Fibonacci word/fractal: Difference between revisions

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The Fibonacci word may be represented as a fractal as described here:

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For F_word_m start with F_wordChar_n=1

Draw a segment forward

If current F_wordChar is 0

Turn left if n is even

Turn right if n is odd

next n and iterate until end of F_word

Task

Create and display a fractal similar to Fig 1.

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AutoHotkey

Prints F_Word₃₀ currently. Segment length and F_Word_n can be adjusted.

Library: GDIP

Also see the Gdip examples.

<lang AutoHotkey>#NoEnv SetBatchLines, -1 p := 0.3 ; Segment length (pixels) F_Word := 30

SysGet, Mon, MonitorWorkArea W := FibWord(F_Word) d := 1 x1 := 0 y1 := MonBottom Width := A_ScreenWidth Height := A_ScreenHeight

If (!pToken := Gdip_Startup()) { MsgBox, 48, Gdiplus Error!, Gdiplus failed to start. Please ensure you have Gdiplus on your system. ExitApp } OnExit, Shutdown

Gui, 1: -Caption +E0x80000 +LastFound +AlwaysOnTop +ToolWindow +OwnDialogs 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, 1)

Loop, Parse, W { if (d = 0) x2 := x1 + p, y2 := y1 else if (d = 1 || d = -3) x2 := x1, y2 := y1 - p else if (d = 2 || d = -2) x2 := x1 - p, y2 := y1 else if (d = 3 || d = -1) x2 := x1, y2 := y1 + p Gdip_DrawLine(G, pPen, x1, y1, x2, y2) if (!Mod(A_Index, 1500)) UpdateLayeredWindow(hwnd1, hdc, 0, 0, Width, Height) if (A_LoopField = 0) { if (!Mod(A_Index, 2)) d += 1 else d -= 1 } x1 := x2, y1 := y2, d := Mod(d, 4) }

Gdip_DeletePen(pPen) UpdateLayeredWindow(hwnd1, hdc, 0, 0, Width, Height) SelectObject(hdc, obm) DeleteObject(hbm) DeleteDC(hdc) Gdip_DeleteGraphics(G) return

FibWord(n, FW1=1, FW2=0) { Loop, % n - 2 FW3 := FW2 FW1, FW1 := FW2, FW2 := FW3 return FW3 }

Esc:: Shutdown: Gdip_DeletePen(pPen) SelectObject(hdc, obm) DeleteObject(hbm) DeleteDC(hdc) Gdip_DeleteGraphics(G) Gdip_Shutdown(pToken) ExitApp</lang>

C

Writes an EPS file that has the 26th fractal. This is probably cheating. <lang c>#include <stdio.h>

int main(void) { puts( "%!PS-Adobe-3.0 EPSF\n" "%%BoundingBox: -10 -10 400 565\n" "/a{0 0 moveto 0 .4 translate 0 0 lineto stroke -1 1 scale}def\n" "/b{a 90 rotate}def");

char i; for (i = 'c'; i <= 'z'; i++) printf("/%c{%c %c}def\n", i, i-1, i-2);

puts("0 setlinewidth z showpage\n%%EOF");

return 0; }</lang>

C++

include <windows.h>
include <string>

using namespace std;

class myBitmap { public:

   myBitmap() : pen( NULL ) {}
   ~myBitmap()
   {
       DeleteObject( pen );
       DeleteDC( hdc );
       DeleteObject( bmp );
   }

   bool create( int w, int h )
   {
       BITMAPINFO	bi;
       ZeroMemory( &bi, sizeof( bi ) );
       bi.bmiHeader.biSize        = sizeof( bi.bmiHeader );
       bi.bmiHeader.biBitCount	   = sizeof( DWORD ) * 8;

bi.bmiHeader.biCompression = BI_RGB; bi.bmiHeader.biPlanes = 1; bi.bmiHeader.biWidth = w; bi.bmiHeader.biHeight = -h; HDC dc = GetDC( GetConsoleWindow() ); bmp = CreateDIBSection( dc, &bi, DIB_RGB_COLORS, &pBits, NULL, 0 ); if( !bmp ) return false; hdc = CreateCompatibleDC( dc ); SelectObject( hdc, bmp ); ReleaseDC( GetConsoleWindow(), dc ); width = w; height = h; clear(); return true;

   }

   void clear()
   {

ZeroMemory( pBits, width * height * sizeof( DWORD ) );

   }

   void setPenColor( DWORD clr )
   {

if( pen ) DeleteObject( pen ); pen = CreatePen( PS_SOLID, 1, clr ); SelectObject( hdc, pen );

   }

   void saveBitmap( string path )
   {

BITMAPFILEHEADER fileheader; BITMAPINFO infoheader; BITMAP bitmap; DWORD* dwpBits; DWORD wb; HANDLE file;

GetObject( bmp, sizeof( bitmap ), &bitmap ); dwpBits = new DWORD[bitmap.bmWidth * bitmap.bmHeight]; ZeroMemory( dwpBits, bitmap.bmWidth * bitmap.bmHeight * sizeof( DWORD ) ); ZeroMemory( &infoheader, sizeof( BITMAPINFO ) ); ZeroMemory( &fileheader, sizeof( BITMAPFILEHEADER ) );

infoheader.bmiHeader.biBitCount = sizeof( DWORD ) * 8; infoheader.bmiHeader.biCompression = BI_RGB; infoheader.bmiHeader.biPlanes = 1; infoheader.bmiHeader.biSize = sizeof( infoheader.bmiHeader ); infoheader.bmiHeader.biHeight = bitmap.bmHeight; infoheader.bmiHeader.biWidth = bitmap.bmWidth; infoheader.bmiHeader.biSizeImage = bitmap.bmWidth * bitmap.bmHeight * sizeof( DWORD );

fileheader.bfType = 0x4D42; fileheader.bfOffBits = sizeof( infoheader.bmiHeader ) + sizeof( BITMAPFILEHEADER ); fileheader.bfSize = fileheader.bfOffBits + infoheader.bmiHeader.biSizeImage;

GetDIBits( hdc, bmp, 0, height, ( LPVOID )dwpBits, &infoheader, DIB_RGB_COLORS );

file = CreateFile( path.c_str(), GENERIC_WRITE, 0, NULL, CREATE_ALWAYS, FILE_ATTRIBUTE_NORMAL, NULL ); WriteFile( file, &fileheader, sizeof( BITMAPFILEHEADER ), &wb, NULL ); WriteFile( file, &infoheader.bmiHeader, sizeof( infoheader.bmiHeader ), &wb, NULL ); WriteFile( file, dwpBits, bitmap.bmWidth * bitmap.bmHeight * 4, &wb, NULL ); CloseHandle( file );

delete [] dwpBits;

   }

   HDC getDC()     { return hdc; }
   int getWidth()  { return width; }
   int getHeight() { return height; }

private:

   HBITMAP bmp;
   HDC	    hdc;
   HPEN    pen;
   void    *pBits;
   int	    width, height;

}; class fiboFractal { public:

   fiboFractal( int l )
   {

bmp.create( 600, 440 ); bmp.setPenColor( 0x00ff00 ); createWord( l ); createFractal(); bmp.saveBitmap( "path_to_save_bitmap" );

private:

   void createWord( int l )
   {

string a = "1", b = "0", c; l -= 2; while( l-- ) { c = b + a; a = b; b = c; } fWord = c;

   void createFractal()
   {

int n = 1, px = 10, dir, py = 420, len = 1, x = 0, y = -len, goingTo = 0;

HDC dc = bmp.getDC(); MoveToEx( dc, px, py, NULL ); for( string::iterator si = fWord.begin(); si != fWord.end(); si++ ) { px += x; py += y; LineTo( dc, px, py ); if( !( *si - 48 ) ) { // odd if( n & 1 ) dir = 1; // right else dir = 0; // left switch( goingTo ) { case 0: // up y = 0; if( dir ){ x = len; goingTo = 1; } else { x = -len; goingTo = 3; } break; case 1: // right x = 0; if( dir ) { y = len; goingTo = 2; } else { y = -len; goingTo = 0; } break; case 2: // down y = 0; if( dir ) { x = -len; goingTo = 3; } else { x = len; goingTo = 1; } break; case 3: // left x = 0; if( dir ) { y = -len; goingTo = 0; } else { y = len; goingTo = 2; } }

n++;

       }
   }

   string fWord;
   myBitmap bmp;

}; int main( int argc, char* argv[] ) {

   fiboFractal ff( 23 );
   return system( "pause" );

} </lang>

D

This uses the turtle module from the Dragon Curve Task, and the module from the Grayscale Image task.

Translation of: Python

<lang d>import std.range, grayscale_image, turtle;

void drawFibonacci(Color)(Image!Color img, ref Turtle t,

                         in string word, in real step) {
   foreach (immutable i, immutable c; word) {
       t.forward(img, step);
       if (c == '0') {
           if ((i + 1) % 2 == 0)
               t.left(90);
           else
               t.right(90);
       }
   }

}

void main() {

   auto img = new Image!Gray(1050, 1050);
   auto t = Turtle(30, 1010, -90);
   const w = recurrence!q{a[n-1] ~ a[n-2]}("1", "0").drop(24).front;
   img.drawFibonacci(t, w, 1);
   img.savePGM("fibonacci_word_fractal.pgm");

}</lang> It prints the level 25 word as the Python entry.

Delphi

Library: System.SysUtils

Library: Vcl.Graphics

<lang Delphi> program Fibonacci_word;

{$APPTYPE CONSOLE} {$R *.res}

uses

 System.SysUtils,
 Vcl.Graphics;

function GetWordFractal(n: Integer): string; var

 f1, f2, tmp: string;
 i: Integer;

begin

 case n of
   0:
     Result := ;
   1:
     Result := '1';
 else
   begin
     f1 := '1';
     f2 := '0';

     for i := n - 2 downto 1 do
     begin
       tmp := f2;
       f2 := f2 + f1;
       f1 := tmp;
     end;

     Result := f2;
   end;
 end;

end;

procedure DrawWordFractal(n: Integer; g: TCanvas; x, y, dx, dy: integer); var

 i, tx: Integer;
 wordFractal: string;

begin

 wordFractal := GetWordFractal(n);
 with g do
 begin
   Brush.Color := clWhite;
   FillRect(ClipRect);
   Pen.Color := clBlack;
   pen.Width := 1;
   MoveTo(x, y);
 end;
 for i := 1 to wordFractal.Length do
 begin
   g.LineTo(x + dx, y + dy);
   inc(x, dx);
   inc(y, dy);
   if wordFractal[i] = '0' then
   begin
     tx := dx;
     if Odd(i) then
     begin
       dx := dy;
       dy := -tx;
     end
     else
     begin
       dx := -dy;
       dy := tx;
     end;
   end;
 end;

end;

function WordFractal2Bitmap(n, x, y, width, height: Integer): TBitmap; begin

 Result := TBitmap.Create;
 Result.SetSize(width, height);
 DrawWordFractal(n, Result.Canvas, x, height - y, 1, 0);

end;

begin

 with WordFractal2Bitmap(23, 20, 20, 450, 620) do
 begin
   SaveToFile('WordFractal.bmp');
   Free;
 end;

end.

</lang>

Elixir

Translation of: Ruby

<lang elixir>defmodule Fibonacci do

 def fibonacci_word, do: Stream.unfold({"1","0"}, fn{a,b} -> {a, {b, b<>a}} end)
 
 def word_fractal(n) do
   word = fibonacci_word |> Enum.at(n)
   walk(to_char_list(word), 1, 0, 0, 0, -1, %{{0,0}=>"S"})
   |> print
 end
 
 defp walk([], _, _, _, _, _, map), do: map
 defp walk([h|t], n, x, y, dx, dy, map) do
   map2 = Map.put(map, {x+dx, y+dy}, (if dx==0, do: "|", else: "-"))
          |> Map.put({x2=x+2*dx, y2=y+2*dy}, "+")
   if h == ?0 do
     if rem(n,2)==0, do: walk(t, n+1, x2, y2, dy, -dx, map2),
                   else: walk(t, n+1, x2, y2, -dy, dx, map2)
   else
     walk(t, n+1, x2, y2, dx, dy, map2)
   end
 end
 
 defp print(map) do
   xkeys = Map.keys(map) |> Enum.map(fn {x,_} -> x end)
   {xmin, xmax} = Enum.min_max(xkeys)
   ykeys = Map.keys(map) |> Enum.map(fn {_,y} -> y end)
   {ymin, ymax} = Enum.min_max(ykeys)
   Enum.each(ymin..ymax, fn y ->
     IO.puts Enum.map(xmin..xmax, fn x -> Map.get(map, {x,y}, " ") end)
   end)
 end

end

Fibonacci.word_fractal(16)</lang> Output is same as Ruby.

F#

We output an SVG or rather an HTML with an embedded SVG

Points to note:

Rather than using the "usual" Fibonacci catamorphismen <lang fsharp>Seq.unfold(fun (f1, f2) -> Some(f1, (f2, f2+f1))) ("1", "0")</lang> we use the morphism σ: 0 → 01, 1 → 0, starting with a single 1, described in the referenced PDF in the task description.
The outer dimension of the SVG is computed. For a simplification we compute bounding boxes for fractals with number 3*k+2 only. These are ∩ formed or ⊃ formed. For 3*k and 3*k+1 fractals the bounding box for the next 3*k+2 fractal is taken. (c/f PDF; Theorem 3, Theorem 4)

<lang fsharp>let sigma s = seq {

   for c in s do if c = '1' then yield '0' else yield '0'; yield '1'

} let rec fibwordIterator s = seq { yield s; yield! fibwordIterator (sigma s) }

let goto (x, y) (dx, dy) c n =

   let (dx', dy') =
       if c = '0' then
           match (dx, dy), n with
           | (1,0),0 -> (0,1)  | (1,0),1 -> (0,-1)
           | (0,1),0 -> (-1,0) | (0,1),1 -> (1,0)
           | (-1,0),0 -> (0,-1)| (-1,0),1 -> (0,1)
           | (0,-1),0 -> (1,0) | (0,-1),1 -> (-1,0)
           | _ -> failwith "not possible (c=0)"
       else
           (dx, dy)
   (x+dx, y+dy), (dx', dy')

// How much longer a line is, compared to its thickness: let factor = 2

let rec draw (x, y) (dx, dy) n = function | [] -> () | z::zs ->

   printf "%d,%d " (factor*(x+dx)) (factor*(y+dy))
   let (xyd, d') = goto (x, y) (dx, dy) z n
   draw xyd d' (n^^^1) zs

// Seq of (width,height). n-th (n>=0) pair is for fibword fractal f(3*n+2) let wh = Seq.unfold (fun ((w1,h1,n),(w2,h2)) ->

   Some((if n=0 then (w1,h1) else (h1,w1)), ((w2,h2,n^^^1),(2*w2+w1,w2+h2)))) ((1,0,1),(3,1))

[<EntryPoint>] let main argv =

   let n = (if argv.Length > 0 then int (System.UInt16.Parse(argv.[0])) else 23)
   let (width,height) = Seq.head <| Seq.skip (n/3) wh
   let fibWord = Seq.toList (Seq.item (n-1) <| fibwordIterator ['1'])
   let (viewboxWidth, viewboxHeight) = ((factor*(width+1)), (factor*(height+1)))
   printf """<!DOCTYPE html>

 <polyline points="0,0 """ viewboxWidth viewboxHeight
   draw (0,0) (0,1) 1 <| Seq.toList fibWord
   printf """" style="fill:white;stroke:red;stroke-width:1" transform="matrix(1,0,0,-1,1,%d)"/>
 Sorry, your browser does not support inline SVG.

