Peano curve: Difference between revisions

Content added Content deleted

Inline

Revision as of 01:09, 28 August 2022

Task

Produce a graphical or ASCII-art representation of a Peano curve of at least order 3.

Action!

Action! language does not support recursion. Therefore an iterative approach with a stack has been proposed.

DEFINE MAXSIZE="12"

INT ARRAY
  angleStack(MAXSIZE)
BYTE ARRAY
  depthStack(MAXSIZE),stageStack(MAXSIZE)
BYTE stacksize=[0]

BYTE FUNC IsEmpty()
  IF stacksize=0 THEN RETURN (1) FI
RETURN (0)

BYTE FUNC IsFull()
  IF stacksize=MAXSIZE THEN RETURN (1) FI
RETURN (0)

PROC Push(INT angle BYTE depth,stage)
  IF IsFull() THEN Break() FI
  angleStack(stacksize)=angle
  depthStack(stacksize)=depth
  stageStack(stackSize)=stage
  stacksize==+1
RETURN

PROC Pop(INT POINTER angle BYTE POINTER depth,stage)
  IF IsEmpty() THEN Break() FI
  stacksize==-1
  angle^=angleStack(stacksize)
  depth^=depthStack(stacksize)
  stage^=stageStack(stacksize)
RETURN

INT FUNC Sin(INT a)
  WHILE a<0 DO a==+360 OD
  WHILE a>360 DO a==-360 OD
  IF a=90 THEN
    RETURN (1)
  ELSEIF a=270 THEN
    RETURN (-1)
  FI
RETURN (0)

INT FUNC Cos(INT a)
RETURN (Sin(a-90))

PROC DrawPeano(INT x BYTE y,len BYTE depth)
  BYTE stage
  INT angle=[90],a
  
  Plot(x,y)
  Push(90,depth,0)

  WHILE IsEmpty()=0
  DO
    Pop(@a,@depth,@stage)
    IF stage<3 THEN
      Push(a,depth,stage+1)
    FI
    IF stage=0 THEN
      angle==+a
      IF depth>1 THEN
        Push(-a,depth-1,0)
      FI
    ELSEIF stage=1 THEN
      x==+len*Cos(angle)
      y==-len*Sin(angle)
      DrawTo(x,y)
      IF depth>1 THEN
        Push(a,depth-1,0)
      FI
    ELSEIF stage=2 THEN
      x==+len*Cos(angle)
      y==-len*Sin(angle)
      DrawTo(x,y)
      IF depth>1 THEN
        Push(-a,depth-1,0)
      FI
    ELSEIF stage=3 THEN
      angle==-a
    FI
  OD
RETURN

PROC Main()
  BYTE CH=$02FC,COLOR1=$02C5,COLOR2=$02C6

  Graphics(8+16)
  Color=1
  COLOR1=$0C
  COLOR2=$02

  DrawPeano(69,186,7,6)

  DO UNTIL CH#$FF OD
  CH=$FF
RETURN

Output:

Screenshot from Atari 8-bit computer

Ada

Translation of: C

Library: APDF

with PDF_Out;  use PDF_Out;

procedure Peano_Curve is

   Filename   : constant String     := "peano-curve.pdf";
   Order      : constant Positive   := 4;
   Scale      : constant Real       := 2.1;
   Line_Width : constant Real       := 2.5;
   Corner     : constant Point      := (150.0, 50.0);
   Background : constant Color_Type := (0.827, 0.816, 0.016);
   Frame      : constant Rectangle  := (10.0, 10.0, 820.0, 575.0);
   PDF        : PDF_Out_File;

   type Coord is record
      X, Y : Natural;
   end record;

   function "+" (Left : Coord; Right : Coord) return Coord
   is ((Left.X + Right.X, Left.Y + Right.Y));

   function "*" (Left : Natural; Right : Coord) return Coord
   is ((Left * Right.X, Left * Right.Y));

   procedure Peano (Pos : Coord; Length : Positive; I1, I2 : Integer) is
      Len : constant Integer := Length / 3;
   begin
      if Length = 1 then
         PDF.Line (Corner + Scale * (Real (3 * Pos.X), Real (3 * Pos.Y)));
      else
         Peano (Pos + Len * (2 * I1,      2 * I1),      Len, I1,     I2);
         Peano (Pos + Len * (I1 - I2 + 1, I1 + I2),     Len, I1,     1 - I2);
         Peano (Pos + Len * (1,           1),           Len, I1,     1 - I2);
         Peano (Pos + Len * (I1 + I2,     I1 - I2 + 1), Len, 1 - I1, 1 - I2);
         Peano (Pos + Len * (2 * I2,      2 - 2 * I2),  Len, I1,     I2);
         Peano (Pos + Len * (1 + I2 - I1, 2 - I1 - I2), Len, I1,     I2);
         Peano (Pos + Len * (2 - 2 * I1,  2 - 2 * I1),  Len, I1,     I2);
         Peano (Pos + Len * (2 - I1 - I2, 1 + I2 - I1), Len, 1 - I1, I2);
         Peano (Pos + Len * (2 - 2 * I2,  2 * I2),      Len, 1 - I1, I2);
      end if;
   end Peano;

   procedure Draw_Peano is
   begin
      PDF.Stroking_Color (Black);
      PDF.Line_Width (Line_Width);
      PDF.Move (Corner);
      Peano ((0, 0), 3**Order, 0, 0);
      PDF.Finish_Path (Close_Path => False,
                       Rendering  => Stroke,
                       Rule       => Nonzero_Winding_Number);
   end Draw_Peano;

begin
   PDF.Create (Filename);
   PDF.Page_Setup (A4_Landscape);

