set_line_width(ctx, 1)
peano(ctx, w/2, h/2, 500, 0, 0)
end
 
show(can)
const cond = Condition()
endit(w) = notify(cond)
signal_connect(endit, win, :destroy)
wait(cond)
 

Perl[edit]

use SVG;
use List::Util qw(max min);
 
use constant pi => 2 * atan2(1, 0);
 
# Compute the curve with a Lindemayer-system
my %rules = (
L => 'LFRFL-F-RFLFR+F+LFRFL',
R => 'RFLFR+F+LFRFL-F-RFLFR'
);
my $peano = 'L';
$peano =~ s/([LR])/$rules{$1}/eg for 1..4;
 
# Draw the curve in SVG
($x, $y) = (0, 0);
$theta = pi/2;
$r = 4;
 
for (split //, $peano) {
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, '>', 'peano_curve.svg';
print $fh $svg->xmlify(-namespace=>'svg');
close $fh;

Peano curve (offsite image)

Perl 6[edit]

Works with: Rakudo version 2018.06
use SVG;
 
role Lindenmayer {
has %.rules;
method succ {
self.comb.map( { %!rules{$^c} // $c } ).join but Lindenmayer(%!rules)
}
}
 
my $peano = 'L' but Lindenmayer( { 'L' => 'LFRFL-F-RFLFR+F+LFRFL', 'R' => 'RFLFR+F+LFRFL-F-RFLFR' } );
 
$peano++ xx 4;
my @points = (10, 10);
 
for $peano.comb {
state ($x, $y) = @points[0,1];
state $d = 0 + 8i;
when 'F' { @points.append: ($x += $d.re).round(1), ($y += $d.im).round(1) }
when /< + - >/ { $d *= "{$_}1i" }
default { }
}
 
say SVG.serialize(
svg => [
:660width, :660height, :style<stroke:lime>,
:rect[:width<100%>, :height<100%>, :fill<black>],
:polyline[ :points(@points.join: ','), :fill<black> ],
],
);

See: Peano curve (SVG image)

Phix[edit]

Library: pGUI

Space key toggles between switchback and meander curves.

-- demo\rosetta\peano_curve.exw
include pGUI.e
 
Ihandle dlg, canvas
cdCanvas cddbuffer, cdcanvas
 
bool meander = false -- space toggles (false==draw switchback curve)
constant width = 81
 
sequence points = {}
 
-- switchback peano:
--
-- There are (as per wp) four shapes to draw:
--
-- 1: +-v ^ 2: ^ v-+ 3: v ^-+ 2: +-^ v
-- | | | | | | | | | | | |
-- ^ v-+ +-v ^ +-^ v v ^-+
--
-- 1 starts bottom left, ends top right
-- 2 starts bottom right, ends top left
-- 3 starts top left, ends bottom right
-- 4 starts top right, ends bottom left
--
-- given the centre point (think {1,1}), and using {0,0} as the bottom left:
--
constant shapes = {{{-1,-1},{-1,0},{-1,+1},{0,+1},{0,0},{0,-1},{+1,-1},{+1,0},{+1,+1}},
{{+1,-1},{+1,0},{+1,+1},{0,+1},{0,0},{0,-1},{-1,-1},{-1,0},{-1,+1}}, -- (== sq_mul(shapes[1],{-1,0}))
{{-1,+1},{-1,0},{-1,-1},{0,-1},{0,0},{0,+1},{+1,+1},{+1,0},{+1,-1}}, -- (== reverse(shapes[2]))
{{+1,+1},{+1,0},{+1,-1},{0,-1},{0,0},{0,+1},{-1,+1},{-1,0},{-1,-1}}} -- (== reverse(shapes[1]))
 
constant subshapes = {{1,2,1,3,4,3,1,2,1},
{2,1,2,4,3,4,2,1,2}, -- == sq_sub({3,3,3,7,7,7,3,3,3},subshapes[1])
{3,4,3,1,2,1,3,4,3}, -- == sq_sub(5,subshapes[2])
{4,3,4,2,1,2,4,3,4}} -- == sq_sub(5,subshapes[1])
 