</svg></body></html>""" (viewboxHeight-1)

   0</lang>

Output:

Since file upload to the Wiki is not possible, the raw output for F₁₁ is given:

<!DOCTYPE html>
<html><body><svg height="100%" width="100%" viewbox="0 0 36 24">
  <polyline points="0,0 0,2 2,2 4,2 4,0 6,0 8,0 8,2 8,4 6,4 6,6 6,8 8,8 8,10 8,12 6,12 4,12 4,10 2,10 0,10 0,12 0,14 2,14 2,16 2,18 0,18 0,20 0,22 2,22 4,22 4,20 6,20 8,20 8,22 10,22 12,22 12,20 12,18 10,18 10,16 10,14 12,14 14,14 14,16 16,16 18,16 18,14 20,14 22,14 22,16 22,18 20,18 20,20 20,22 22,22 24,22 24,20 26,20 28,20 28,22 30,22 32,22 32,20 32,18 30,18 30,16 30,14 32,14 32,12 32,10 30,10 28,10 28,12 26,12 24,12 24,10 24,8 26,8 26,6 26,4 24,4 24,2 24,0 26,0 28,0 28,2 30,2 32,2 32,0 34,0 " style="fill:white;stroke:red;stroke-width:1" transform="matrix(1,0,0,-1,1,23)"/>
  Sorry, your browser does not support inline SVG.
</svg></body></html>

Factor

<lang factor>USING: accessors arrays combinators fry images images.loader kernel literals make match math math.vectors pair-rocket sequences ; FROM: fry => '[ _ ; IN: rosetta-code.fibonacci-word-fractal

! === Turtle code ==============================================

TUPLE: turtle heading loc ; C: <turtle> turtle

forward ( turtle -- turtle' )

   dup heading>> [ v+ ] curry change-loc ;

MATCH-VARS: ?a ;

CONSTANT: left { { 0 ?a } => [ ?a 0 ] { ?a 0 } => [ 0 ?a neg ] } CONSTANT: right { { 0 ?a } => [ ?a neg 0 ] { ?a 0 } => [ 0 ?a ] }

turn ( turtle left/right -- turtle' )

   [ dup heading>> ] dip match-cond 2array >>heading ; inline

! === Fib word =================================================

fib-word ( n -- str )

   {
       1 => [ "1" ]
       2 => [ "0" ]
       [ [ 1 - fib-word ] [ 2 - fib-word ] bi append ]
   } case ;

! === Fractal ==================================================

fib-word-fractal ( n -- seq )

   [
       [ { 0 -1 } { 10 417 } dup , <turtle> ] dip fib-word
       [
           1 + -rot forward dup loc>> ,
           -rot CHAR: 0 = [
               even? [ left turn ] [ right turn ] if
           ] [ drop ] if drop
       ] with each-index
   ] { } make ;

! === Image ====================================================

CONSTANT: w 598 CONSTANT: h 428

init-img-data ( -- seq )

   w h * 4 * [ 255 ] B{ } replicate-as ;

<fib-word-fractal-img> ( -- img )

   <image>
   ${ w h }         >>dim
   BGRA             >>component-order
   ubyte-components >>component-type
   init-img-data    >>bitmap ;

fract>img ( seq -- img' )

   [ <fib-word-fractal-img> dup ] dip [
       '[ B{ 33 33 33 255 } _ first2 ] dip set-pixel-at
   ] with each ;

main ( -- )

   23 fib-word-fractal fract>img "fib-word-fractal.png"
   save-graphic-image ;

MAIN: main</lang>

Output:

Similar to fig. 1 from the paper and the image at the top of this page.

FreeBASIC

On a Windows 32bit system F_word35 is the biggest that can be drawn. <lang FreeBASIC>' version 23-06-2015 ' compile with: fbc -s console "filename".bas

Dim As String fw1, fw2, fw3 Dim As Integer a, b, d , i, n , x, y, w, h Dim As Any Ptr img_ptr, scr_ptr

' data for screen/buffer size Data 1, 2, 3, 2, 2, 2, 2, 2, 7, 10, 8, 14 Dim As Integer s(38,2) For i = 3 To 9

   Read s(i,1) : Read s(i,2)

Next For i = 9 To 38 Step 6

   s(i, 1) = s(i -1, 1) +2 : s(i, 2) = s(i -1, 1) + s(i -1, 2)
   s(i +1, 1) = s(i, 2) +2 : s(i +1, 2) = s(i, 2)
   s(i +2, 1) = s(i, 1) + s(i, 2) : s(i +2, 2) = s(i, 2)
   s(i +3, 1) = s(i +1, 1 ) + s(i +2, 1) : s(i +3, 2) = s(i ,2)
   s(i +4, 1) = s(i +3, 1) : s(i +4, 2) = s(i +3, 1) + 2
   s(i +5, 1) = s(i +3, 1) : s(i +5, 2) = s(i +3, 2) + s(i +4, 2) +2

   Print "Error: graphics screen not initialized."
   Sleep
   End -1

End If

Do

   Cls
   Do

       Print
       Print "For wich n do you want the Fibonacci Word fractal (3 to 35)."
       While Inkey <> "" : fw1 = Inkey : Wend ' empty keyboard buffer
       Input "Enter or a value smaller then 3 to stop: "; n
       If n < 3 Then
           Print : Print "Stopping."
           Sleep 3000,1
           End
       EndIf
       If n > 35 then
           Print : Print "Fractal is to big, unable to create it."
           Sleep 3000,1
           Continue Do
       End If
   Loop Until n < 36

   fw1 = "1" : fw2 = "0" ' construct the string
   For i = 3 To n
       fw3 = fw2 + fw1
       Swap fw1, fw2    ' swap pointers of fw1 and fw2
       Swap fw2, fw3    ' swap pointers of fw2 and fw3
   Next
   fw1 = "" : fw3 = ""  ' free up memory

   w = s(n, 1) +1 : h = s(n, 2) +1
   ' allocate memory for a buffer to hold the image
   ' use 8 bits to hold the color
   img_ptr = ImageCreate(w,h,0,8)
   If img_ptr = 0 Then  ' check if we have created a image buffer
       Print "Failed to create image."
       Sleep
       End -1
   End If

   x = 0:  y = h -1  : d = 1    ' set starting point and direction flag
   PSet img_ptr, (x, y)         ' set start point
   For a = 1 To Len(fw2)
       Select Case As Const d
           Case 0
               x = x + 2
           Case 1
               y = y - 2
           Case 2
               x = x - 2
           Case 3
               y = y + 2
       End Select
       Line  img_ptr, -(x, y)
       b = fw2[a-1] - Asc("0")
       If b = 0 Then
           If (a And 1) Then
               d = d + 3    ' a = odd
           Else
               d = d + 1    ' a = even
           End If
           d = d And 3
       End If
   Next

   If n < 24 Then  ' size is smaller then screen dispay fractal
       Cls
       Put (5, 5),img_ptr, PSet
   Else
       Print
       Print "Fractal is to big for display."
   End If
   ' saves fractal as bmp file (8 bit palette)
   If n > 23 Then h = 80
   Draw String (0, h +16), "saving fractal as fibword" + Str(n) + ".bmp."
   BSave "F_Word" + Str(n) + ".bmp", img_ptr
   Draw String (0, h +32), "Hit any key to continue."
   Sleep
   ImageDestroy(img_ptr) ' free memory holding the image

Loop</lang>

Fōrmulæ

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.

Go

Library: Go Graphics

Translation of: Kotlin

<lang go>package main

import (

   "github.com/fogleman/gg"
   "strings"

)

func wordFractal(i int) string {

   if i < 2 {
       if i == 1 {
           return "1"
       }
       return ""
   }
   var f1 strings.Builder
   f1.WriteString("1")
   var f2 strings.Builder
   f2.WriteString("0")
   for j := i - 2; j >= 1; j-- {
       tmp := f2.String()
       f2.WriteString(f1.String())
       f1.Reset()
       f1.WriteString(tmp)
   }
   return f2.String()

}

func draw(dc *gg.Context, x, y, dx, dy float64, wf string) {

   for i, c := range wf {
       dc.DrawLine(x, y, x+dx, y+dy)
       x += dx
       y += dy
       if c == '0' {
           tx := dx
           dx = dy
           if i%2 == 0 {
               dx = -dy
           }
           dy = -tx
           if i%2 == 0 {
               dy = tx
           }
       }
   }

}

func main() {

   dc := gg.NewContext(450, 620)
   dc.SetRGB(0, 0, 0)
   dc.Clear()
   wf := wordFractal(23)
   draw(dc, 20, 20, 1, 0, wf)
   dc.SetRGB(0, 1, 0)
   dc.SetLineWidth(1)
   dc.Stroke()
   dc.SavePNG("fib_wordfractal.png")

}</lang>

Output:

Image similar to Java entry except green on black background.

Icon and Unicon

This probably only works in Unicon. It also defaults to showing the factal for F_word₂₅ as larger Fibonacci words quickly exceed the size of window I can display, even with a line segment length of a single pixel.

<lang unicon>global width, height

procedure main(A)

   n := integer(A[1]) | 25			    # F_word to use
   sl := integer(A[2]) | 1             # Segment length
   width := integer(A[3]) | 1050       # Width of plot area
   height := integer(A[4]) | 1050      # Height of plot area
   w := fword(n)
   drawFractal(n,w,sl)

end

procedure fword(n)

   static fcache
   initial fcache := table()
   /fcache[n] := case n of {
                    1: "1"
                    2: "0"
                    default: fword(n-1)||fword(n-2)
                    }
   return fcache[n]

end

record loc(x,y)

procedure drawFractal(n,w,sl)

   static lTurn, rTurn
   initial {
       every (lTurn|rTurn) := table()
       lTurn["north"] := "west"; lTurn["west"] := "south"
       lTurn["south"] := "east"; lTurn["east"] := "north"
       rTurn["north"] := "east"; rTurn["east"] := "south"
       rTurn["south"] := "west"; rTurn["west"] := "north"
       }
   
   wparms := ["FibFractal "||n,"g","bg=white","canvas=normal",
              "fg=black","size="||width||","||height,"dx=10","dy=10"]
   &window := open!wparms | stop("Unable to open window")
   p := loc(10,10)
   d := "north"
   every i := 1 to *w do {
      p := draw(p,d,sl)
      if w[i] == "0" then d := if i%2 = 0 then lTurn[d] else rTurn[d]
      }

   until Event() == &lpress
   WriteImage("FibFract"||n||".png")
   close(&window)

end

procedure draw(p,d,sl)

   if d == "north"      then p1 := loc(p.x,p.y+sl)
   else if d == "south" then p1 := loc(p.x,p.y-sl)
   else if d == "east"  then p1 := loc(p.x+sl,p.y)
   else                      p1 := loc(p.x-sl,p.y)
   DrawLine(p.x,p.y, p1.x,p1.y)
   return p1

end</lang>

J

Plotting the fractal as a parametric equation, this looks reasonably nice:

<lang J>require 'plot' plot }:+/\ 0,*/\(^~ 0j_1 0j1 $~ #)'0'=_1{::F_Words 20</lang>

Note that we need the definition of F_Words from the Fibonacci word page:

<lang J>F_Words=: (,<@;@:{~&_1 _2)@]^:(2-~[)&('1';'0')</lang>

However, image uploads are currently disabled, and rendering images of this sort as wikitext gets bulky.

Instead, I'll just describe the algorithm:

This draws a discrete parametric curve. Right turn is 0j_1, left turn is 0j1 (negative and positive square roots of negative 1), straight ahead is 1. So: build a list of alternating 0j_1 and 0j1 and raise them to the first power for the 0s in the fibonacci word list and raise them to the 0th power for the 1s in that list. Then compute the running product, shift a 0 onto the front of the list of products and compute the running sum. (Of course, this would translate to a rather simple loop, also, once you see the pattern.)