   PDF.Color (Background);
   PDF.Draw (Frame, Fill);

   Draw_Peano;
   PDF.Close;
end Peano_Curve;

AutoHotkey

Translation of: C

Requires Gdip Library

gdip1()
PeanoX := A_ScreenWidth/2 - 100, PeanoY := A_ScreenHeight/2 - 100
Peano(PeanoX, PeanoY, 3**3, 5, 5, Arr:=[])
xmin := xmax := ymin := ymax := 0
for i, point in Arr
{
	xmin := A_Index = 1 ? point.x : xmin < point.x ? xmin : point.x
	xmax := point.x > xmax ? point.x : xmax
	ymin := A_Index = 1 ? point.y : ymin < point.y ? ymin : point.y
	ymax := point.y > ymax ? point.y : ymax
}
for i, point in Arr
	points .= point.x - xmin + PeanoX "," point.y - ymin + PeanoY "|"
points := Trim(points, "|")
Gdip_DrawLines(G, pPen, Points)
UpdateLayeredWindow(hwnd1, hdc, 0, 0, Width, Height)
return
; ---------------------------------------------------------------
Peano(x, y, lg, i1, i2, Arr) {
	if (lg =1 ) 
	{
		Arr[Arr.count()+1, "x"] := x
		Arr[Arr.count(), "y"] := y
		return
	}
	lg := lg/3
	Peano(x+(2*i1*lg)	, y+(2*i1*lg)		, lg	, i1	, i2	, Arr)
	Peano(x+((i1-i2+1)*lg)	, y+((i1+i2)*lg)	, lg	, i1	, 1-i2	, Arr)
	Peano(x+lg		, y+lg			, lg	, i1	, 1-i2	, Arr)
	Peano(x+((i1+i2)*lg)	, y+((i1-i2+1)*lg)	, lg	, 1-i1	, 1-i2	, Arr)
	Peano(x+(2*i2*lg)	, y+(2*(1-i2)*lg)	, lg	, i1	, i2	, Arr)
	Peano(x+((1+i2-i1)*lg)	, y+((2-i1-i2)*lg)	, lg	, i1	, i2	, Arr)
	Peano(x+(2*(1-i1)*lg)	, y+(2*(1-i1)*lg)	, lg	, i1	, i2	, Arr)
	Peano(x+((2-i1-i2)*lg)	, y+((1+i2-i1)*lg)	, lg	, 1-i1	, i2	, Arr)
	Peano(x+(2*(1-i2)*lg)	, y+(2*i2*lg)		, lg	, 1-i1	, i2	, Arr)
}
; ---------------------------------------------------------------
gdip1(){
	global
	If !pToken := Gdip_Startup()
	{
		MsgBox, 48, gdiplus error!, Gdiplus failed to start. Please ensure you have gdiplus on your system
		ExitApp
	}
	OnExit, Exit
	Width := A_ScreenWidth, Height := A_ScreenHeight
	Gui, 1: -Caption +E0x80000 +LastFound +OwnDialogs +Owner +AlwaysOnTop
	Gui, 1: Show, NA
	hwnd1 := WinExist()
	hbm := CreateDIBSection(Width, Height)
	hdc := CreateCompatibleDC()
	obm := SelectObject(hdc, hbm)
	G := Gdip_GraphicsFromHDC(hdc)
	Gdip_SetSmoothingMode(G, 4)
	pPen := Gdip_CreatePen(0xFFFF0000, 2)
}
; ---------------------------------------------------------------
gdip2(){
	global
	Gdip_DeleteBrush(pBrush)
	Gdip_DeletePen(pPen)
	SelectObject(hdc, obm)
	DeleteObject(hbm)
	DeleteDC(hdc)
	Gdip_DeleteGraphics(G)
}
; ---------------------------------------------------------------
Exit:
gdip2()
Gdip_Shutdown(pToken)
ExitApp
Return

C

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;
}

C++

#include <cmath>
#include <fstream>
#include <iostream>
#include <string>

class peano_curve {
public:
    void write(std::ostream& out, int size, int length, int order);
private:
    static std::string rewrite(const std::string& s);
    void line(std::ostream& out);
    void execute(std::ostream& out, const std::string& s);
    double x_;
    double y_;
    int angle_;
    int length_;
};

void peano_curve::write(std::ostream& out, int size, int length, int order) {
    length_ = length;
    x_ = length;
    y_ = length;
    angle_ = 90;
    out << "<svg xmlns='http://www.w3.org/2000/svg' width='"
        << size << "' height='" << size << "'>\n";
    out << "<rect width='100%' height='100%' fill='white'/>\n";
    out << "<path stroke-width='1' stroke='black' fill='none' d='";
    std::string s = "L";
    for (int i = 0; i < order; ++i)
        s = rewrite(s);
    execute(out, s);
    out << "'/>\n</svg>\n";
}

std::string peano_curve::rewrite(const std::string& s) {
    std::string t;
    for (char c : s) {
        switch (c) {
        case 'L':
            t += "LFRFL-F-RFLFR+F+LFRFL";
            break;
        case 'R':
            t += "RFLFR+F+LFRFL-F-RFLFR";
            break;
        default:
            t += c;
            break;
        }
    }
    return t;
}

void peano_curve::line(std::ostream& out) {
    double theta = (3.14159265359 * angle_)/180.0;
    x_ += length_ * std::cos(theta);
    y_ += length_ * std::sin(theta);
    out << " L" << x_ << ',' << y_;
}

void peano_curve::execute(std::ostream& out, const std::string& s) {
    out << 'M' << x_ << ',' << y_;
    for (char c : s) {
        switch (c) {
        case 'F':
            line(out);
            break;
        case '+':
            angle_ = (angle_ + 90) % 360;
            break;
        case '-':
            angle_ = (angle_ - 90) % 360;
            break;
        }
    }
}

int main() {
    std::ofstream out("peano_curve.svg");
    if (!out) {
        std::cerr << "Cannot open output file\n";
        return 1;
    }
    peano_curve pc;
    pc.write(out, 656, 8, 4);
    return 0;
}