-- As noted, it should theoretically be possible to simplify/shorten/remove/inline those tables
 
procedure switchback_peano(integer x, y, level, shape)
-- (written from scratch, with a nod to the meander algorithm [below])
if level<=1 then
points = append(points, {x*10, y*10})
return
end if
level /= 3
for i=1 to 9 do
integer {dx,dy} = shapes[shape][i]
switchback_peano(x+dx*level,y+dy*level,level,subshapes[shape][i])
end for
end procedure
 
procedure meander_peano(integer x, y, lg, i1, i2)
-- (translated from Go)
if lg=1 then
integer px := (width-x) * 10,
py := (width-y) * 10
points = append(points, {px, py})
return
end if
lg /= 3
meander_peano(x+2*i1*lg, y+2*i1*lg, lg, i1, i2)
meander_peano(x+(i1-i2+1)*lg, y+(i1+i2)*lg, lg, i1, 1-i2)
meander_peano(x+lg, y+lg, lg, i1, 1-i2)
meander_peano(x+(i1+i2)*lg, y+(i1-i2+1)*lg, lg, 1-i1, 1-i2)
meander_peano(x+2*i2*lg, y+2*(1-i2)*lg, lg, i1, i2)
meander_peano(x+(1+i2-i1)*lg, y+(2-i1-i2)*lg, lg, i1, i2)
meander_peano(x+2*(1-i1)*lg, y+2*(1-i1)*lg, lg, i1, i2)
meander_peano(x+(2-i1-i2)*lg, y+(1+i2-i1)*lg, lg, 1-i1, i2)
meander_peano(x+2*(1-i2)*lg, y+2*i2*lg, lg, 1-i1, i2)
end procedure
 
function redraw_cb(Ihandle /*ih*/, integer /*posx*/, integer /*posy*/)
if length(points)=0 then
if meander then
meander_peano(0, 0, width, 0, 0)
else
switchback_peano(41, 41, width, 1)
end if
end if
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
 
function esc_close(Ihandle /*ih*/, atom c)
if c=K_ESC then return IUP_CLOSE end if
if c=' ' then
meander = not meander
points = {}
cdCanvasClear(cddbuffer)
IupUpdate(canvas)
end if
return IUP_CONTINUE
end function
 
procedure main()
IupOpen()
 
canvas = IupCanvas(NULL)
IupSetAttribute(canvas, "RASTERSIZE", "822x822") -- initial size
IupSetCallback(canvas, "MAP_CB", Icallback("map_cb"))
 
dlg = IupDialog(canvas)
IupSetAttribute(dlg, "TITLE", "Peano Curve")
IupSetAttribute(dlg, "DIALOGFRAME", "YES") -- no resize here
IupSetCallback(dlg, "K_ANY", Icallback("esc_close"))
IupSetCallback(canvas, "ACTION", Icallback("redraw_cb"))
 
IupMap(dlg)
IupShowXY(dlg,IUP_CENTER,IUP_CENTER)
IupMainLoop()
IupClose()
end procedure
main()

Python[edit]

Library: turtle

This implementation is, as I think, a variant of the Peano curve (just because it's different in the images). And it's supposed to be like a fullscreen app. And because of scale, the "steps" of the curve will be different in horizontal and vertical (it'll be quite nice if your screen is square :D). If peano(4) (in the last line of code) is runned with the input higher than 8, the void between the steps will be filled with steps, and the hole screen will fill (of course, this depends of your screen size). It's also produces a graphic with the current stack pilled, timed by the current function runned.

 
import turtle as tt
import inspect
 
stack = [] # Mark the current stacks in run.
def peano(iterations=1):
global stack
 
# The turtle Ivan:
ivan = tt.Turtle(shape = "classic", visible = True)
 
 
# The app window:
screen = tt.Screen()
screen.title("Desenhin do Peano")
screen.bgcolor("#232323")
screen.delay(0) # Speed on drawing (if higher, more slow)
screen.setup(width=0.95, height=0.9)
 
# The size of each step walked (here, named simply "walk"). It's not a pixel scale. This may stay still:
walk = 1
 
def screenlength(k):
# A function to make the image good to see (without it would result in a partial image).
# This will guarantee that we can see the the voids and it's steps.
if k != 0:
length = screenlength(k-1)
return 2*length + 1
else: return 0
 
kkkj = screenlength(iterations)
screen.setworldcoordinates(-1, -1, kkkj + 1, kkkj + 1)
ivan.color("#EEFFFF", "#FFFFFF")
 