Java

Works with: Java version 8

<lang java>import java.awt.*; import javax.swing.*;

public class FibonacciWordFractal extends JPanel {

   String wordFractal;

   FibonacciWordFractal(int n) {
       setPreferredSize(new Dimension(450, 620));
       setBackground(Color.white);
       wordFractal = wordFractal(n);
   }

   public String wordFractal(int n) {
       if (n < 2)
           return n == 1 ? "1" : "";

       // we should really reserve fib n space here
       StringBuilder f1 = new StringBuilder("1");
       StringBuilder f2 = new StringBuilder("0");

       for (n = n - 2; n > 0; n--) {
           String tmp = f2.toString();
           f2.append(f1);

           f1.setLength(0);
           f1.append(tmp);
       }

       return f2.toString();
   }

   void drawWordFractal(Graphics2D g, int x, int y, int dx, int dy) {
       for (int n = 0; n < wordFractal.length(); n++) {
           g.drawLine(x, y, x + dx, y + dy);
           x += dx;
           y += dy;
           if (wordFractal.charAt(n) == '0') {
               int tx = dx;
               dx = (n % 2 == 0) ? -dy : dy;
               dy = (n % 2 == 0) ? tx : -tx;
           }
       }
   }

   @Override
   public void paintComponent(Graphics gg) {
       super.paintComponent(gg);
       Graphics2D g = (Graphics2D) gg;
       g.setRenderingHint(RenderingHints.KEY_ANTIALIASING,
               RenderingHints.VALUE_ANTIALIAS_ON);

       drawWordFractal(g, 20, 20, 1, 0);
   }

   public static void main(String[] args) {
       SwingUtilities.invokeLater(() -> {
           JFrame f = new JFrame();
           f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
           f.setTitle("Fibonacci Word Fractal");
           f.setResizable(false);
           f.add(new FibonacciWordFractal(23), BorderLayout.CENTER);
           f.pack();
           f.setLocationRelativeTo(null);
           f.setVisible(true);
       });
   }

}</lang>

JavaScript

Translation of: PARI/GP

File:FiboWFractal2.png

Output FiboWFractal2.png

File:FiboWFractal1.png

Output FiboWFractal1.png

<lang javascript> // Plot Fibonacci word/fractal // FiboWFractal.js - 6/27/16 aev function pFibowFractal(n,len,canvasId,color) {

 // DCLs
 var canvas = document.getElementById(canvasId);
 var ctx = canvas.getContext("2d"); 
 var w = canvas.width; var h = canvas.height;
 var fwv,fwe,fn,tx,x=10,y=10,dx=len,dy=0,nr;
 // Cleaning canvas, setting plotting color, etc 
 ctx.fillStyle="white"; ctx.fillRect(0,0,w,h);
 ctx.beginPath();
 ctx.moveTo(x,y);
 fwv=fibword(n); fn=fwv.length;
 // MAIN LOOP
 for(var i=0; i<fn; i++) {
   ctx.lineTo(x+dx,y+dy); fwe=fwv[i]; 
   if(fwe=="0") {tx=dx; nr=i%2;
     if(nr==0) {dx=-dy;dy=tx} else {dx=dy;dy=-tx}};
   x+=dx; y+=dy;
 }//fend i
 ctx.strokeStyle = color; ctx.stroke();

}//func end // Create and return Fibonacci word function fibword(n) {

 var f1="1",f2="0",fw,fwn,n2,i;
 if (n<5) {n=5}; n2=n+2;
 for (i=0; i<n2; i++) {fw=f2+f1;f1=f2;f2=fw};
 return(fw)

} </lang>

Executing: <lang html> <html> <head>

 <title>Fibonacci word/fractal</title>
 <script src="FiboWFractal.js"></script>

</head> <body onload="pFibowFractal(31,2,'canvid','red')">

Fibonacci word/fractal: n=31, len=2

  <canvas id="canvid" width="850" height="1150" style="border: 2px inset;"></canvas>

</body> </html>

 <title>Fibonacci word/fractal</title>
 <script src="FiboWFractal.js"></script>

</head> <body onload="pFibowFractal(31,1,'canvid','navy')">

Fibonacci word/fractal: n=31, len=1

  <canvas id="canvid" width="1400" height="1030" style="border: 2px inset;"></canvas>

</body> </html> </lang>

Output:

Page with FiboWFractal2.png
Page with FiboWFractal1.png

Julia

Works with: Julia version 0.6

<lang julia>using Luxor, Colors

function fwfractal!(word::AbstractString, t::Turtle)

   left  =  90
   right = -90
   for (n, c) in enumerate(word)
       Forward(t)
       if c == '0'
           Turn(t, ifelse(iseven(n), left, right))
       end
   end
   return t

end

word = last(fiboword(25))

touch("data/fibonaccifractal.png") Drawing(800, 800, "data/fibonaccifractal.png"); background(colorant"white") t = Turtle(100, 300) fwfractal!(word, t) finish() preview()</lang>

Kotlin

Translation of: Java

<lang scala>// version 1.1.2

import java.awt.* import javax.swing.*

class FibonacciWordFractal(n: Int) : JPanel() {

   private val wordFractal: String 

   init {
       preferredSize = Dimension(450, 620)
       background = Color.black
       wordFractal = wordFractal(n)
   }

   fun wordFractal(i: Int): String {
       if (i < 2) return if (i == 1) "1" else ""
       val f1 = StringBuilder("1")
       val f2 = StringBuilder("0")

       for (j in i - 2 downTo 1) {
           val tmp = f2.toString()
           f2.append(f1)
           f1.setLength(0)
           f1.append(tmp)
       }

       return f2.toString()
   }

   private fun drawWordFractal(g: Graphics2D, x: Int, y: Int, dx: Int, dy: Int) {
       var x2 = x
       var y2 = y
       var dx2 = dx
       var dy2 = dy 
       for (i in 0 until wordFractal.length) {
           g.drawLine(x2, y2, x2 + dx2, y2 + dy2)
           x2 += dx2
           y2 += dy2
           if (wordFractal[i] == '0') {
               val tx = dx2
               dx2 = if (i % 2 == 0) -dy2 else dy2
               dy2 = if (i % 2 == 0) tx else -tx
           }
       }
   }

   override fun paintComponent(gg: Graphics) {
       super.paintComponent(gg)
       val g = gg as Graphics2D
       g.color = Color.green
       g.setRenderingHint(RenderingHints.KEY_ANTIALIASING,
                          RenderingHints.VALUE_ANTIALIAS_ON)
       drawWordFractal(g, 20, 20, 1, 0)
   }

}

fun main(args: Array<String>) {

   SwingUtilities.invokeLater {
       val f = JFrame()
       with(f) {
           defaultCloseOperation = JFrame.EXIT_ON_CLOSE
           title = "Fibonacci Word Fractal"
           isResizable = false
           add(FibonacciWordFractal(23), BorderLayout.CENTER)
           pack()
           setLocationRelativeTo(null)
           isVisible = true
       }
   }

}</lang>

Logo

fibonacci.word.fractal can draw any number of line segments. A Fibonacci number shows the self-similar nature of the fractal. The Fibonacci word values which control the turns are generated here by some bit-twiddling iteration.

Works with: UCB Logo

<lang Logo>; Return the low 1-bits of :n

For example if n = binary 10110111 = 183
then return binary 111 = 7

to low.ones :n

 output ashift (bitxor :n (:n+1)) -1

end

: fibbinary should be a fibbinary value
return the next larger fibbinary value

to fibbinary.next :fibbinary

 localmake "filled  bitor :fibbinary (ashift :fibbinary -1)
 localmake "mask    low.ones :filled
 output (bitor :fibbinary :mask) + 1

end

to fibonacci.word.fractal :steps

 localmake "step.length 5  ; length of each step
 localmake "fibbinary 0
 repeat :steps [
   forward :step.length
   if (bitand 1 :fibbinary) = 0 [
     ifelse (bitand repcount 1) = 1 [right 90] [left 90]
   ]
   make "fibbinary  fibbinary.next :fibbinary
 ]

end

setheading 0 ; initial line North fibonacci.word.fractal 377</lang>

Lua

LÖVE

Needs LÖVE 2D Engine <lang lua> RIGHT, LEFT, UP, DOWN = 1, 2, 4, 8 function drawFractals( w )

   love.graphics.setCanvas( canvas )
   love.graphics.clear()
   love.graphics.setColor( 255, 255, 255 )
   local dir, facing, lineLen, px, py, c = RIGHT, UP, 1, 10, love.graphics.getHeight() - 20, 1
   local x, y = 0, -lineLen
   local pts = {}
   table.insert( pts, px + .5 ); table.insert( pts, py + .5 )
   for i = 1, #w do
       px = px + x; table.insert( pts, px + .5 )
       py = py + y; table.insert( pts, py + .5 )
       if w:sub( i, i ) == "0" then 
           if c % 2 == 1 then dir = RIGHT else dir = LEFT end
           if facing == UP then
               if dir == RIGHT then x = lineLen; facing = RIGHT
               else x = -lineLen; facing = LEFT end; y = 0
           elseif facing == RIGHT then
               if dir == RIGHT then y = lineLen; facing = DOWN
               else y = -lineLen; facing = UP end; x = 0
           elseif facing == DOWN then
               if dir == RIGHT then x = -lineLen; facing = LEFT
               else x = lineLen; facing = RIGHT end; y = 0
           elseif facing == LEFT then
               if dir == RIGHT then y = -lineLen; facing = UP
               else y = lineLen; facing = DOWN end; x = 0
           end
       end
       c = c + 1
   end
   love.graphics.line( pts )
   love.graphics.setCanvas()

end function createWord( wordLen )

   local a, b, w = "1", "0"
   repeat
       w = b .. a; a = b; b = w; wordLen = wordLen - 1
   until wordLen == 0
   return w

end function love.load()

   wid, hei = love.graphics.getWidth(), love.graphics.getHeight()
   canvas = love.graphics.newCanvas( wid, hei )
   drawFractals( createWord( 21 ) )

end function love.draw()

   love.graphics.draw( canvas )

end </lang>

ASCII

Uses the Bitmap class here, with an ASCII pixel representation, then extending.. <lang lua>function Bitmap:fiboword(n)

 local function fw(n) return n==1 and "1" or n==2 and "0" or fw(n-1)..fw(n-2) end
 local word, x, y, dx, dy = fw(n), 0, self.height-1, 0, -1
 for i = 1, #word do
   self:set(x, y, "+")
   x, y = x+dx, y+dy
   self:set(x, y, dx==0 and "|" or "-")
   x, y = x+dx, y+dy
   if word:sub(i,i)=="0" then
     dx, dy = i%2==0 and dy or -dy, i%2==0 and -dx or dx
   end
 end

end

function Bitmap:render()

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

end

bitmap = Bitmap(58,82) bitmap:clear(" ") bitmap:fiboword(14) bitmap:render()</lang>

Output:

|
+   +-+-+               +-+-+   +-+-+       +-+-+   +-+-+
|   |   |               |   |   |   |       |   |   |   |
+-+-+   +               +   +-+-+   +       +   +-+-+   +
        |               |           |       |           |
      +-+               +-+       +-+       +-+       +-+
      |                   |       |           |       |
      +                   +       +   +-+-+   +       +
      |                   |       |   |   |   |       |
      +-+               +-+       +-+-+   +-+-+       +-+
        |               |                               |
+-+-+   +               +   +-+-+               +-+-+   +
|   |   |               |   |   |               |   |   |
+   +-+-+               +-+-+   +               +   +-+-+
|                               |               |
+-+       +-+-+   +-+-+       +-+               +-+
  |       |   |   |   |       |                   |
  +       +   +-+-+   +       +                   +
  |       |           |       |                   |
+-+       +-+       +-+       +-+               +-+
|           |       |           |               |
+   +-+-+   +       +   +-+-+   +               +   +-+-+
|   |   |   |       |   |   |   |               |   |   |
+-+-+   +-+-+       +-+-+   +-+-+               +-+-+   +
                                                        |
                                  +-+-+   +-+-+       +-+
                                  |   |   |   |       |
                                  +   +-+-+   +       +
                                  |           |       |
                                  +-+       +-+       +-+
                                    |       |           |
                                    +       +   +-+-+   +
                                    |       |   |   |   |
                                  +-+       +-+-+   +-+-+
                                  |
                                  +   +-+-+
                                  |   |   |
                                  +-+-+   +
                                          |
                                        +-+
                                        |
                                        +
                                        |
                                        +-+
                                          |
                                  +-+-+   +
                                  |   |   |
                                  +   +-+-+
                                  |
                                  +-+       +-+-+   +-+-+
                                    |       |   |   |   |
                                    +       +   +-+-+   +
                                    |       |           |
                                  +-+       +-+       +-+
                                  |           |       |
                                  +   +-+-+   +       +
                                  |   |   |   |       |
                                  +-+-+   +-+-+       +-+
                                                        |
+-+-+   +-+-+       +-+-+   +-+-+               +-+-+   +
|   |   |   |       |   |   |   |               |   |   |
+   +-+-+   +       +   +-+-+   +               +   +-+-+
|           |       |           |               |
+-+       +-+       +-+       +-+               +-+
  |       |           |       |                   |
  +       +   +-+-+   +       +                   +
  |       |   |   |   |       |                   |
+-+       +-+-+   +-+-+       +-+               +-+
|                               |               |
+   +-+-+               +-+-+   +               +   +-+-+
|   |   |               |   |   |               |   |   |
+-+-+   +               +   +-+-+               +-+-+   +
        |               |                               |
      +-+               +-+       +-+-+   +-+-+       +-+
      |                   |       |   |   |   |       |
      +                   +       +   +-+-+   +       +
      |                   |       |           |       |
      +-+               +-+       +-+       +-+       +-+
        |               |           |       |           |
+-+-+   +               +   +-+-+   +       +   +-+-+   +
|   |   |               |   |   |   |       |   |   |   |
+   +-+-+               +-+-+   +-+-+       +-+-+   +-+-+

Mathematica / Wolfram Language

<lang mathematica>(*note, this usage of Module allows us to memoize FibonacciWord

 without exposing it to the global scope*)

Module[{FibonacciWord, step},

 FibonacciWord[1] = "1";
 FibonacciWord[2] = "0";
 FibonacciWord[n_Integer?(# > 2 &)] :=
  (FibonacciWord[n] = FibonacciWord[n - 1] <> FibonacciWord[n - 2]);
 
 step["0", {_?EvenQ}] = N@RotationTransform[Pi/2];
 step["0", {_?OddQ}] = N@RotationTransform[-Pi/2];
 step[___] = Identity;
 
 FibonacciFractal[n_] := Module[{steps, dirs},
   steps = MapIndexed[step, Characters[FibonacciWord[n]]];
   dirs = ComposeList[steps, {0, 1}];
   Graphics[Line[FoldList[Plus, {0, 0}, dirs]]]]];</lang>

Nim

Library: imageman

<lang Nim>import imageman

const

 Width = 1000
 Height = 1000
 LineColor = ColorRGBU [byte 64, 192, 96]
 Output = "fibword.png"

proc fibword(n: int): string =

 ## Return the nth fibword.
 var a = "1"
 result = "0"
 for _ in 1..n:
   a = result & a
   swap a, result

proc drawFractal(image: var Image; fw: string) =

 # Draw the fractal.
 var
   x = 0
   y = image.h - 1
   dx = 1
   dy = 0

 for i, ch in fw:
   let (nextx, nexty) = (x + dx, y + dy)
   image.drawLine((x, y), (nextx, nexty), LineColor)
   (x, y) = (nextx, nexty)
   if ch == '0':
     if (i and 1) == 0:
       (dx, dy) = (dy, -dx)
     else:
       (dx, dy) = (-dy, dx)

———————————————————————————————————————————————————————————————————————————————————————————————————

var image = initImage[ColorRGBU](Width, Height) image.fill(ColorRGBU [byte 0, 0, 0]) image.drawFractal(fibword(23))

Save into a PNG file.

image.savePNG(Output, compression = 9)</lang>

PARI/GP

Version #1.

In this version only function plotfibofract() was translated from C++, plus upgraded to plot different kind/size of Fibonacci word/fractals.