Output:

See: peano_curve.svg (offsite SVG image)

Factor

Works with: Factor version 0.99 2020-08-14

USING: accessors L-system ui ;

: peano ( L-system -- L-system )
    L-parser-dialect >>commands
    [ 90 >>angle ] >>turtle-values
    "L" >>axiom
    {
        { "L" "LFRFL-F-RFLFR+F+LFRFL" }
        { "R" "RFLFR+F+LFRFL-F-RFLFR" }
    } >>rules ;

[ <L-system> peano "Peano curve" open-window ] with-ui

When using the L-system visualizer, the following controls apply:

Camera controls
Button	Command
a	zoom in
z	zoom out
left arrow	turn left
right arrow	turn right
up arrow	pitch down
down arrow	pitch up
q	roll left
w	roll right

Other controls
Button	Command
x	iterate L-system

Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text. 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 storage and transfer purposes more than visualization and edition.

Programs in Fōrmulæ are created/edited online in its website, However they run on execution servers. By default remote servers are used, but they are limited in memory and processing power, since they are intended for demonstration and casual use. A local server can be downloaded and installed, it has no limitations (it runs in your own computer). Because of that, example programs can be fully visualized and edited, but some of them will not run if they require a moderate or heavy computation/memory resources, and no local server is being used.

In this page you can see the program(s) related to this task and their results.

FreeBASIC

Translation of: Yabasic

Const anchura = 243 'una potencia de 3 para una curva uniformemente espaciada

Screenres 700,700

Sub Peano(x As Integer, y As Integer, lg As Integer, i1 As Integer, i2 As Integer)
    If lg = 1 Then
        Line - (x * 3, y * 3)
        Return
    End If
    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

Peano(0, 0, anchura, 0, 0)

Sleep

Go

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

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

J

This Hilbert variant is taken directly from the j lab "viewmat".

load'viewmat'
hp=: 3 : '(|.,]) 1 (0 _2 _2 ,&.> _2 _1 0 + #y) } (,.|:) y'
HP=: 3 3 $ 0 0 0 0 1
WR=: 16777215 16711680
viewrgb WR {~ hp ^:7 HP

Or, a smaller example (6 iterations instead of 7) and a different color selection:

   require 'viewmat'
   hp=: 3 : '(|.,]) 1 (0 _2 _2 ,&.> _2 _1 0 + #y) } (,.|:) y'
   MG=: 256 #. 128 0 128,:0 192 0
   viewrgb 2 ([ # #"1) MG {~ hp ^:6 [ 0, 0 1 0 ,: 0,

Java

Output is a file in SVG format.

import java.io.*;

public class PeanoCurve {
    public static void main(final String[] args) {
        try (Writer writer = new BufferedWriter(new FileWriter("peano_curve.svg"))) {
            PeanoCurve s = new PeanoCurve(writer);
            final int length = 8;
            s.currentAngle = 90;
            s.currentX = length;
            s.currentY = length;
            s.lineLength = length;
            s.begin(656);
            s.execute(rewrite(4));
            s.end();
        } catch (final Exception ex) {
            ex.printStackTrace();
        }
    }

    private PeanoCurve(final Writer writer) {
        this.writer = writer;
    }

    private void begin(final int size) throws IOException {
        write("<svg xmlns='http://www.w3.org/2000/svg' width='%d' height='%d'>\n", size, size);
        write("<rect width='100%%' height='100%%' fill='white'/>\n");
        write("<path stroke-width='1' stroke='black' fill='none' d='");
    }

    private void end() throws IOException {
        write("'/>\n</svg>\n");
    }

    private void execute(final String s) throws IOException {
        write("M%g,%g\n", currentX, currentY);
        for (int i = 0, n = s.length(); i < n; ++i) {
            switch (s.charAt(i)) {
                case 'F':
                    line(lineLength);
                    break;
                case '+':
                    turn(ANGLE);
                    break;
                case '-':
                    turn(-ANGLE);
                    break;
            }
        }
    }

    private void line(final double length) throws IOException {
        final double theta = (Math.PI * currentAngle) / 180.0;
        currentX += length * Math.cos(theta);
        currentY += length * Math.sin(theta);
        write("L%g,%g\n", currentX, currentY);
    }

    private void turn(final int angle) {
        currentAngle = (currentAngle + angle) % 360;
    }

    private void write(final String format, final Object... args) throws IOException {
        writer.write(String.format(format, args));
    }

    private static String rewrite(final int order) {
        String s = "L";
        for (int i = 0; i < order; ++i) {
            final StringBuilder sb = new StringBuilder();
            for (int j = 0, n = s.length(); j < n; ++j) {
                final char ch = s.charAt(j);
                if (ch == 'L')
                    sb.append("LFRFL-F-RFLFR+F+LFRFL");
                else if (ch == 'R')
                    sb.append("RFLFR+F+LFRFL-F-RFLFR");
                else
                    sb.append(ch);
            }
            s = sb.toString();
        }
        return s;
    }

    private final Writer writer;
    private double lineLength;
    private double currentX;
    private double currentY;
    private int currentAngle;
    private static final int ANGLE = 90;
}

Output:

See: peano_curve.svg (offsite SVG image)

jq

Works with: jq

Works with gojq, the Go implementation of jq

This entry includes two distinct solutions. In both cases, the jq program generates a SVG document, which can be viewed directly in the browser, at least if the file suffix is ".svg".