 
# The magic \(^-^)/:
def step1(k):
global stack
stack.append(len(inspect.stack()))
if k != 0:
ivan.left(90)
step2(k - 1)
ivan.forward(walk)
ivan.right(90)
step1(k - 1)
ivan.forward(walk)
step1(k - 1)
ivan.right(90)
ivan.forward(walk)
step2(k - 1)
ivan.left(90)
def step2(k):
global stack
stack.append(len(inspect.stack()))
if k != 0:
ivan.right(90)
step1(k - 1)
ivan.forward(walk)
ivan.left(90)
step2(k - 1)
ivan.forward(walk)
step2(k - 1)
ivan.left(90)
ivan.forward(walk)
step1(k - 1)
ivan.right(90)
 
# Making the program work:
ivan.left(90)
step2(iterations)
 
tt.done()
 
if __name__ == "__main__":
peano(4)
import pylab as P # This plot, after closing the drawing window, the "stack" graphic.
P.plot(stack)
P.show()
 

You can see the output image here and the output stack graphic here.

R[edit]

HilberCurve Library from bioconductor is used to produce 4th order peano curve, for more details please refer to Bioconductor[1]


 
#to install hilbercurve library, biocmanager needs to be installed first
install.packages("BiocManager")
BiocManager::install("HilbertCurve")
#loading library and setting seed for random numbers
library(HilbertCurve)
library(circlize)
set.seed(123)
 
#4th order peano curve is generated
for(i in 1:512) {
peano = HilbertCurve(1, 512, level = 4, reference = TRUE, arrow = FALSE)
hc_points(peano, x1 = i, np = NULL, pch = 16, size = unit(3, "mm"))
}


Racket[edit]

Draw the Peano curve using the classical turtle style known from Logo.

The MetaPict library is used to implement a turtle.

See also https://pdfs.semanticscholar.org/fee6/187cc2dd1679d4976db9522b06a49f63be46.pdf

 
/* Jens Axel Søgaard, 27th December 2018*/
#lang racket
(require metapict metapict/mat)
 
;;; Turtle State
(define p (pt 0 0))  ; current position
(define d (vec 0 1)) ; current direction
(define c '())  ; line segments drawn so far
 
;;; Turtle Operations
(define (jump q) (set! p q))
(define (move q) (set! c (cons (curve p -- q) c)) (set! p q))
(define (forward x) (move (pt+ p (vec* x d))))
(define (left a) (set! d (rot a d)))
(define (right a) (left (- a)))
 
;;; Peano
(define (peano n a h)
(unless (= n 0)
(right a)
(peano (- n 1) (- a) h)
(forward h)
(peano (- n 1) a h)
(forward h)
(peano (- n 1) (- a) h)
(left a)))
 
;;; Produce image
(set-curve-pict-size 400 400)
(with-window (window -1 81 -1 82)
(peano 6 90 3)
(draw* c))
 

Sidef[edit]

Using the LSystem class defined at Hilbert curve.

var rules = Hash(
L => 'LFRFL-F-RFLFR+F+LFRFL',
R => 'RFLFR+F+LFRFL-F-RFLFR',
)
 
var lsys = LSystem(
width: 325,
height: 650,
 
xoff: -3,
yoff: -3,
 
len: 4,
angle: 90,
color: 'dark green',
)
 
lsys.execute('L', 4, "peano_curve.png", rules)

Output image: Peano curve

VBA[edit]