Translation of: C++

Works with: PARI/GP version 2.7.4 and above

<lang parigp> \\ Fibonacci word/fractals \\ 4/25/16 aev fibword(n)={ my(f1="1",f2="0",fw,fwn,n2); if(n<=4, n=5);n2=n-2; for(i=1,n2, fw=Str(f2,f1); f1=f2;f2=fw;); fwn=#fw; fw=Vecsmall(fw); for(i=1,fwn,fw[i]-=48); return(fw); }

nextdir(n,d)={ my(dir=-1); if(d==0, if(n%2==0, dir=0,dir=1)); \\0-left,1-right return(dir); }

plotfibofract(n,sz,len)={ my(fwv,fn,dr,px=10,py=420,x=0,y=-len,g2=0,

  ttl="Fibonacci word/fractal: n=");

plotinit(0); plotcolor(0,6); \\green plotscale(0, -sz,sz, -sz,sz); plotmove(0, px,py); fwv=fibword(n); fn=#fwv; for(i=1,fn,

   plotrline(0,x,y);
   dr=nextdir(i,fwv[i]);
   if(dr==-1, next);
   \\up
   if(g2==0, y=0; if(dr, x=len;g2=1, x=-len;g2=3); next);
   \\right
   if(g2==1, x=0; if(dr, y=len;g2=2, y=-len;g2=0); next);
   \\down
   if(g2==2, y=0; if(dr, x=-len;g2=3, x=len;g2=1); next);
   \\left
   if(g2==3, x=0; if(dr, y=-len;g2=0, y=len;g2=2); next);
  );\\fend i

plotdraw([0,-sz,-sz]); print(" *** ",ttl,n," sz=",sz," len=",len," fw-len=",fn);

}

{\\ Executing: plotfibofract(11,430,20); \\ Fibofrac1.png plotfibofract(21,430,2); \\ Fibofrac2.png } </lang>

Output:

> plotfibofract(11,430,20); \\ Fibofrac1.png
 *** Fibonacci word/fractal: n=11 sz=430 len=20 fw-len=89

> plotfibofract(21,430,2);  \\ Fibofrac2.png
 *** Fibonacci word/fractal: n=21 sz=430 len=2 fw-len=10946

Version #2.

In this version only function plotfibofract1() was translated from Java, plus upgraded to plot different kind/size of Fibonacci word/fractals.

Output Fibofrac4.png

Translation of: Java

Works with: PARI/GP version 2.7.4 and above

<lang parigp> \\ Fibonacci word/fractals 2nd version \\ 4/26/16 aev fibword(n)={ my(f1="1",f2="0",fw,fwn,n2); \\check n2 in v2 ADD it!! if(n<=4, n=5); n2=n-2; for(i=1,n2, fw=Str(f2,f1); f1=f2;f2=fw;); fwn=#fw; fw=Vecsmall(fw); for(i=1,fwn,fw[i]-=48); return(fw); }

plotfibofract1(n,sz,len)={ my(fwv,fn,dx=len,dy=0,nr,ttl="Fibonacci word/fractal, n="); plotinit(0); plotcolor(0,5); \\red plotscale(0, -sz,sz, -sz,sz); plotmove(0, 0,0); fwv=fibword(n); fn=#fwv; for(i=1,fn, plotrline(0,dx,dy);

   if(fwv[i]==0, tx=dx; nr=i%2; if(!nr,dx=-dy;dy=tx, dx=dy;dy=-tx));
  );\\fend i

plotdraw([0,0,0]); print(" *** ",ttl,n," sz=",sz," len=",len," fw-len=",fn); }

{\\ Executing: plotfibofract1(17,500,6); \\ Fibofrac3.png plotfibofract1(21,600,1); \\ Fibofrac4.png } </lang>

Output:

> plotfibofract1(17,500,6); \\ Fibofrac3.png
 *** Fibonacci word/fractal: n=17 sz=500 len=6 fw-len=1597

> plotfibofract1(21,600,1); \\ Fibofrac4.png
 *** Fibonacci word/fractal: n=21 sz=600 len=1 fw-len=10946

Perl

Creates file fword.png containing the Fibonacci Fractal. <lang perl>use strict; use warnings; use GD;

my @fword = ( undef, 1, 0 );

sub fword { my $n = shift; return $fword[$n] if $n<3; return $fword[$n] //= fword($n-1).fword($n-2); }

my $size = 3000; my $im = new GD::Image($size,$size); my $white = $im->colorAllocate(255,255,255); my $black = $im->colorAllocate(0,0,0); $im->transparent($white); $im->interlaced('true');

my @pos = (0,0); my @dir = (0,5); my @steps = split //, fword 23; my $i = 1; for( @steps ) { my @next = ( $pos[0]+$dir[0], $pos[1]+$dir[1] ); $im->line( @pos, @next, $black ); @dir = ( $dir[1], -$dir[0] ) if 0==$_ && 1==$i%2; # odd @dir = ( -$dir[1], $dir[0] ) if 0==$_ && 0==$i%2; # even $i++; @pos = @next; }

open my $out, ">", "fword.png" or die "Cannot open output file.\n"; binmode $out; print $out $im->png; close $out; </lang>

Using Tk

This draws a segment at a time so you can watch it grow :) <lang perl>#!/usr/bin/perl

use strict; # https://rosettacode.org/wiki/Fibonacci_word use warnings; use Tk;

my @fword = ( 1, 0 ); push @fword, $fword[-1] . $fword[-2] for 1 .. 21;

use Data::Dump 'dd'; dd@fword;

my $mw = MainWindow->new; my $c = $mw->Canvas( -width => 1185, -height => 860,

 )->pack;

$mw->Button(-text => 'Exit', -command => sub {$mw->destroy},

 )->pack(-fill => 'x', -side => 'right');

$mw->Button(-text => 'Redraw', -command => sub {draw($fword[-1])},

 )->pack(-fill => 'x', -side => 'right');

$mw->update; draw($fword[-1]);

MainLoop; -M $0 < 0 and exec $0;

sub draw

 {
 $c->delete('all');
 my $string = shift;
 my ($x, $y) = ($c->width - 20, $c->height - 20);
 my ($dx, $dy) = (0, -2);
 my $count = 0;
 for my $ch ( split //, $string )
   {
   my ($nx, $ny) = ($x + $dx, $y + $dy);
   $c->createLine($x, $y, $nx, $ny);
   $mw->update;
   ($x, $y) = ($nx, $ny);
   $count++;
   $ch or ($dx, $dy) = $count % 2 ? ($dy, -$dx) : (-$dy, $dx);
   }
 }

</lang>

Phix

Library: Phix/pGUI

Library: Phix/online

You can run this online here. Output matches Fig 1 (at the top of the page)

--
-- demo\rosetta\FibonacciFractal.exw
--
with javascript_semantics
include pGUI.e

Ihandle dlg, canvas
cdCanvas cddbuffer, cdcanvas

procedure drawFibonacci(integer x, y, dx, dy, n)
    string prev = "1", word = "0"
    for i=3 to n do {prev,word} = {word,word&prev} end for
    for i=1 to length(word) do
        cdCanvasLine(cddbuffer, x, y, x+dx, y+dy)
        x += dx   y += dy
        if word[i]=='0' then
            {dx,dy} = iff(remainder(i,2)?{dy,-dx}:{-dy,dx})
        end if
    end for
end procedure

function redraw_cb(Ihandle /*ih*/, integer /*posx*/, /*posy*/)
    cdCanvasActivate(cddbuffer)
    cdCanvasClear(cddbuffer)
    drawFibonacci(20, 20, 0, 1, 23)
    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_GREEN)
    return IUP_DEFAULT
end function

procedure main()
    IupOpen()
    canvas = IupCanvas("RASTERSIZE=620x450")
    IupSetCallbacks(canvas, {"MAP_CB", Icallback("map_cb"),
                             "ACTION", Icallback("redraw_cb")})
    dlg = IupDialog(canvas, `RESIZE=NO, TITLE="Fibonacci Fractal"`)
    IupShow(dlg)
    if platform()!=JS then
        IupMainLoop()
        IupClose()
    end if
end procedure

main()

Processing

Written in Processing (Processing)

<lang processing> int n = 18; String f1 = "1"; String f2 = "0"; String f3;

void setup(){

 size(600,600);
 background(255);
 translate(10, 10);
 createSeries();

}

void createSeries(){

 for(int i=0; i<n; i++){
   f3 = f2+f1;
   f1 = f2;
   f2 = f3;
 }
 drawFractal();

}

void drawFractal(){

 char[] a = f3.toCharArray();
 for(int i=0; i<a.length; i++){
   if(a[i]=='0'){
     if(i%2==0){
       rotate(PI/2);
     }
     else{
       rotate(-PI/2);
     }
   }
   line(0,0,2,0);
   translate(2,0);
 }

} </lang>

Python

Translation of: Unicon

Note that for Python 3, functools.lru_cache could be used instead of the memoize decorator below. <lang python>from functools import wraps from turtle import *

def memoize(obj):

   cache = obj.cache = {}
   @wraps(obj)
   def memoizer(*args, **kwargs):
       key = str(args) + str(kwargs)
       if key not in cache:
           cache[key] = obj(*args, **kwargs)
       return cache[key]
   return memoizer

@memoize def fibonacci_word(n):

   assert n > 0
   if n == 1:
       return "1"
   if n == 2:
       return "0"
   return fibonacci_word(n - 1) + fibonacci_word(n - 2)

def draw_fractal(word, step):

   for i, c in enumerate(word, 1):
       forward(step)
       if c == "0":
           if i % 2 == 0:
               left(90)
           else:
               right(90)

def main():

   n = 25 # Fibonacci Word to use.
   step = 1 # Segment length.
   width = 1050 # Width of plot area.
   height = 1050 # Height of plot area.
   w = fibonacci_word(n)

   setup(width=width, height=height)
   speed(0)
   setheading(90)
   left(90)
   penup()
   forward(500)
   right(90)
   backward(500)
   pendown()
   tracer(10000)
   hideturtle()

   draw_fractal(w, step)

   # Save Poscript image.
   getscreen().getcanvas().postscript(file="fibonacci_word_fractal.eps")
   exitonclick()

if __name__ == '__main__':

   main()</lang>

The output image is probably the same.

R

Translation of: PARI/GP

Works with: R version 3.3.1 and above

File:FiboFractR23.png

Output FiboFractR23.png

File:FiboFractR25.png

Output FiboFractR25.png

1. Fibonacci word/fractal 2/20/17 aev
2. Create Fibonacci word order n

fibow <- function(n) {

 t2="0"; t1="01"; t="";
 if(n<2) {n=2}
 for (i in 2:n) {t=paste0(t1,t2); t2=t1; t1=t}
 return(t)

}

1. Plot Fibonacci word/fractal:
2. n - word order, w - width, h - height, d - segment size, clr - color.

pfibofractal <- function(n, w, h, d, clr) {

 dx=d; x=y=x2=y2=tx=dy=nr=0;
 if(n<2) {n=2}
 fw=fibow(n); nf=nchar(fw);
 pf = paste0("FiboFractR", n, ".png");
 ttl=paste0("Fibonacci word/fractal, n=",n);
 cat(ttl,"nf=", nf, "pf=", pf,"\n");
 plot(NA, xlim=c(0,w), ylim=c(-h,0), xlab="", ylab="", main=ttl)
 for (i in 1:nf) {
   fwi=substr(fw, i, i);
   x2=x+dx; y2=y+dy;
   segments(x, y, x2, y2, col=clr); x=x2; y=y2;
   if(fwi=="0") {tx=dx; nr=i%%2;
     if(nr==0) {dx=-dy;dy=tx} else {dx=dy;dy=-tx}}
 }
 dev.copy(png, filename=pf, width=w, height=h); # plot to png-file
 dev.off(); graphics.off();  # Cleaning

}

1. Executing:

pfibofractal(23, 1000, 1000, 1, "navy") pfibofractal(25, 2300, 1000, 1, "red") </lang>

Output:

> pfibofractal(23, 1000, 1000, 1, "navy")
Fibonacci word/fractal, n=23 nf= 75025 pf= FiboFractR23.png 
> pfibofractal(25, 2300, 1000, 1, "red")
Fibonacci word/fractal, n=25 nf= 196418 pf= FiboFractR25.png

Racket

Prime candidate for Turtle Graphics. I've used a values-turtle, which means you don't get the joy of seeing the turltle bimble around the screen. But it allows the size of the image to be set (useful if you want to push the _n much higher than 23 or so!

We use word-order 23, which gives a classic n shape (inverted horseshoe).

Save the (first) implementation of Fibonacci word to Fibonacci-word.rkt; since we do not generate the words here.

<lang racket>#lang racket (require "Fibonacci-word.rkt") (require graphics/value-turtles)

(define word-order 23) ; is a 3k+2 fractal, shaped like an n (define height 420) (define width 600)

(define the-word

 (parameterize ((f-word-max-length #f))
   (F-Word word-order)))

(for/fold ((T (turtles width height

                      0 height ; in BL corner
                      (/ pi -2)))) ; point north
 ((i (in-naturals))
  (j (in-string (f-word-str the-word))))
 (match* (i j)
   ((_ #\1) (draw 1 T))
   (((? even?) #\0) (turn -90 (draw 1 T)))
   ((_ #\0) (turn 90 (draw 1 T)))))</lang>

Raku

(formerly Perl 6) <lang perl6>constant @fib-word = '1', '0', { $^b ~ $^a } ... *;

sub MAIN($m = 17, $scale = 3) {

   (my %world){0}{0} = 1;
   my $loc = 0+0i;
   my $dir = i;
   my $n = 1;

   for @fib-word[$m].comb {
       when '0' {
           step;
           if $n %% 2 { turn-left }
           else { turn-right; }
       }
       $n++;
   }

   braille-graphics %world;

   sub step {
       for ^$scale {
           $loc += $dir;
           %world{$loc.im}{$loc.re} = 1;
       }
   }

   sub turn-left  { $dir *= i; }
   sub turn-right { $dir *= -i; }

}

sub braille-graphics (%a) {

   my ($ylo, $yhi, $xlo, $xhi);
   for %a.keys -> $y {

$ylo min= +$y; $yhi max= +$y; for %a{$y}.keys -> $x { $xlo min= +$x; $xhi max= +$x; }

   for $ylo, $ylo + 4 ...^ * > $yhi -> \y {

for $xlo, $xlo + 2 ...^ * > $xhi -> \x { my $cell = 0x2800; $cell += 1 if %a{y + 0}{x + 0}; $cell += 2 if %a{y + 1}{x + 0}; $cell += 4 if %a{y + 2}{x + 0}; $cell += 8 if %a{y + 0}{x + 1}; $cell += 16 if %a{y + 1}{x + 1}; $cell += 32 if %a{y + 2}{x + 1}; $cell += 64 if %a{y + 3}{x + 0}; $cell += 128 if %a{y + 3}{x + 1}; print chr($cell); } print "\n";

}</lang>

Output:

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⠀⡤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠃⠘⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣇⣸⠉⣇⣀⠀⣀⣸⠉⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠼⠀⠧⢤⠀⡤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢲⠀⡖⠚⠀⠓⢲⠀⡖⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⡁⠀⠀⠀⢈⣉⡁⢈⣉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠼⠀⠧⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠼⠀⠧⢤⠀⡤⠼⠀⠧⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢲⠀⡖⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢲⠀⡖⠚⠀⠓⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡏⢹⣀⡏⠉⠀⠉⢹⣀⡏⢹⣀⡀⢀⣀⡏⢹⣀⡏⠉⠀⠉⢹⣀⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⡄⢠⠤⡄⠀⠀⠀⢠⠤⡄⢠⠤⠇⠸⠤⡄⢠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠀⠓⢲⠀⡖⠚⠀⠓⠚⠀⠀⠀⠀⠓⠚⠀⠓⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⡏⢹⣀⡀⢀⣀⡏⢹⣀⡏⠉⠀⠉⢹⣀⡏⢹⣀⡀⢀⣀⡏⢹⣀⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⠤⡄⢠⠤⠇⠸⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠇⠸⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢰⠒⡆⢰⠒⠃⠘⠒⡆⢰⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⡆⢰⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣏⣉⠀⣉⣉⠀⠀⠀⠀⣉⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠸⠤⠇⠸⠤⡄⢠⠤⠇⠸⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠇⠸⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠇⠸⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⠒⠃⠘⠒⡆⢰⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⡆⢰⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⡆⢰⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠉⣇⣸⠉⠁⠈⠉⣇⣸⠉⣇⣀⠀⣀⣸⠉⣇⣸⠉⠁⠈⠉⣇⣸⠉⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⠉⣇⣸⠉⠁⠈⠉⣇⣸⠉⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⠀⡤⠼⠀⠧⢤⠀⡤⢤⠀⠀⠀⠀⡤⢤⠀⡤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢤⠀⡤⢤⠀⠀⠀⠀⡤⢤⠀⡤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠃⠘⠒⠃⠀⠀⠀⠘⠒⠃⠘⠒⡆⢰⠒⠃⠘⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠃⠘⠒⡆⢰⠒⠃⠘⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣇⣸⠉⣇⣀⠀⣀⣸⠉⣇⣸⠉⠁⠈⠉⣇⣸⠉⣇⣀⠀⣀⣸⠉⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⠉⣇⣀⠀⣀⣸⠉⣇⣸⠉⠁⠈⠉⣇⣸⠉⣇⣀⠀⣀⣸⠉⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠼⠀⠧⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠼⠀⠧⢤⠀⡤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢤⠀⡤⠼⠀⠧⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠼⠀⠧⢤⠀⡤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢲⠀⡖⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢲⠀⡖⠚⠀⠓⢲⠀⡖⢲⠀⠀⠀⠀⡖⢲⠀⡖⠚⠀⠓⢲⠀⡖⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢲⠀⡖⠚⠀⠓⢲⠀⡖⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⡁⠀⠀⠀⢈⣉⡁⢈⣉⡇⢸⣉⡁⢈⣉⡁⠀⠀⠀⢈⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⡁⠀⠀⠀⢈⣉⡁⢈⣉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠼⠀⠧⢤⠀⡤⠼⠀⠧⠼⠀⠀⠀⠀⠧⠼⠀⠧⢤⠀⡤⠼⠀⠧⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠼⠀⠧⢤⠀⡤⠼⠀⠧⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢲⠀⡖⠚⠀⠓⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠚⠀⠓⢲⠀⡖⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢲⠀⡖⠚⠀⠓⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡏⢹⣀⡏⠉⠀⠉⢹⣀⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣀⡏⠉⠀⠉⢹⣀⡏⢹⣀⡀⢀⣀⡏⢹⣀⡏⠉⠀⠉⢹⣀⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⡄⢠⠤⡄⠀⠀⠀⢠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡄⠀⠀⠀⢠⠤⡄⢠⠤⠇⠸⠤⡄⢠⠤⡄⠀⠀⠀⢠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠀⠓⢲⠀⡖⠚⠀⠓⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠚⠀⠓⢲⠀⡖⠚⠀⠓⠚⠀⠀⠀⠀⠓⠚⠀⠓⢲⠀⡖⠚⠀⠓⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠚⠀⠓⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⠀⣉⣹⠀⣏⣉⠀⣀⣀⠀⠀⠀⠀⣀⣀⠀⣉⣹⠀⣏⣉⠀⣉⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⠀⣉⣹⠀⣏⣉⠀⣀⣀⠀⠀⠀⠀⣀⣀⠀⣉⣹⠀⣏⣉⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠇⠀⠀⠀⠸⠤⠇⠸⠤⡄⢠⠤⠇⠸⠤⠇⠀⠀⠀⠸⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠇⠀⠀⠀⠸⠤⠇⠸⠤⡄⢠⠤⠇⠸⠤⠇⠀⠀⠀⠸⠤⠇⠸⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⡆⢰⠒⠃⠘⠒⡆⢰⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⡆⢰⠒⠃⠘⠒⡆⢰⠒⡆⠀⠀⠀⢰⠒⡆⢰⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⠀⣉⣉⠀⠀⠀⠀⣉⣉⠀⣉⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⠀⣉⣉⠀⠀⠀⠀⣉⣉⠀⣉⣹⠀⣏⣉⠀⣉⣉⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠇⠸⠤⡄⢠⠤⠇⠸⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠇⠸⠤⡄⢠⠤⠇⠸⠤⠇⠀⠀⠀⠸⠤⠇⠸⠤⡄⢠⠤⠇⠸⠤⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠃⠘⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠃⠘⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠃⠘⠒⡆⢰⠒⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣇⣸⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣇⣸⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣇⣸⠉⠁⠈⠉⣇⣸⠉⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⠀⠀⠀⠀⡤⢤⠀⡤⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠃⠘⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠃⠘⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠃⠘⠒⡆⢰⠒⠃⠘⠒⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢈⣉⡇⢸⣉⡁⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢈⣉⡇⢸⣉⡁⢀⣀⡀⠀⠀⠀⢀⣀⡀⢈⣉⡇⢸⣉⡁⢈⣉⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠼⠀⠧⠼⠀⠀⠀⠀⠧⠼⠀⠧⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠼⠀⠧⠼⠀⠀⠀⠀⠧⠼⠀⠧⢤⠀⡤⠼⠀⠧⠼⠀⠀⠀⠀⠧⠼⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢲⠀⡖⢲⠀⠀⠀⠀⡖⢲⠀⡖⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢲⠀⡖⢲⠀⠀⠀⠀⡖⢲⠀⡖⠚⠀⠓⢲⠀⡖⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢈⣉⡁⢈⣉⡇⢸⣉⡁⢈⣉⡁⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢈⣉⡁⢈⣉⡇⢸⣉⡁⢈⣉⡁⠀⠀⠀⢈⣉⡁⢈⣉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠼⠀⠧⢤⠀⡤⠼⠀⠧⠼⠀⠀⠀⠀⠧⠼⠀⠧⢤⠀⡤⠼⠀⠧⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠼⠀⠧⢤⠀⡤⠼⠀⠧⠼⠀⠀⠀⠀⠧⠼⠀⠧⢤⠀⡤⠼⠀⠧⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢲⠀⡖⠚⠀⠓⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠚⠀⠓⢲⠀⡖⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢲⠀⡖⠚⠀⠓⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠚⠀⠓⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡏⢹⣀⡏⠉⠀⠉⢹⣀⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣀⡏⠉⠀⠉⢹⣀⡏⢹⣀⡀⢀⣀⡏⢹⣀⡏⠉⠀⠉⢹⣀⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣀⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⡄⢠⠤⡄⠀⠀⠀⢠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡄⠀⠀⠀⢠⠤⡄⢠⠤⠇⠸⠤⡄⢠⠤⡄⠀⠀⠀⢠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠀⠓⢲⠀⡖⠚⠀⠓⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠚⠀⠓⢲⠀⡖⠚⠀⠓⠚⠀⠀⠀⠀⠓⠚⠀⠓⢲⠀⡖⠚⠀⠓⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⠀⣉⣹⠀⣏⣉⠀⣀⣀⠀⠀⠀⠀⣀⣀⠀⣉⣹⠀⣏⣉⠀⣉⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⠀⣉⣹⠀⣏⣉⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠇⠀⠀⠀⠸⠤⠇⠸⠤⡄⢠⠤⠇⠸⠤⠇⠀⠀⠀⠸⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠇⠀⠀⠀⠸⠤⠇⠸⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⡆⠀⠀⠀⢰⠒⡆⢰⠒⠃⠘⠒⡆⢰⠒⡆⠀⠀⠀⢰⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⡆⠀⠀⠀⢰⠒⡆⢰⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⠀⣉⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⠀⣉⣹⠀⣏⣉⠀⠉⠉⠀⠀⠀⠀⠉⠉⠀⣉⣹⠀⣏⣉⠀⣉⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⠀⣉⣹⠀⣏⣉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⠀⡤⠼⠀⠧⢤⠀⡤⢤⠀⠀⠀⠀⡤⢤⠀⡤⠼⠀⠧⢤⠀⡤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢤⠀⡤⠼⠀⠧⢤⠀⡤⢤⠀⠀⠀⠀⡤⢤⠀⡤⠼⠀⠧⢤⠀⡤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠃⠘⠒⠃⠀⠀⠀⠘⠒⠃⠘⠒⡆⢰⠒⠃⠘⠒⠃⠀⠀⠀⠘⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠃⠀⠀⠀⠘⠒⠃⠘⠒⡆⢰⠒⠃⠘⠒⠃⠀⠀⠀⠘⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣇⣸⠉⣇⣀⠀⣀⣸⠉⣇⣸⠉⠁⠈⠉⣇⣸⠉⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⠉⣇⣸⠉⠁⠈⠉⣇⣸⠉⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡤⢤⠀⠀⠀⠀⡤⢤⠀⡤⠼⠀⠧⢤⠀⡤⢤⠀⠀⠀⠀⡤⢤⠀⡤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢤⠀⡤⢤⠀⠀⠀⠀⡤⢤⠀⡤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⠒⠃⠘⠒⡆⢰⠒⠃⠘⠒⠃⠀⠀⠀⠘⠒⠃⠘⠒⡆⢰⠒⠃⠘⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠃⠘⠒⡆⢰⠒⠃⠘⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣀⡀⢈⣉⡇⢸⣉⡁⢈⣉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣉⡁⢈⣉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣉⡁⢈⣉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡤⠼⠀⠧⠼⠀⠀⠀⠀⠧⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠓⢲⠀⡖⢲⠀⠀⠀⠀⡖⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠉⠁⢈⣉⡇⢸⣉⡁⢈⣉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣉⡁⢈⣉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⠤⡄⢠⠤⠇⠸⠤⡄⢠⠤⡄⠀⠀⠀⢠⠤⡄⢠⠤⠇⠸⠤⡄⢠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠓⠚⠀⠀⠀⠀⠓⠚⠀⠓⢲⠀⡖⠚⠀⠓⠚⠀⠀⠀⠀⠓⠚⠀⠓⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡏⢹⣀⡏⠉⠀⠉⢹⣀⡏⢹⣀⡀⢀⣀⡏⢹⣀⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⡄⢠⠤⡄⠀⠀⠀⢠⠤⡄⢠⠤⠇⠸⠤⡄⢠⠤⡄⠀⠀⠀⢠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠀⠓⢲⠀⡖⠚⠀⠓⠚⠀⠀⠀⠀⠓⠚⠀⠓⢲⠀⡖⠚⠀⠓⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⠀⣉⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⠀⣉⣹⠀⣏⣉⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠇⠀⠀⠀⠸⠤⠇⠸⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⡆⠀⠀⠀⢰⠒⡆⢰⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⠀⣉⣹⠀⣏⣉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⠀⡤⠼⠀⠧⢤⠀⡤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠃⠘⠒⠃⠀⠀⠀⠘⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣇⣸⠉⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

REXX

Programming note: the starting point (.) and the ending point (∙) are also shown to help visually identify the end points.

About half of the REXX program is dedicated to plotting the appropriate characters.

If the order of the graph is negative, the graph isn't displayed to the terminal screen.

The output of this REXX program is always written to a disk file (named FIBFRACT.OUT). <lang rexx>/*REXX program generates a Fibonacci word, then (normally) displays the fractal curve.*/ parse arg order . /*obtain optional arguments from the CL*/ if order== | order=="," then order= 23 /*Not specified? Then use the default*/ tell= order>=0 /*Negative order? Then don't display. */ s= FibWord( abs(order) ) /*obtain the order of Fibonacci word.*/

                         x= 0;       maxX= 0;    dx= 0;    b= ' ';     @.   = b;    xp= 0
                         y= 0;       maxY= 0;    dy= 1;                @.0.0= .;    yp= 0
 do n=1  for length(s);  x= x + dx;  y= y + dy  /*advance the plot for the next point. */
 maxX= max(maxX, x);     maxY= max(maxY, y)     /*set the maximums for displaying plot.*/
                 c= '│'                         /*glyph (character) used for the plot. */
 if dx\==0  then c= "─"                         /*if  x+dx   isn't zero, use this char.*/
 if n==1    then c= '┌'                         /*is this the first part to be graphed?*/
 @.x.y= c                                       /*assign a plotting character for curve*/
 if @(xp-1, yp)\==b  then if  @(xp, yp-1)\==b  then call @ xp,yp,'┐'  /*fix─up a corner*/
 if @(xp-1, yp)\==b  then if  @(xp, yp+1)\==b  then call @ xp,yp,'┘'  /*   "   "    "  */
 if @(xp+1, yp)\==b  then if  @(xp, yp-1)\==b  then call @ xp,yp,'┌'  /*   "   "    "  */
 if @(xp+1, yp)\==b  then if  @(xp, yp+1)\==b  then call @ xp,yp,'└'  /*   "   "    "  */
 xp= x;     yp= y                               /*save the old   x  &  y   coördinates.*/
 z= substr(s, n, 1)                             /*assign a plot character for the graph*/
 if z==1    then iterate                        /*Is Z equal to unity?  Then ignore it.*/
 ox= dx;    oy= dy                              /*save    DX,DY   as the old versions. */
 dx= 0;     dy= 0                               /*define  DX,DY    "  "  new     "     */
 d= -n//2;         if d==0  then d= 1           /*determine the sign for the chirality.*/
 if oy\==0  then dx= -sign(oy) * d              /*Going  north│south?   Go  east|west  */
 if ox\==0  then dy=  sign(ox) * d              /*  "     east│west?     " south|north */
 end   /*n*/

call @ x, y, '∙' /*set the last point that was plotted. */

      do r=maxY   to 0  by -1;  _=              /*show single row at a time, top first.*/
         do c=0  for maxX+1;    _= _  ||  @.c.r /*add a plot character (glyph) to line.*/
         end   /*c*/                            /* [↑]  construct a line char by char. */
      _= strip(_, 'T')                          /*construct a line of the graph.       */
      if _==  then iterate                    /*Is the line blank?   Then ignore it. */
      if tell  then say _                       /*Display the line to the terminal ?   */
      call lineout "FIBFRACT.OUT", _            /*write graph to disk  (FIBFRACT.OUT). */
      end      /*r*/                            /* [↑]  only display the non-blank rows*/

exit 0 /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ @: parse arg xx,yy,p; if arg(3)== then return @.xx.yy; @.xx.yy= p; return /*──────────────────────────────────────────────────────────────────────────────────────*/ FibWord: procedure; parse arg x; !.= 0; !.1= 1 /*obtain the order of Fibonacci word. */

                   do k=3  to x                 /*generate the   Kth       "       "   */
                          k1= k-1;    k2= k - 2 /*calculate the  K-1  &  K-2  shortcut.*/
                   !.k= !.k1    ||  !.k2        /*construct the next   Fibonacci word. */
                   end   /*k*/                  /* [↑]  generate a         "       "   */
        return !.x                              /*return the    Xth        "       "   */</lang>

output when using the input of: 17

(The output is shown ¹/₈ size.)

┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ │ └─┘ │ │ └─┘ │ │ └─┘ │ │ └─┘ │ │ └─┘ │ │ └─┘ │ │ └─┘ │ │ └─┘ │ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ │ │ ┌─┐ │ │ │ │ ┌─┐ │ │ │ │ ┌─┐ │ │ │ │ ┌─┐ │ │ ┌┘ └─┘ └─┘ └┐ ┌┘ └─┘ └─┘ └┐ ┌┘ └─┘ └─┘ └┐ ┌┘ └─┘ └─┘ └┐ │ ┌─┐ ┌─┐ │ │ ┌─┐ ┌─┐ │ │ ┌─┐ ┌─┐ │ │ ┌─┐ ┌─┐ │ └─┘ │ │ └─┘ └─┘ │ │ └─┘ └─┘ │ │ └─┘ └─┘ │ │ └─┘ ┌┘ └┐ ┌─┐ ┌─┐ ┌┘ └┐ ┌┘ └┐ ┌─┐ ┌─┐ ┌┘ └┐ │ │ │ └─┘ │ │ │ │ │ │ └─┘ │ │ │ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ ┌─┐ │ │ ┌─┐ │ │ ┌─┐ │ │ ┌─┐ ┌─┐ │ │ ┌─┐ │ │ ┌─┐ │ │ ┌─┐ │ └─┘ └─┘ └─┘ └─┘ └─┘ └─┘ │ │ └─┘ └─┘ └─┘ └─┘ └─┘ └─┘ │ └┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌┘ └┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌┘ │ │ └─┘ │ │ └─┘ │ │ │ │ └─┘ │ │ └─┘ │ │ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ │ ┌─┐ │ │ │ │ ┌─┐ │ │ ┌─┐ │ │ │ │ ┌─┐ │ └─┘ └─┘ └┐ ┌┘ └─┘ └─┘ └─┘ └─┘ └┐ ┌┘ └─┘ └─┘ ┌─┐ │ │ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ │ │ ┌─┐ │ └─┘ └─┘ │ │ └─┘ │ │ └─┘ │ │ └─┘ └─┘ │ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ │ │ │ │ ┌─┐ │ │ │ │ ┌┘ └┐ ┌┘ └─┘ └─┘ └┐ ┌┘ └┐ │ ┌─┐ ┌─┐ │ │ ┌─┐ ┌─┐ │ │ ┌─┐ ┌─┐ │ └─┘ │ │ └─┘ └─┘ │ │ └─┘ └─┘ │ │ └─┘ ┌─┐ ┌─┐ ┌┘ └┐ ┌─┐ ┌─┐ ┌┘ └┐ ┌─┐ ┌─┐ ┌┘ └┐ ┌─┐ ┌─┐ │ └─┘ │ │ │ │ └─┘ │ │ │ │ └─┘ │ │ │ │ └─┘ │ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ │ │ ┌─┐ │ │ ┌─┐ │ │ ┌─┐ │ │ ┌─┐ │ │ ┌─┐ │ │ ┌─┐ │ │ ┌┘ └─┘ └─┘ └─┘ └─┘ └─┘ └─┘ └─┘ └─┘ └─┘ └─┘ └─┘ └─┘ └┐ │ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ │ └─┘ │ │ └─┘ │ │ └─┘ │ │ └─┘ │ │ └─┘ │ │ └─┘ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ │ │ │ ┌─┐ │ │ │ │ ┌─┐ │ │ │ └┐ ┌┘ └─┘ └─┘ └┐ ┌┘ └─┘ └─┘ └┐ ┌┘ ┌─┐ │ │ ┌─┐ ┌─┐ │ │ ┌─┐ ┌─┐ │ │ ┌─┐ │ └─┘ └─┘ │ │ └─┘ └─┘ │ │ └─┘ └─┘ │ └┐ ┌─┐ ┌─┐ ┌┘ └┐ ┌┘ └┐ ┌─┐ ┌─┐ ┌┘ │ │ └─┘ │ │ │ │ │ │ └─┘ │ │ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ │ ┌─┐ │ │ ┌─┐ │ │ ┌─┐ ┌─┐ │ │ ┌─┐ │ │ ┌─┐ │ └─┘ └─┘ └─┘ └─┘ └─┘ │ │ └─┘ └─┘ └─┘ └─┘ └─┘ ┌─┐ ┌─┐ ┌┘ └┐ ┌─┐ ┌─┐ │ └─┘ │ │ │ │ └─┘ │ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ │ │ ┌─┐ │ │ ┌─┐ │ │ ┌┘ └─┘ └─┘ └─┘ └─┘ └┐ │ ┌─┐ ┌─┐ │ └─┘ │ │ └─┘ ┌┘ └┐ │ │ └┐ ┌┘ ┌─┐ │ │ ┌─┐ │ └─┘ └─┘ │ └┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌┘ │ │ └─┘ │ │ └─┘ │ │ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ │ ┌─┐ │ │ │ │ ┌─┐ │ └─┘ └─┘ └┐ ┌┘ └─┘ └─┘ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ │ │ ┌─┐ ┌─┐ ┌─┐ ┌─┐ ┌─┐ │ └─┘ │ │ └─┘ │ │ └─┘ └─┘ │ │ └─┘ │ │ └─┘ │ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ │ │ ┌─┐ │ │ │ │ │ │ ┌─┐ │ │ ┌┘ └─┘ └─┘ └┐ ┌┘ └┐ ┌┘ └─┘ └─┘ └┐ │ ┌─┐ ┌─┐ │ │ ┌─┐ ┌─┐ │ │ ┌─┐ ┌─┐ │ └─┘ │ │ └─┘ └─┘ │ │ └─┘ └─┘ │ │ └─┘ ┌┘ └┐ ┌─┐ ┌─┐ ┌┘ └┐ ┌─┐ ┌─┐ ┌┘ └┐ │ │ │ └─┘ │ │ │ │ └─┘ │ │ │ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ └┐ ┌┘ ┌─┐ │ │ ┌─┐ │ │ ┌─┐ │ │ ┌─┐ │ │ ┌─┐ │ │ ┌─┐ . └─┘ └─┘ └─┘ └─┘ └─┘ └─┘ └─┘ └─┘ └─┘ └─┘ └∙

The output of this REXX program for this Rosetta Code task requirements can be seen here ───► Fibonacci word/fractal/FIBFRACT.REX.

Ruby

<lang ruby>def fibonacci_word(n)

 words = ["1", "0"]
 (n-1).times{ words << words[-1] + words[-2] }
 words[n]

end

def print_fractal(word)

 area = Hash.new(" ")
 x = y = 0
 dx, dy = 0, -1
 areax,y = "S"
 word.each_char.with_index(1) do |c,n|
   areax+dx, y+dy = dx.zero? ? "|" : "-"
   x, y = x+2*dx, y+2*dy
   areax, y = "+"
   dx,dy = n.even? ? [dy,-dx] : [-dy,dx]  if c=="0"
 end
 
 (xmin, xmax), (ymin, ymax) = area.keys.transpose.map(&:minmax)
 for y in ymin..ymax
   puts (xmin..xmax).map{|x| areax,y}.join
 end

end

word = fibonacci_word(16) print_fractal(word)</lang>

Output:

+-+-+   +-+-+       +-+-+   +-+-+               +-+-+   +-+-+       +-+-+   +-+-+                                   +-+-+   +-+-+       +-+-+   +-+-+               +-+-+   +-+-+       +-+-+   +-+-+  
|   |   |   |       |   |   |   |               |   |   |   |       |   |   |   |                                   |   |   |   |       |   |   |   |               |   |   |   |       |   |   |   |  
+   +-+-+   +       +   +-+-+   +               +   +-+-+   +       +   +-+-+   +                                   +   +-+-+   +       +   +-+-+   +               +   +-+-+   +       +   +-+-+   +  
|           |       |           |               |           |       |           |                                   |           |       |           |               |           |       |           |  
+-+       +-+       +-+       +-+               +-+       +-+       +-+       +-+                                   +-+       +-+       +-+       +-+               +-+       +-+       +-+       +-+  
  |       |           |       |                   |       |           |       |                                       |       |           |       |                   |       |           |       |    
  +       +   +-+-+   +       +                   +       +   +-+-+   +       +                                       +       +   +-+-+   +       +                   +       +   +-+-+   +       +    
  |       |   |   |   |       |                   |       |   |   |   |       |                                       |       |   |   |   |       |                   |       |   |   |   |       |    
+-+       +-+-+   +-+-+       +-+               +-+       +-+-+   +-+-+       +-+                                   +-+       +-+-+   +-+-+       +-+               +-+       +-+-+   +-+-+       +-+  
|                               |               |                               |                                   |                               |               |                               |  
+   +-+-+               +-+-+   +               +   +-+-+               +-+-+   +                                   +   +-+-+               +-+-+   +               +   +-+-+               +-+-+   +  
|   |   |               |   |   |               |   |   |               |   |   |                                   |   |   |               |   |   |               |   |   |               |   |   |  
+-+-+   +               +   +-+-+               +-+-+   +               +   +-+-+                                   +-+-+   +               +   +-+-+               +-+-+   +               +   +-+-+  
        |               |                               |               |                                                   |               |                               |               |          
      +-+               +-+       +-+-+   +-+-+       +-+               +-+                                               +-+               +-+       +-+-+   +-+-+       +-+               +-+        
      |                   |       |   |   |   |       |                   |                                               |                   |       |   |   |   |       |                   |        
      +                   +       +   +-+-+   +       +                   +                                               +                   +       +   +-+-+   +       +                   +        
      |                   |       |           |       |                   |                                               |                   |       |           |       |                   |        
      +-+               +-+       +-+       +-+       +-+               +-+                                               +-+               +-+       +-+       +-+       +-+               +-+        
        |               |           |       |           |               |                                                   |               |           |       |           |               |          
+-+-+   +               +   +-+-+   +       +   +-+-+   +               +   +-+-+                                   +-+-+   +               +   +-+-+   +       +   +-+-+   +               +   +-+-+  
|   |   |               |   |   |   |       |   |   |   |               |   |   |                                   |   |   |               |   |   |   |       |   |   |   |               |   |   |  
+   +-+-+               +-+-+   +-+-+       +-+-+   +-+-+               +-+-+   +                                   +   +-+-+               +-+-+   +-+-+       +-+-+   +-+-+               +-+-+   +  
|                                                                               |                                   |                                                                               |  
+-+       +-+-+   +-+-+                                   +-+-+   +-+-+       +-+                                   +-+       +-+-+   +-+-+                                   +-+-+   +-+-+       +-+  
  |       |   |   |   |                                   |   |   |   |       |                                       |       |   |   |   |                                   |   |   |   |       |    
  +       +   +-+-+   +                                   +   +-+-+   +       +                                       +       +   +-+-+   +                                   +   +-+-+   +       +    
  |       |           |                                   |           |       |                                       |       |           |                                   |           |       |    
+-+       +-+       +-+                                   +-+       +-+       +-+                                   +-+       +-+       +-+                                   +-+       +-+       +-+  
|           |       |                                       |       |           |                                   |           |       |                                       |       |           |  
+   +-+-+   +       +                                       +       +   +-+-+   +                                   +   +-+-+   +       +                                       +       +   +-+-+   +  
|   |   |   |       |                                       |       |   |   |   |                                   |   |   |   |       |                                       |       |   |   |   |  
+-+-+   +-+-+       +-+                                   +-+       +-+-+   +-+-+                                   +-+-+   +-+-+       +-+                                   +-+       +-+-+   +-+-+  
                      |                                   |                                                                               |                                   |                        
              +-+-+   +                                   +   +-+-+               +-+-+   +-+-+       +-+-+   +-+-+               +-+-+   +                                   +   +-+-+                
              |   |   |                                   |   |   |               |   |   |   |       |   |   |   |               |   |   |                                   |   |   |                
              +   +-+-+                                   +-+-+   +               +   +-+-+   +       +   +-+-+   +               +   +-+-+                                   +-+-+   +                
              |                                                   |               |           |       |           |               |                                                   |                
              +-+                                               +-+               +-+       +-+       +-+       +-+               +-+                                               +-+                
                |                                               |                   |       |           |       |                   |                                               |                  
                +                                               +                   +       +   +-+-+   +       +                   +                                               +                  
                |                                               |                   |       |   |   |   |       |                   |                                               |                  
              +-+                                               +-+               +-+       +-+-+   +-+-+       +-+               +-+                                               +-+                
              |                                                   |               |                               |               |                                                   |                
              +   +-+-+                                   +-+-+   +               +   +-+-+               +-+-+   +               +   +-+-+                                   +-+-+   +                
              |   |   |                                   |   |   |               |   |   |               |   |   |               |   |   |                                   |   |   |                
              +-+-+   +                                   +   +-+-+               +-+-+   +               +   +-+-+               +-+-+   +                                   +   +-+-+                
                      |                                   |                               |               |                               |                                   |                        
+-+-+   +-+-+       +-+                                   +-+       +-+-+   +-+-+       +-+               +-+       +-+-+   +-+-+       +-+                                   +-+       +-+-+   +-+-+  
|   |   |   |       |                                       |       |   |   |   |       |                   |       |   |   |   |       |                                       |       |   |   |   |  
+   +-+-+   +       +                                       +       +   +-+-+   +       +                   +       +   +-+-+   +       +                                       +       +   +-+-+   +  
|           |       |                                       |       |           |       |                   |       |           |       |                                       |       |           |  
+-+       +-+       +-+                                   +-+       +-+       +-+       +-+               +-+       +-+       +-+       +-+                                   +-+       +-+       +-+  
  |       |           |                                   |           |       |           |               |           |       |           |                                   |           |       |    
  +       +   +-+-+   +                                   +   +-+-+   +       +   +-+-+   +               +   +-+-+   +       +   +-+-+   +                                   +   +-+-+   +       +    
  |       |   |   |   |                                   |   |   |   |       |   |   |   |               |   |   |   |       |   |   |   |                                   |   |   |   |       |    
+-+       +-+-+   +-+-+                                   +-+-+   +-+-+       +-+-+   +-+-+               +-+-+   +-+-+       +-+-+   +-+-+                                   +-+-+   +-+-+       +-+  
|                                                                                                                                                                                                   |  
+   +-+-+               +-+-+   +-+-+       +-+-+   +-+-+                                                                                   +-+-+   +-+-+       +-+-+   +-+-+               +-+-+   +  
|   |   |               |   |   |   |       |   |   |   |                                                                                   |   |   |   |       |   |   |   |               |   |   |  
+-+-+   +               +   +-+-+   +       +   +-+-+   +                                                                                   +   +-+-+   +       +   +-+-+   +               +   +-+-+  
        |               |           |       |           |                                                                                   |           |       |           |               |          
      +-+               +-+       +-+       +-+       +-+                                                                                   +-+       +-+       +-+       +-+               +-+        
      |                   |       |           |       |                                                                                       |       |           |       |                   |        
      +                   +       +   +-+-+   +       +                                                                                       +       +   +-+-+   +       +                   +        
      |                   |       |   |   |   |       |                                                                                       |       |   |   |   |       |                   |        
      +-+               +-+       +-+-+   +-+-+       +-+                                                                                   +-+       +-+-+   +-+-+       +-+               +-+        
        |               |                               |                                                                                   |                               |               |          
+-+-+   +               +   +-+-+               +-+-+   +                                                                                   +   +-+-+               +-+-+   +               +   +-+-+  
|   |   |               |   |   |               |   |   |                                                                                   |   |   |               |   |   |               |   |   |  
+   +-+-+               +-+-+   +               +   +-+-+                                                                                   +-+-+   +               +   +-+-+               +-+-+   +  
|                               |               |                                                                                                   |               |                               |  
+-+       +-+-+   +-+-+       +-+               +-+                                                                                               +-+               +-+       +-+-+   +-+-+       +-+  
  |       |   |   |   |       |                   |                                                                                               |                   |       |   |   |   |       |    
  +       +   +-+-+   +       +                   +                                                                                               +                   +       +   +-+-+   +       +    
  |       |           |       |                   |                                                                                               |                   |       |           |       |    
+-+       +-+       +-+       +-+               +-+                                                                                               +-+               +-+       +-+       +-+       +-+  
|           |       |           |               |                                                                                                   |               |           |       |           |  
+   +-+-+   +       +   +-+-+   +               +   +-+-+                                                                                   +-+-+   +               +   +-+-+   +       +   +-+-+   +  
|   |   |   |       |   |   |   |               |   |   |                                                                                   |   |   |               |   |   |   |       |   |   |   |  
+-+-+   +-+-+       +-+-+   +-+-+               +-+-+   +                                                                                   +   +-+-+               +-+-+   +-+-+       +-+-+   +-+-+  
                                                        |                                                                                   |                                                          
                                  +-+-+   +-+-+       +-+                                                                                   +-+       +-+-+   +-+-+                                    
                                  |   |   |   |       |                                                                                       |       |   |   |   |                                    
                                  +   +-+-+   +       +                                                                                       +       +   +-+-+   +                                    
                                  |           |       |                                                                                       |       |           |                                    
                                  +-+       +-+       +-+                                                                                   +-+       +-+       +-+                                    
                                    |       |           |                                                                                   |           |       |                                      
                                    +       +   +-+-+   +                                                                                   +   +-+-+   +       +                                      
                                    |       |   |   |   |                                                                                   |   |   |   |       |                                      
                                  +-+       +-+-+   +-+-+                                                                                   +-+-+   +-+-+       +-+                                    
                                  |                                                                                                                               |                                    
                                  +   +-+-+                                                                                                               +-+-+   +                                    
                                  |   |   |                                                                                                               |   |   |                                    
                                  +-+-+   +                                                                                                               +   +-+-+                                    
                                          |                                                                                                               |                                            
                                        +-+                                                                                                               +-+                                          
                                        |                                                                                                                   |                                          
                                        +                                                                                                                   +                                          
                                        |                                                                                                                   |                                          
                                        +-+                                                                                                               +-+                                          
                                          |                                                                                                               |                                            
                                  +-+-+   +                                                                                                               +   +-+-+                                    
                                  |   |   |                                                                                                               |   |   |                                    
                                  +   +-+-+                                                                                                               +-+-+   +                                    
                                  |                                                                                                                               |                                    
                                  +-+       +-+-+   +-+-+                                                                                   +-+-+   +-+-+       +-+                                    
                                    |       |   |   |   |                                                                                   |   |   |   |       |                                      
                                    +       +   +-+-+   +                                                                                   +   +-+-+   +       +                                      
                                    |       |           |                                                                                   |           |       |                                      
                                  +-+       +-+       +-+                                                                                   +-+       +-+       +-+                                    
                                  |           |       |                                                                                       |       |           |                                    
                                  +   +-+-+   +       +                                                                                       +       +   +-+-+   +                                    
                                  |   |   |   |       |                                                                                       |       |   |   |   |                                    
                                  +-+-+   +-+-+       +-+                                                                                   +-+       +-+-+   +-+-+                                    
                                                        |                                                                                   |                                                          
+-+-+   +-+-+       +-+-+   +-+-+               +-+-+   +                                                                                   +   +-+-+               +-+-+   +-+-+       +-+-+   +-+-+  
|   |   |   |       |   |   |   |               |   |   |                                                                                   |   |   |               |   |   |   |       |   |   |   |  
+   +-+-+   +       +   +-+-+   +               +   +-+-+                                                                                   +-+-+   +               +   +-+-+   +       +   +-+-+   +  
|           |       |           |               |                                                                                                   |               |           |       |           |  
+-+       +-+       +-+       +-+               +-+                                                                                               +-+               +-+       +-+       +-+       +-+  
  |       |           |       |                   |                                                                                               |                   |       |           |       |    
  +       +   +-+-+   +       +                   +                                                                                               +                   +       +   +-+-+   +       +    
  |       |   |   |   |       |                   |                                                                                               |                   |       |   |   |   |       |    
+-+       +-+-+   +-+-+       +-+               +-+                                                                                               +-+               +-+       +-+-+   +-+-+       +-+  
|                               |               |                                                                                                   |               |                               |  
+   +-+-+               +-+-+   +               +   +-+-+                                                                                   +-+-+   +               +   +-+-+               +-+-+   +  
|   |   |               |   |   |               |   |   |                                                                                   |   |   |               |   |   |               |   |   |  
+-+-+   +               +   +-+-+               +-+-+   +                                                                                   +   +-+-+               +-+-+   +               +   +-+-+  
        |               |                               |                                                                                   |                               |               |          
      +-+               +-+       +-+-+   +-+-+       +-+                                                                                   +-+       +-+-+   +-+-+       +-+               +-+        
      |                   |       |   |   |   |       |                                                                                       |       |   |   |   |       |                   |        
      +                   +       +   +-+-+   +       +                                                                                       +       +   +-+-+   +       +                   +        
      |                   |       |           |       |                                                                                       |       |           |       |                   |        
      +-+               +-+       +-+       +-+       +-+                                                                                   +-+       +-+       +-+       +-+               +-+        
        |               |           |       |           |                                                                                   |           |       |           |               |          
+-+-+   +               +   +-+-+   +       +   +-+-+   +                                                                                   +   +-+-+   +       +   +-+-+   +               +   +-+-+  
|   |   |               |   |   |   |       |   |   |   |                                                                                   |   |   |   |       |   |   |   |               |   |   |  
S   +-+-+               +-+-+   +-+-+       +-+-+   +-+-+                                                                                   +-+-+   +-+-+       +-+-+   +-+-+               +-+-+   +-+

Rust

The output of this program is a file in SVG format. <lang rust>// [dependencies] // svg = "0.8.0"

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

fn fibonacci_word(n: usize) -> Vec<u8> {

   let mut f0 = vec![1];
   let mut f1 = vec![0];
   if n == 0 {
       return f0;
   } else if n == 1 {
       return f1;
   }
   let mut i = 2;
   loop {
       let mut f = Vec::with_capacity(f1.len() + f0.len());
       f.extend(&f1);
       f.extend(f0);
       if i == n {
           return f;
       }
       f0 = f1;
       f1 = f;
       i += 1;
   }

}

struct FibwordFractal {

   current_x: f64,
   current_y: f64,
   current_angle: i32,
   line_length: f64,
   max_x: f64,
   max_y: f64,

}

impl FibwordFractal {

   fn new(x: f64, y: f64, length: f64, angle: i32) -> FibwordFractal {
       FibwordFractal {
           current_x: x,
           current_y: y,
           current_angle: angle,
           line_length: length,
           max_x: 0.0,
           max_y: 0.0,
       }
   }
   fn execute(&mut self, n: usize) -> Path {
       let mut data = Data::new().move_to((self.current_x, self.current_y));
       for (i, byte) in fibonacci_word(n).iter().enumerate() {
           data = self.draw_line(data);
           if *byte == 0u8 {
               self.turn(if i % 2 == 1 { -90 } else { 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();
       if self.current_x > self.max_x {
           self.max_x = self.current_x;
       }
       if self.current_y > self.max_y {
           self.max_y = self.current_y;
       }
       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, order: usize) -> std::io::Result<()> {
       use svg::node::element::Rectangle;
       let x = 5.0;
       let y = 5.0;
       let rect = Rectangle::new()
           .set("width", "100%")
           .set("height", "100%")
           .set("fill", "white");
       let mut ff = FibwordFractal::new(x, y, 1.0, 0);
       let path = ff.execute(order);
       let document = svg::Document::new()
           .set("width", 5 + ff.max_x as usize)
           .set("height", 5 + ff.max_y as usize)
           .add(rect)
           .add(path);
       svg::save(file, &document)
   }

}

fn main() {

   FibwordFractal::save("fibword_fractal.svg", 22).unwrap();

}</lang>

Output:

See: fibword_fractal.svg (offsite SVG image)

Scala

Note: will be computing an SVG image - not very efficient, but very cool. worked for me in the scala REPL with -J-Xmx2g argument. <lang scala> def fibIt = Iterator.iterate(("1","0")){case (f1,f2) => (f2,f1+f2)}.map(_._1)

def turnLeft(c: Char): Char = c match {

 case 'R' => 'U'
 case 'U' => 'L'
 case 'L' => 'D'
 case 'D' => 'R'

}

def turnRight(c: Char): Char = c match {

 case 'R' => 'D'
 case 'D' => 'L'
 case 'L' => 'U'
 case 'U' => 'R'

}

def directions(xss: List[(Char,Char)], current: Char = 'R'): List[Char] = xss match {

 case Nil => current :: Nil
 case x :: xs => x._1 match {
   case '1' => current :: directions(xs, current)
   case '0' => x._2 match {
     case 'E' => current :: directions(xs, turnLeft(current))
     case 'O' => current :: directions(xs, turnRight(current))
   }
 }

}

def buildIt(xss: List[Char], old: Char = 'X', count: Int = 1): List[String] = xss match {

 case Nil => s"$old$count" :: Nil
 case x :: xs if x == old => buildIt(xs,old,count+1)
 case x :: xs => s"$old$count" :: buildIt(xs,x)

}

def convertToLine(s: String, c: Int): String = (s.head, s.tail) match {

 case ('R',n) => s"l ${c * n.toInt} 0"
 case ('U',n) => s"l 0 ${-c * n.toInt}"
 case ('L',n) => s"l ${-c * n.toInt} 0"
 case ('D',n) => s"l 0 ${c * n.toInt}"

}

def drawSVG(xStart: Int, yStart: Int, width: Int, height: Int, fibWord: String, lineMultiplier: Int, color: String): String = {

 val xs = fibWord.zipWithIndex.map{case (c,i) => (c, if(c == '1') '_' else i % 2 match{case 0 => 'E'; case 1 => 'O'})}.toList
 val fractalPath = buildIt(directions(xs)).tail.map(convertToLine(_,lineMultiplier))
 s"""<?xml version="1.0" encoding="utf-8"?><!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN" "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd"><svg version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" x="0px" y="0px" width="${width}px" height="${height}px" viewBox="0 0 $width $height"><path d="M $xStart $yStart ${fractalPath.mkString(" ")}" style="stroke:#$color;stroke-width:1" stroke-linejoin="miter" fill="none"/></svg>"""

}

drawSVG(0,25,550,530,fibIt.drop(18).next,3,"000") </lang>

Output:

output string saved as an SVG file - BTW, would appreciate help on getting the image to display here nicely. couldn't figure out how to do that...

Scilab

This script uses Scilab's iterative solution to generate Fibonacci words, and the interpreting the words to generate the fractal is similar to Langton's ant. The result is displayed in a graphic window.

<lang>final_length = 37;

word_n = ; word_n_1 = ; word_n_2 = ;

for i = 1:final_length

   if i == 1 then
       word_n = '1';
   elseif i == 2
       word_n = '0';
   elseif i == 3
       word_n = '01';
       word_n_1 = '0';
   else
       word_n_2 = word_n_1;
       word_n_1 = word_n;
       word_n = word_n_1 + word_n_2;
   end

end

word = strsplit(word_n); fractal_size = sum(word' == '0'); fractal = zeros(1+fractal_size,2);

direction_vectors = [1,0; 0,-1; -1,0; 0,1]; direction = direction_vectors(4,:); direction_name = 'N';

for j = 1:length(word_n);

   fractal(j+1,:) = fractal(j,:) + direction;
   if word(j) == '0' then
       if pmodulo(j,2) then
           //right
           select direction_name
           case 'N' then
               direction = direction_vectors(1,:);
               direction_name = 'E';
           case 'E' then
               direction = direction_vectors(2,:);
               direction_name = 'S';
           case 'S' then
               direction = direction_vectors(3,:);
               direction_name = 'W';
           case 'W' then
               direction = direction_vectors(4,:);
               direction_name = 'N';
           end
       else
           //left
           select direction_name
           case 'N' then
               direction = direction_vectors(3,:);
               direction_name = 'W';
           case 'W' then
               direction = direction_vectors(2,:);
               direction_name = 'S';
           case 'S' then
               direction = direction_vectors(1,:);
               direction_name = 'E';
           case 'E' then
               direction = direction_vectors(4,:);
               direction_name = 'N';
           end
       end
   end

end

scf(0); clf(); plot2d(fractal(:,1),fractal(:,2)); set(gca(),'isoview','on');</lang>

Sidef

Translation of: Raku

<lang ruby>var(m=17, scale=3) = ARGV.map{.to_i}...