Using a Lindenmayer System

In this section, a Lindenmayer system of rules is used with turtle graphics.

The output converted to a .png file can be viewed at https://imgur.com/gallery/4QbUN7I

Simple Turtle Graphics

# => =   0 degrees
# ^  =  90 degrees
# <= = 180 degrees
# v  = 270 degrees

# $start : [$x, $y]
def turtle($start):
  $start
  | if type == "array"  then "M \($start|join(","))" else "M 0,0" end
  | {svg: ., up:true, angle:0};

def turtleUp:   .up=true;
def turtleDown: .up=false;

def turtleRotate($angle): .angle = (360 + (.angle + $angle)) % 360;

def turtleForward($d):
  if .up
  then if   .angle==  0 then .svg += " m \($d),0"
       elif .angle== 90 then .svg += " m 0,-\($d)"
       elif .angle==180 then .svg += " m -\($d),0"
       elif .angle==270 then .svg += " m 0,\($d)"
       else "unsupported angle \(.angle)" | error
       end
  else if   .angle==  0 then .svg += " h \($d)"
       elif .angle== 90 then .svg += " v -\($d)"
       elif .angle==180 then .svg += " h -\($d)"
       elif .angle==270 then .svg += " v \($d)"
       else "unsupported angle \(.angle)" | error
       end
  end;

def svg($size):
  "<svg viewBox=\"0 0 \($size) \($size)\" xmlns=\"http://www.w3.org/2000/svg\">",
  .,
  "</svg>";
  
def path($fill; $stroke; $width):
  "<path fill=\"\($fill)\" stroke=\"\($stroke)\" stroke-width=\"\($width)\" d=\"\(.svg)\" />";

def draw:
  path("none"; "red"; "0.1") | svg(100) ;

Peano Curve

# Compute the curve using a Lindenmayer system of rules
def rules:
  { L: "LFRFL-F-RFLFR+F+LFRFL",
    R: "RFLFR+F+LFRFL-F-RFLFR" } ;

def peano($count):
  rules as $rules
  | def p($count):
      if $count <= 0 then .
      else gsub("L"; "l") | gsub("R"; $rules["R"]) |  gsub("l"; $rules["L"]) | p($count-1)
      end;
  "L" | p($count) ;

def interpret($x):
  if   $x == "+" then turtleRotate(90)
  elif $x == "-" then turtleRotate(-90)
  elif $x == "F" then turtleForward(1)
  else .
  end;

def peano_curve($n):
  peano($n)
  | split("") 
  | reduce .[] as $action (turtle([1,1]) | turtleDown;
      interpret($action) ) ;

peano_curve(4)
| draw

Output:

See https://imgur.com/gallery/4QbUN7I

Peano-Meander curve

Adapted from #Go

A .png version of the SVG image generated using an invocation such as the following can be viewed at https://imgur.com/a/RGQr17J

jq -nr -f peano-curve.jq > peano-curve.svg

# Input: an array
# Output: the array augmented with another x,y pair
def peano($x; $y; $lg; $i1; $i2):
  $lg as $width
  | def p($x; $y; $lg; $i1; $i2):
    if $lg == 1
    then (($width - $x) * 10) as $px
    | (($width - $y) * 10) as $py
    | . + [[$px,$py]]
    else (($lg/3) | floor) as $lg
    | p($x+2*$i1*$lg; $y+2*$i1*$lg; $lg; $i1; $i2)
    | p($x+($i1-$i2+1)*$lg; $y+($i1+$i2)*$lg; $lg; $i1; 1-$i2)
    | p($x+$lg; $y+$lg; $lg; $i1; 1-$i2)
    | p($x+($i1+$i2)*$lg; $y+($i1-$i2+1)*$lg; $lg; 1-$i1; 1-$i2)
    | p($x+2*$i2*$lg; $y+2*(1-$i2)*$lg; $lg; $i1; $i2)
    | p($x+(1+$i2-$i1)*$lg; $y+(2-$i1-$i2)*$lg; $lg; $i1; $i2)
    | p($x+2*(1-$i1)*$lg; $y+2*(1-$i1)*$lg; $lg; $i1; $i2)
    | p($x+(2-$i1-$i2)*$lg; $y+(1+$i2-$i1)*$lg; $lg; 1-$i1; $i2)
    | p($x+2*(1-$i2)*$lg; $y+2*$i2*$lg; $lg; 1-$i1; $i2)
  end;
  p($x; $y; $lg; $i1; $i2);

def svg: 
  "<svg viewBox=\"0 0 820 820\" xmlns=\"http://www.w3.org/2000/svg\">" ;

def path($fill; $stroke):
  "<path fill=\"\($fill)\" stroke=\"\($stroke)\" d=\"M ";

def endpath:
  " \" /> </svg>";
  
def peanoCurve:
  null | peano(0; 0; 81; 0; 0) | map(join(",")) | join(" "); 

svg,
( path("none"; "red") + peanoCurve + endpath)