Translation of: C
Const WIDTH = 243 'a power of 3 for a evenly spaced curve
Dim n As Long
Dim points() As Single
Dim flag As Boolean
'Store the coordinate pairs (x, y) generated by Peano into
'a SafeArrayOfPoints with lineto. The number of points
'generated depend on WIDTH. Peano is called twice. Once
'to count the number of points, and twice to generate
'the points after the dynamic array has been
'redimensionalised.
'VBA doesn't have a lineto method. Instead of AddLine, which
'requires four parameters, including the begin pair of
'coordinates, the method AddPolyline is used, which is
'called from main after all the points are generated.
'This creates a single object, whereas AddLine would
'create thousands of small unconnected line objects.
Private Sub lineto(x As Integer, y As Integer)
If flag Then
points(n, 1) = x
points(n, 2) = y
End If
n = n + 1
End Sub
Private Sub Peano(ByVal x As Integer, ByVal y As Integer, ByVal lg As Integer, _
ByVal i1 As Integer, ByVal i2 As Integer)
If (lg = 1) Then
Call lineto(x * 3, y * 3)
Exit Sub
End If
lg = lg / 3
Call Peano(x + (2 * i1 * lg), y + (2 * i1 * lg), lg, i1, i2)
Call Peano(x + ((i1 - i2 + 1) * lg), y + ((i1 + i2) * lg), lg, i1, 1 - i2)
Call Peano(x + lg, y + lg, lg, i1, 1 - i2)
Call Peano(x + ((i1 + i2) * lg), y + ((i1 - i2 + 1) * lg), lg, 1 - i1, 1 - i2)
Call Peano(x + (2 * i2 * lg), y + (2 * (1 - i2) * lg), lg, i1, i2)
Call Peano(x + ((1 + i2 - i1) * lg), y + ((2 - i1 - i2) * lg), lg, i1, i2)
Call Peano(x + (2 * (1 - i1) * lg), y + (2 * (1 - i1) * lg), lg, i1, i2)
Call Peano(x + ((2 - i1 - i2) * lg), y + ((1 + i2 - i1) * lg), lg, 1 - i1, i2)
Call Peano(x + (2 * (1 - i2) * lg), y + (2 * i2 * lg), lg, 1 - i1, i2)
End Sub
Sub main()
n = 1: flag = False
Call Peano(0, 0, WIDTH, 0, 0) 'Start Peano recursion to count number of points
ReDim points(1 To n - 1, 1 To 2)
n = 1: flag = True
Call Peano(0, 0, WIDTH, 0, 0) 'Start Peano recursion to generate and store points
ActiveSheet.Shapes.AddPolyline points 'Excel assumed
End Sub

Yabasic[edit]

Translation of: VBA
WIDTH = 243 //a power of 3 for a evenly spaced curve
 
open window 700, 700
 
Peano(0, 0, WIDTH, 0, 0)
 
Sub Peano(x, y, lg, i1, i2)
If (lg = 1) Then
line x * 3, y * 3
return
End If
lg = lg / 3
Peano(x + (2 * i1 * lg), y + (2 * i1 * lg), lg, i1, i2)
Peano(x + ((i1 - i2 + 1) * lg), y + ((i1 + i2) * lg), lg, i1, 1 - i2)
Peano(x + lg, y + lg, lg, i1, 1 - i2)
Peano(x + ((i1 + i2) * lg), y + ((i1 - i2 + 1) * lg), lg, 1 - i1, 1 - i2)
Peano(x + (2 * i2 * lg), y + (2 * (1 - i2) * lg), lg, i1, i2)
Peano(x + ((1 + i2 - i1) * lg), y + ((2 - i1 - i2) * lg), lg, i1, i2)
Peano(x + (2 * (1 - i1) * lg), y + (2 * (1 - i1) * lg), lg, i1, i2)
Peano(x + ((2 - i1 - i2) * lg), y + ((1 + i2 - i1) * lg), lg, 1 - i1, i2)
Peano(x + (2 * (1 - i2) * lg), y + (2 * i2 * lg), lg, 1 - i1, i2)
End Sub

zkl[edit]

Using a Lindenmayer system and turtle graphics & turned 90°:

lsystem("L",					// axiom
Dictionary("L","LFRFL-F-RFLFR+F+LFRFL", "R","RFLFR+F+LFRFL-F-RFLFR"), # rules
"+-F", 4) // constants, order
: turtle(_);
 
fcn lsystem(axiom,rules,consts,n){ // Lindenmayer system --> string
foreach k in (consts){ rules.add(k,k) }
buf1,buf2 := Data(Void,axiom).howza(3), Data().howza(3); // characters
do(n){
buf1.pump(buf2.clear(), rules.get);
t:=buf1; buf1=buf2; buf2=t; // swap buffers
}
buf1.text // n=4 --> 16,401 characters
}

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

fcn turtle(koch){
const D=10.0;
dir,angle, x,y := 0.0, (90.0).toRad(), 20.0, 830.0; // turtle; x,y are float
img,color := PPM(850,850), 0x00ff00;
foreach c in (koch){
switch(c){
case("F"){ // draw forward
dx,dy := D.toRectangular(dir);
tx,ty := x,y; x,y = (x+dx),(y+dy);
img.line(tx.toInt(),ty.toInt(), x.toInt(),y.toInt(), color);
}
case("-"){ dir-=angle } // turn right
case("+"){ dir+=angle } // turn left
}
}
img.writeJPGFile("peanoCurve.zkl.jpg");
}
Output:

Image at Peano curve