Output:

https://imgur.com/a/RGQr17J

Julia

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)

Lua

Using the Bitmap class here, with an ASCII pixel representation, then extending..

local PeanoLSystem = {
  axiom = "L",
  rules = {
    L = "LFRFL-F-RFLFR+F+LFRFL",
    R = "RFLFR+F+LFRFL-F-RFLFR"
  },
  eval = function(self, n)
    local source, result = self.axiom
    for i = 1, n do
      result = ""
      for j = 1, #source do
        local ch = source:sub(j,j)
        result = result .. (self.rules[ch] and self.rules[ch] or ch)
      end
      source = result
    end
    return result
  end
}

function Bitmap:drawPath(path, x, y, dx, dy)
  self:set(x, y, "@")
  for i = 1, #path do
    local ch = path:sub(i,i)
    if (ch == "F") then
      local reps = dx==0 and 1 or 3 -- aspect correction
      for r = 1, reps do
        x, y = x+dx, y+dy
        self:set(x, y, dx==0 and "|" or "-")
      end
      x, y = x+dx, y+dy
      self:set(x, y, "+")
    elseif (ch =="-") then
      dx, dy = dy, -dx
    elseif (ch == "+") then
      dx, dy = -dy, dx
    end
  end
  self:set(x, y, "X")
end

function Bitmap:render()
  for y = 1, self.height do
    print(table.concat(self.pixels[y]))
  end
end

bitmap = Bitmap(53*2,53)
bitmap:clear(" ")
bitmap:drawPath(PeanoLSystem:eval(3), 0, 0, 0, 1)
bitmap:render()

Output:

@   +---+   +---+   +---+   +---+   +---+   +---+   +---+   +---+   +---+   +---+   +---+   +---+   +---+
|   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |
+   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +
|   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |
+---+   +   +   +---+   +---+   +   +   +---+   +---+   +   +   +---+   +---+   +   +   +---+   +---+   +
        |   |                   |   |                   |   |                   |   |                   |
+---+   +   +   +---+   +---+   +   +   +---+   +---+   +   +   +---+   +---+   +   +   +---+   +---+   +
|   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |
+   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +
|   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |
+   +---+   +---+   +   +   +---+   +---+   +   +   +---+   +---+   +   +   +---+   +---+   +   +   +---+
|                   |   |                   |   |                   |   |                   |   |
+   +---+   +---+   +   +   +---+   +---+   +   +   +---+   +---+   +   +   +---+   +---+   +   +   +---+
|   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |
+   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +
|   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |
+---+   +---+   +---+   +---+   +   +   +---+   +---+   +---+   +---+   +---+   +---+   +---+   +---+   +
                                |   |                                                                   |
+---+   +---+   +---+   +---+   +   +   +---+   +---+   +---+   +---+   +---+   +---+   +---+   +---+   +
|   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |
+   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +
|   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |
+   +---+   +---+   +   +   +---+   +---+   +   +   +---+   +---+   +   +   +---+   +---+   +   +   +---+
|                   |   |                   |   |                   |   |                   |   |
+   +---+   +---+   +   +   +---+   +---+   +   +   +---+   +---+   +   +   +---+   +---+   +   +   +---+
|   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |
+   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +
|   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |
+---+   +   +   +---+   +---+   +   +   +---+   +---+   +   +   +---+   +---+   +   +   +---+   +---+   +
        |   |                   |   |                   |   |                   |   |                   |
+---+   +   +   +---+   +---+   +   +   +---+   +---+   +   +   +---+   +---+   +   +   +---+   +---+   +
|   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |
+   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +
|   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |
+   +---+   +---+   +---+   +---+   +---+   +---+   +---+   +---+   +   +   +---+   +---+   +---+   +---+
|                                                                   |   |
+   +---+   +---+   +---+   +---+   +---+   +---+   +---+   +---+   +   +   +---+   +---+   +---+   +---+
|   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |
+   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +
|   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |
+---+   +   +   +---+   +---+   +   +   +---+   +---+   +   +   +---+   +---+   +   +   +---+   +---+   +
        |   |                   |   |                   |   |                   |   |                   |
+---+   +   +   +---+   +---+   +   +   +---+   +---+   +   +   +---+   +---+   +   +   +---+   +---+   +
|   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |
+   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +
|   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |
+   +---+   +---+   +   +   +---+   +---+   +   +   +---+   +---+   +   +   +---+   +---+   +   +   +---+
|                   |   |                   |   |                   |   |                   |   |
+   +---+   +---+   +   +   +---+   +---+   +   +   +---+   +---+   +   +   +---+   +---+   +   +   +---+
|   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |
+   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +   +
|   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |
+---+   +---+   +---+   +---+   +---+   +---+   +---+   +---+   +---+   +---+   +---+   +---+   +---+   X

M2000 Interpreter

Draw to M2000 console (which has graphic capabilities). Sub is a copy from freebasic, changed *Line* statement to *Draw to*

Module Peano_curve {
Cls 1, 0
Const Center=2
Report Center, "Peano curve"
let factor=.9, k=3, wi=k^4
let wi2=min.data(scale.x*factor, scale.y*factor), n=wi2/wi
let (dx, dy)=((scale.x-wi2)/2, (scale.y-wi2)/2)
dx+=k*1.2*twipsX
dy+=k*1.2*twipsY
move dx, dy
pen 11 {
      Peano(0,0,wi,0, 0)
}

sub Peano(x, y, lg, i1, i2)
      if lg ==1  then 
            draw to  x*n+dx , y*n+dy
            return
      end if
      lg/=k
      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
}
Peano_curve

Mathematica/Wolfram Language

Graphics[PeanoCurve[4]]

Output:

Outputs a graphical representation of a 4th order PeanoCurve.

Nim

Translation of: Go

Library: imageman

import imageman

const Width = 81

proc peano(points: var seq[Point]; x, y, lg, i1, i2: int) =

  if lg == 1:
    points.add ((Width - x) * 10, (Width - y) * 10)
    return

  let lg = lg div 3
  points.peano(x + 2 * i1 * lg, y + 2 * i1 * lg, lg, i1, i2)
  points.peano(x + (i1 - i2 + 1) * lg, y + (i1 + i2) * lg, lg, i1, 1 - i2)
  points.peano(x + lg, y + lg, lg, i1, 1 - i2)
  points.peano(x + (i1 + i2) * lg, y + (i1 - i2 + 1) * lg, lg, 1 - i1, 1 - i2)
  points.peano(x + 2 * i2 * lg, y + 2 * (1-i2) * lg, lg, i1, i2)
  points.peano(x + (1 + i2 - i1) * lg, y + (2 - i1 - i2) * lg, lg, i1, i2)
  points.peano(x + 2 * (1 - i1) * lg, y + 2 * (1 - i1) * lg, lg, i1, i2)
  points.peano(x + (2 - i1 - i2) * lg, y + (1 + i2 - i1) * lg, lg, 1 - i1, i2)
  points.peano(x + 2 * (1 - i2) * lg, y + 2 * i2 * lg, lg, 1 - i1, i2)


var points: seq[Point]
points.peano(0, 0, Width, 0, 0)
var image = initImage[ColorRGBU](820, 820)
let color = ColorRGBU([byte 255, 255, 0])
for i in 1..points.high:
  image.drawLine(points[i - 1], points[i], color)
image.savePNG("peano.png", compression = 9)

Perl

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)

Phix

Library: Phix/pGUI

Library: Phix/online

You can run this online here. Space key toggles between switchback and meander curves.

--
-- demo\rosetta\peano_curve.exw
-- ============================
--
--  Draws a peano curve. Space key toggles between switchback and meander curves.
--
with javascript_semantics
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*/, /*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 key_cb(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("RASTERSIZE=822x822")
    IupSetCallbacks(canvas, {"MAP_CB", Icallback("map_cb"),
                             "ACTION", Icallback("redraw_cb")})
    dlg = IupDialog(canvas,`TITLE="Peano Curve"`)
    IupSetAttribute(dlg, "DIALOGFRAME", "YES")  -- no resize here
    IupSetCallback(dlg, "KEY_CB", Icallback("key_cb"))
    IupShow(dlg)
    if platform()!=JS then
        IupMainLoop()
        IupClose()
    end if
end procedure

main()

Processing

Translation of: C

//Abhishek Ghosh, 28th June 2022

void Peano(int x, int y, int lg, int i1, int i2) {
 
  if (lg == 1) {
    ellipse(x,y,1,1);
    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);
}

void setup(){
  size(1000,1000);
  Peano(0, 0, 1000, 0, 0);
}

Prolog

Works with: SWI Prolog

main:-
    write_peano_curve('peano_curve.svg', 656, 4).

write_peano_curve(File, Size, Order):-
    open(File, write, Stream),
    format(Stream,
           "<svg xmlns='http://www.w3.org/2000/svg' width='~d' height='~d'>\n",
           [Size, Size]),
    write(Stream, "<rect width='100%' height='100%' fill='white'/>\n"),
    peano_curve(Stream, "L", 8, 8, 8, 90, Order),
    write(Stream, "</svg>\n"),
    close(Stream).

peano_curve(Stream, Axiom, X, Y, Length, Angle, Order):-
    write(Stream, "<path stroke-width='1' stroke='black' fill='none' d='"),
    format(Stream, 'M~g,~g\n', [X, Y]),
    rewrite(Axiom, Order, S),
    string_chars(S, Chars),
    execute(Stream, X, Y, Length, Angle, Chars),
    write(Stream, "'/>\n").

rewrite(S, 0, S):-!.
rewrite(S0, N, S):-
    string_chars(S0, Chars0),
    rewrite1(Chars0, '', S1),
    N1 is N - 1,
    rewrite(S1, N1, S).

rewrite1([], S, S):-!.
rewrite1([C|Chars], T, S):-
    rewrite2(C, X),
    string_concat(T, X, T1),
    rewrite1(Chars, T1, S).

rewrite2('L', "LFRFL-F-RFLFR+F+LFRFL"):-!.
rewrite2('R', "RFLFR+F+LFRFL-F-RFLFR"):-!.
rewrite2(X, X).

execute(_, _, _, _, _, []):-!.
execute(Stream, X, Y, Length, Angle, ['F'|Chars]):-
    !,
    Theta is (pi * Angle) / 180.0,
    X1 is X + Length * cos(Theta),
    Y1 is Y + Length * sin(Theta),
    format(Stream, 'L~g,~g\n', [X1, Y1]),
    execute(Stream, X1, Y1, Length, Angle, Chars).
execute(Stream, X, Y, Length, Angle, ['+'|Chars]):-
    !,
    Angle1 is (Angle + 90) mod 360,
    execute(Stream, X, Y, Length, Angle1, Chars).
execute(Stream, X, Y, Length, Angle, ['-'|Chars]):-
    !,
    Angle1 is (Angle - 90) mod 360,
    execute(Stream, X, Y, Length, Angle1, Chars).
execute(Stream, X, Y, Length, Angle, [_|Chars]):-
    execute(Stream, X, Y, Length, Angle, Chars).

Output:

See: peano_curve.svg (offsite SVG image)

Python

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.

Quackery

  [ $ "turtleduck.qky" loadfile ] now!
 
  [ stack ]                      is switch.arg (   --> [ )
  
  [ switch.arg put ]             is switch     ( x -->   )
 
  [ switch.arg release ]         is otherwise  (   -->   )
 
  [ switch.arg share 
    != iff ]else[ done  
    otherwise ]'[ do ]done[ ]    is case       ( x -->   )
  
  [ $ "" swap witheach 
      [ nested quackery join ] ] is expand     ( $ --> $ )
  
  [ $ "F" ]                      is F          ( $ --> $ )
  
  [ $ "L" ]                      is L          ( $ --> $ )
 
  [ $ "R" ]                      is R          ( $ --> $ )
 
  [ $ "AFBFARFRBFAFBLFLAFBFA" ]  is A          ( $ --> $ )
 
  [ $ "BFAFBLFLAFBFARFRBFAFB" ]  is B          ( $ --> $ )
 
  $ "A"
  
  4 times expand
  
  turtle
  witheach
    [ switch
        [ char F case [  4 1 walk ]
          char L case [ -1 4 turn ]
          char R case [  1 4 turn ]
          otherwise ( ignore ) ] ]

Output:

https://imgur.com/PCi2cSZ

R

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

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

The MetaPict library is used to implement a turtle.

/* 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))

Raku

(formerly Perl 6)

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)

Ruby

Library: RubyGems

Library: JRubyArt

Implemented as a Lindenmayer System, depends on JRuby or JRubyComplete see Hilbert for grammar

load_library :grammar

# Peano class
class Peano
  include Processing::Proxy
  attr_reader :draw_length, :vec, :theta, :axiom, :grammar
  DELTA = 60 # degrees
  def initialize(vec)
    @axiom = 'XF' # Axiom
    rules = {
      'X' => 'X+YF++YF-FX--FXFX-YF+', # LSystem Rules
      'Y' => '-FX+YFYF++YF+FX--FX-Y'
    }
    @grammar = Grammar.new(axiom, rules)
    @theta   = 0
    @draw_length = 100
    @vec = vec
  end

  def generate(gen)
    @draw_length = draw_length * 0.6**gen
    grammar.generate gen
  end

  def translate_rules(prod)
    coss = ->(orig, alpha, len) { orig + len * DegLut.cos(alpha) }
    sinn = ->(orig, alpha, len) { orig - len * DegLut.sin(alpha) }
    [].tap do |pts| # An array to store line vertices as Vec2D
      prod.scan(/./) do |ch|
        case ch
        when 'F'
          pts << vec.copy
          @vec = Vec2D.new(
            coss.call(vec.x, theta, draw_length),
            sinn.call(vec.y, theta, draw_length)
          )
          pts << vec
        when '+'
          @theta += DELTA
        when '-'
          @theta -= DELTA
        when 'X', 'Y'
        else
          puts("character #{ch} not in grammar")
        end
      end
    end
  end
end

attr_reader :points

def setup
  sketch_title 'Peano'
  peano = Peano.new(Vec2D.new(width * 0.65, height * 0.9))
  production = peano.generate 4 # 4 generations looks OK
  @points = peano.translate_rules(production)
  no_loop
end

def draw
  background(0)
  render points
end

def render(points)
  no_fill
  stroke 200.0
  stroke_weight 3
  begin_shape
  points.each_slice(2) do |v0, v1|
    v0.to_vertex(renderer)
    v1.to_vertex(renderer)
  end
  end_shape
end

def renderer
  @renderer ||= GfxRender.new(g)
end

def settings
  size(800, 800)
end

Rust

// [dependencies]
// svg = "0.8.0"

use svg::node::element::path::Data;
use svg::node::element::Path;

struct PeanoCurve {
    current_x: f64,
    current_y: f64,
    current_angle: i32,
    line_length: f64,
}

impl PeanoCurve {
    fn new(x: f64, y: f64, length: f64, angle: i32) -> PeanoCurve {
        PeanoCurve {
            current_x: x,
            current_y: y,
            current_angle: angle,
            line_length: length,
        }
    }
    fn rewrite(order: usize) -> String {
        let mut str = String::from("L");
        for _ in 0..order {
            let mut tmp = String::new();
            for ch in str.chars() {
                match ch {
                    'L' => tmp.push_str("LFRFL-F-RFLFR+F+LFRFL"),
                    'R' => tmp.push_str("RFLFR+F+LFRFL-F-RFLFR"),
                    _ => tmp.push(ch),
                }
            }
            str = tmp;
        }
        str
    }
    fn execute(&mut self, order: usize) -> Path {
        let mut data = Data::new().move_to((self.current_x, self.current_y));
        for ch in PeanoCurve::rewrite(order).chars() {
            match ch {
                'F' => data = self.draw_line(data),
                '+' => self.turn(90),
                '-' => self.turn(-90),
                _ => {}
            }
        }
        Path::new()
            .set("fill", "none")
            .set("stroke", "black")
            .set("stroke-width", "1")
            .set("d", data)
    }
    fn draw_line(&mut self, data: Data) -> Data {
        let theta = (self.current_angle as f64).to_radians();
        self.current_x += self.line_length * theta.cos();
        self.current_y += self.line_length * theta.sin();
        data.line_to((self.current_x, self.current_y))
    }
    fn turn(&mut self, angle: i32) {
        self.current_angle = (self.current_angle + angle) % 360;
    }
    fn save(file: &str, size: usize, order: usize) -> std::io::Result<()> {
        use svg::node::element::Rectangle;
        let rect = Rectangle::new()
            .set("width", "100%")
            .set("height", "100%")
            .set("fill", "white");
        let mut p = PeanoCurve::new(8.0, 8.0, 8.0, 90);
        let document = svg::Document::new()
            .set("width", size)
            .set("height", size)
            .add(rect)
            .add(p.execute(order));
        svg::save(file, &document)
    }
}

fn main() {
    PeanoCurve::save("peano_curve.svg", 656, 4).unwrap();
}

Output:

See: peano_curve.svg (offsite SVG image)

Sidef

Uses 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:  500,
    height: 500,

    xoff: -50,
    yoff: -50,

    len:   5,
    angle: 90,
    color: 'dark green',
)

lsys.execute('l', 4, "peano_curve.png", rules)

Output image: Peano curve

VBA

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

VBScript

VBSCript does'nt have access to Windows graphics so I write SVG commands into an HML file and display it using the default browser. A turtle graphics class makes the recursive definition of the curve easy.

option explicit
'outputs turtle graphics to svg file and opens it

const pi180= 0.01745329251994329576923690768489 ' pi/180 
const pi=3.1415926535897932384626433832795 'pi
class turtle
   
   dim fso
   dim fn
   dim svg
   
   dim iang  'radians
   dim ori   'radians
   dim incr
   dim pdown
   dim clr
   dim x
   dim y

   public property let orient(n):ori = n*pi180 :end property
   public property let iangle(n):iang= n*pi180 :end property
   public sub pd() : pdown=true: end sub 
   public sub pu()  :pdown=FALSE :end sub 
   
   public sub rt(i)  
     ori=ori - i*iang:
     if ori<0 then ori = ori+pi*2
   end sub 
   public sub lt(i):  
     ori=(ori + i*iang) 
     if ori>(pi*2) then ori=ori-pi*2
   end sub
   
   public sub bw(l)
      x= x+ cos(ori+pi)*l*incr
      y= y+ sin(ori+pi)*l*incr
   end sub 
   
   public sub fw(l)
      dim x1,y1 
      x1=x + cos(ori)*l*incr
      y1=y + sin(ori)*l*incr
      if pdown then line x,y,x1,y1
      x=x1:y=y1
   end sub
   
   Private Sub Class_Initialize()
      setlocale "us"   
      initsvg
      pdown=true
   end sub
   
   Private Sub Class_Terminate()   
      disply
   end sub
   
   private sub line (x,y,x1,y1)
      svg.WriteLine "<line x1=""" & x & """ y1= """& y & """ x2=""" & x1& """ y2=""" & y1 & """/>"
   end sub 

   private sub disply()
       dim shell
       svg.WriteLine "</svg></body></html>"
       svg.close
       Set shell = CreateObject("Shell.Application") 
       shell.ShellExecute fn,1,False
   end sub 

   private sub initsvg()
     dim scriptpath
     Set fso = CreateObject ("Scripting.Filesystemobject")
     ScriptPath= Left(WScript.ScriptFullName, InStrRev(WScript.ScriptFullName, "\"))
     fn=Scriptpath & "SIERP.HTML"
     Set svg = fso.CreateTextFile(fn,True)
     if SVG IS nothing then wscript.echo "Can't create svg file" :vscript.quit
     svg.WriteLine "<!DOCTYPE html>" &vbcrlf & "<html>" &vbcrlf & "<head>"
     svg.writeline "<style>" & vbcrlf & "line {stroke:rgb(255,0,0);stroke-width:.5}" &vbcrlf &"</style>"
     svg.writeline "</head>"&vbcrlf & "<body>"
     svg.WriteLine "<svg xmlns=""http://www.w3.org/2000/svg"" width=""800"" height=""800"" viewBox=""0 0 800 800"">" 
   end sub 
end class

sub peano (n,a)
  if n=0 then exit sub
  x.rt a 
  peano n-1, -a
  x.fw 1
  peano n-1, a
  x.fw 1
  peano n-1, -a
  x.lt a
end sub

 dim x,i
set x=new turtle
x.iangle=90
x.orient=0
x.incr=7
x.x=100:x.y=500
peano 7,1
set x=nothing  'show image in browser

Wren

Translation of: Go

Library: DOME

import "graphics" for Canvas, Color, Point
import "dome" for Window

class Game {
    static init() {
        Window.title = "Peano curve"
        Canvas.resize(820, 820)
        Window.resize(820, 820)
        Canvas.cls(Color.white) // white background
        __points = []
        __width = 81
        peano(0, 0, __width, 0, 0)
        var col = Color.rgb(255, 0, 255) // magenta
        var prev = __points[0]
        for (p in __points.skip(1)) {
            var curr = p
            Canvas.line(prev.x, prev.y, curr.x, curr.y, col)
            prev = curr
        }
    }

    static peano(x, y, lg, i1, i2) {
        if (lg == 1) {
            var px = (__width - x) * 10
            var py = (__width - y) * 10
            __points.add(Point.new(px, py))
            return
        }
        lg = (lg/3).floor
        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)
    }

    static update() {}

    static draw(dt) {}
}

Yabasic

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

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