(var world = Hash.new){0}{0} = 1 var loc = 0 var dir = 1i

var fib = ['1', '0'] func fib_word(n) {

   fib[n] \\= (fib_word(n-1) + fib_word(n-2))

}

func step {

   scale.times {
       loc += dir
       world{loc.im}{loc.re} = 1
   }

}

func turn_left { dir *= 1i } func turn_right { dir *= -1i }

var n = 1 fib_word(m).each { |c|

   if (c == '0') {
       step()
       n % 2 == 0 ? turn_left()
                  : turn_right()
   } else { n++ }

}

func braille_graphics(a) {

   var (xlo, xhi, ylo, yhi) = ([Inf, -Inf]*2)...

   a.each_key { |y|
       ylo.min!(y.to_i)
       yhi.max!(y.to_i)
       a{y}.each_key { |x|
           xlo.min!(x.to_i)
           xhi.max!(x.to_i)
       }
   }

   for y in (ylo..yhi `by` 4) {
       for x in (xlo..xhi `by` 2) {
           var cell = 0x2800

           a{y+0}{x+0} && (cell += 1)
           a{y+1}{x+0} && (cell += 2)
           a{y+2}{x+0} && (cell += 4)
           a{y+0}{x+1} && (cell += 8)
           a{y+1}{x+1} && (cell += 16)
           a{y+2}{x+1} && (cell += 32)
           a{y+3}{x+0} && (cell += 64)
           a{y+3}{x+1} && (cell += 128)

           print cell.chr
       }
       print "\n"
   }

}

braille_graphics(world)</lang>

Output:

$ sidef fib_word_fractal.sf 12 3
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⠀⡤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠃⠘⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣇⣸⠉⣇⣀⠀⣀⣸⠉⣇⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠼⠀⠧⢤⠀⡤⠼⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢲⠀⡖⠚⠀⠓⢲⠀⡖⢲⠀⠀
⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⡁⠀⠀⠀⢈⣉⡁⢈⣉⡇
⠀⠀⠀⡤⠼⠀⠧⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠼⠀⠧⢤⠀⡤⠼⠀⠧⠼⠀⠀
⠀⠀⠀⠓⢲⠀⡖⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢲⠀⡖⠚⠀⠓⢲⠀⠀⠀⠀⠀
⠉⢹⣀⡏⠉⠀⠉⢹⣀⡏⢹⣀⡀⢀⣀⡏⢹⣀⡏⠉⠀⠉⢹⣀⡏⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⠤⡄⢠⠤⠇⠸⠤⡄⢠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡖⠚⠀⠓⠚⠀⠀⠀⠀⠓⠚⠀⠓⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⢹⣀⡏⢹⣀⡀⢀⣀⡏⢹⣀⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠇⠸⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⡆⢰⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Tcl

Library: Tk

<lang tcl>package require Tk

OK, this stripped down version doesn't work for n<2…

proc fibword {n} {

   set fw {1 0}
   while {[llength $fw] < $n} {

lappend fw [lindex $fw end][lindex $fw end-1]

   }
   return [lindex $fw end]

} proc drawFW {canv fw {w {[$canv cget -width]}} {h {[$canv cget -height]}}} {

   set w [subst $w]
   set h [subst $h]

   # Generate the coordinate list using line segments of unit length
   set d 3; # Match the orientation in the sample paper
   set eo [set x [set y 0]]
   set coords [list $x $y]
   foreach c [split $fw ""] {

switch $d { 0 {lappend coords [incr x] $y} 1 {lappend coords $x [incr y]} 2 {lappend coords [incr x -1] $y} 3 {lappend coords $x [incr y -1]} } if {$c == 0} { set d [expr {($d + ($eo ? -1 : 1)) % 4}] } set eo [expr {!$eo}]

   # Draw, and rescale to fit in canvas
   set id [$canv create line $coords]
   lassign [$canv bbox $id] x1 y1 x2 y2
   set sf [expr {min(($w-20.) / ($y2-$y1), ($h-20.) / ($x2-$x1))}]
   $canv move $id [expr {-$x1}] [expr {-$y1}]
   $canv scale $id 0 0 $sf $sf
   $canv move $id 10 10
   # Return the item ID to allow user reconfiguration
   return $id

}

pack [canvas .c -width 500 -height 500] drawFW .c [fibword 23]</lang>

Wren

Translation of: Go

Library: DOME

<lang ecmascript>import "graphics" for Canvas, Color import "dome" for Window

class FibonacciWordFractal {

   construct new(width, height, n) {
       Window.title = "Fibonacci Word Fractal"
       Window.resize(width, height)
       Canvas.resize(width, height)
       _fore = Color.green
       _wordFractal = wordFractal(n)
   }

   init() {
       drawWordFractal(20, 20, 1, 0)
   }

   wordFractal(i) {
       if (i < 2) return (i == 1) ? "1" : ""
       var f1 = "1"
       var f2 = "0"
       for (j in i-2...0) {
           var tmp = f2
           f2 = f2 + f1
           f1 = tmp
       }
       return f2
   }

   drawWordFractal(x, y, dx, dy) {
       for (i in 0..._wordFractal.count) {
           Canvas.line(x, y, x + dx, y + dy, _fore)
           x = x + dx
           y = y + dy
           if (_wordFractal[i] == "0") {
               var tx = dx
               dx = (i % 2 == 0) ? -dy : dy
               dy = (i % 2 == 0) ?  tx : - tx
           }
       }
   }

   update() {}

   draw(alpha) {}

}

var Game = FibonacciWordFractal.new(450, 620, 23)</lang>

zkl

Uses the PPM class from http://rosettacode.org/wiki/Bitmap/Bresenham%27s_line_algorithm#zkl

Translation of: D

<lang zkl>fcn drawFibonacci(img,x,y,word){ // word is "01001010...", 75025 characters

  dx:=0; dy:=1; // turtle direction
  foreach i,c in ([1..].zip(word)){ // Walker.zip(list)-->Walker of zipped list
     a:=x; b:=y; x+=dx; y+=dy;
     img.line(a,b, x,y, 0x00ff00);
     if (c=="0"){
        dxy:=dx+dy;

if(i.isEven){ dx=(dx - dxy)%2; dy=(dxy - dy)%2; }// turn left else { dx=(dxy - dx)%2; dy=(dy - dxy)%2; }// turn right

     }
  }

}

img:=PPM(1050,1050); fibWord:=L("1","0"); do(23){ fibWord.append(fibWord[-1] + fibWord[-2]); } drawFibonacci(img,20,20,fibWord[-1]); img.write(File("foo.ppm","wb"));</lang>

@@ Line 1,563: / Line 1,563: @@
 =={{header|Phix}}==
-Output matches Fig 1 (at the top of the page)
 {{libheader|Phix/pGUI}}
+{{libheader|Phix/online}}
-<lang Phix>-- demo\rosetta\FibonacciFractal.exw
+You can run this online [http://phix.x10.mx/p2js/fibonaccifractal.htm here].
-include pGUI.e
+Output matches Fig 1 (at the top of the page)
+<!--<lang Phix>(phixonline)-->
-Ihandle dlg, canvas
+ <span style="color: #000080;font-style:italic;">--
-cdCanvas cddbuffer, cdcanvas
+ -- demo\rosetta\FibonacciFractal.exw
+ --</span>
-procedure drawFibonacci(integer x, y, dx, dy, n)
+ <span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
-string prev = "1", word = "0"
+ <span style="color: #008080;">include</span> <span style="color: #000000;">pGUI</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
-    for i=3 to n do {prev,word} = {word,word&prev} end for
-    for i=1 to length(word) do
+ <span style="color: #004080;">Ihandle</span> <span style="color: #000000;">dlg</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">canvas</span>
-        cdCanvasLine(cddbuffer, x, y, x+dx, y+dy)
+ <span style="color: #004080;">cdCanvas</span> <span style="color: #000000;">cddbuffer</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">cdcanvas</span>
-        x += dx   y += dy
-        if word[i]=='0' then
+ <span style="color: #008080;">procedure</span> <span style="color: #000000;">drawFibonacci</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">dx</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">dy</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
-            {dx,dy} = iff(remainder(i,2)?{dy,-dx}:{-dy,dx})
+     <span style="color: #004080;">string</span> <span style="color: #000000;">prev</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"1"</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">word</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"0"</span>
-        end if
+     <span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">3</span> <span style="color: #008080;">to</span> <span style="color: #000000;">n</span> <span style="color: #008080;">do</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">prev</span><span style="color: #0000FF;">,</span><span style="color: #000000;">word</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">word</span><span style="color: #0000FF;">,</span><span style="color: #000000;">word</span><span style="color: #0000FF;">&</span><span style="color: #000000;">prev</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
-    end for
+     <span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">word</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
-end procedure
+         <span style="color: #7060A8;">cdCanvasLine</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cddbuffer</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">+</span><span style="color: #000000;">dx</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">+</span><span style="color: #000000;">dy</span><span style="color: #0000FF;">)</span>
+         <span style="color: #000000;">x</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">dx</span>   <span style="color: #000000;">y</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">dy</span>
-function redraw_cb(Ihandle /*ih*/, integer /*posx*/, integer /*posy*/)
+         <span style="color: #008080;">if</span> <span style="color: #000000;">word</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]==</span><span style="color: #008000;">'0'</span> <span style="color: #008080;">then</span>
-    cdCanvasActivate(cddbuffer)
+             <span style="color: #0000FF;">{</span><span style="color: #000000;">dx</span><span style="color: #0000FF;">,</span><span style="color: #000000;">dy</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)?{</span><span style="color: #000000;">dy</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">dx</span><span style="color: #0000FF;">}:{-</span><span style="color: #000000;">dy</span><span style="color: #0000FF;">,</span><span style="color: #000000;">dx</span><span style="color: #0000FF;">})</span>
-    cdCanvasClear(cddbuffer)
+         <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
-    drawFibonacci(20, 20, 0, 1, 23)
+     <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
-    cdCanvasFlush(cddbuffer)
+ <span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
-    return IUP_DEFAULT
-end function
+ <span style="color: #008080;">function</span> <span style="color: #000000;">redraw_cb</span><span style="color: #0000FF;">(</span><span style="color: #004080;">Ihandle</span> <span style="color: #000080;font-style:italic;">/*ih*/</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000080;font-style:italic;">/*posx*/</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">/*posy*/</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">cdCanvasActivate</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cddbuffer</span><span style="color: #0000FF;">)</span>
-function map_cb(Ihandle ih)
+     <span style="color: #7060A8;">cdCanvasClear</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cddbuffer</span><span style="color: #0000FF;">)</span>
-    cdcanvas = cdCreateCanvas(CD_IUP, ih)
+     <span style="color: #000000;">drawFibonacci</span><span style="color: #0000FF;">(</span><span style="color: #000000;">20</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">20</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">23</span><span style="color: #0000FF;">)</span>
-    cddbuffer = cdCreateCanvas(CD_DBUFFER, cdcanvas)
+     <span style="color: #7060A8;">cdCanvasFlush</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cddbuffer</span><span style="color: #0000FF;">)</span>
-    cdCanvasSetBackground(cddbuffer, CD_WHITE)
+     <span style="color: #008080;">return</span> <span style="color: #004600;">IUP_DEFAULT</span>
-    cdCanvasSetForeground(cddbuffer, CD_GREEN)
+ <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
-    return IUP_DEFAULT
-end function
+ <span style="color: #008080;">function</span> <span style="color: #000000;">map_cb</span><span style="color: #0000FF;">(</span><span style="color: #004080;">Ihandle</span> <span style="color: #000000;">ih</span><span style="color: #0000FF;">)</span>
+     <span style="color: #000000;">cdcanvas</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">cdCreateCanvas</span><span style="color: #0000FF;">(</span><span style="color: #004600;">CD_IUP</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">ih</span><span style="color: #0000FF;">)</span>
-procedure main()
+     <span style="color: #000000;">cddbuffer</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">cdCreateCanvas</span><span style="color: #0000FF;">(</span><span style="color: #004600;">CD_DBUFFER</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">cdcanvas</span><span style="color: #0000FF;">)</span>
-    IupOpen()
+     <span style="color: #7060A8;">cdCanvasSetBackground</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cddbuffer</span><span style="color: #0000FF;">,</span> <span style="color: #004600;">CD_WHITE</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">cdCanvasSetForeground</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cddbuffer</span><span style="color: #0000FF;">,</span> <span style="color: #004600;">CD_GREEN</span><span style="color: #0000FF;">)</span>
-    canvas = IupCanvas(NULL)
+     <span style="color: #008080;">return</span> <span style="color: #004600;">IUP_DEFAULT</span>
-    IupSetAttribute(canvas, "RASTERSIZE", "620x450")
+ <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
-    IupSetCallback(canvas, "MAP_CB", Icallback("map_cb"))
+ <span style="color: #008080;">procedure</span> <span style="color: #000000;">main</span><span style="color: #0000FF;">()</span>
-    dlg = IupDialog(canvas, "RESIZE=NO")
+     <span style="color: #7060A8;">IupOpen</span><span style="color: #0000FF;">()</span>
-    IupSetAttribute(dlg, "TITLE", "Fibonacci Fractal")
+     <span style="color: #000000;">canvas</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">IupCanvas</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"RASTERSIZE=620x450"</span><span style="color: #0000FF;">)</span>
-    IupSetCallback(canvas, "ACTION", Icallback("redraw_cb"))
+     <span style="color: #7060A8;">IupSetCallbacks</span><span style="color: #0000FF;">(</span><span style="color: #000000;">canvas</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #008000;">"MAP_CB"</span><span style="color: #0000FF;">,</span> <span style="color: #7060A8;">Icallback</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"map_cb"</span><span style="color: #0000FF;">),</span>
+                              <span style="color: #008000;">"ACTION"</span><span style="color: #0000FF;">,</span> <span style="color: #7060A8;">Icallback</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"redraw_cb"</span><span style="color: #0000FF;">)})</span>
-    IupMap(dlg)
+     <span style="color: #000000;">dlg</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">IupDialog</span><span style="color: #0000FF;">(</span><span style="color: #000000;">canvas</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">`RESIZE=NO, TITLE="Fibonacci Fractal"`</span><span style="color: #0000FF;">)</span>
-    IupShowXY(dlg,IUP_CENTER,IUP_CENTER)
+     <span style="color: #7060A8;">IupShow</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dlg</span><span style="color: #0000FF;">)</span>
-    IupMainLoop()
+     <span style="color: #008080;">if</span> <span style="color: #7060A8;">platform</span><span style="color: #0000FF;">()!=</span><span style="color: #004600;">JS</span> <span style="color: #008080;">then</span>
-    IupClose()
+         <span style="color: #7060A8;">IupMainLoop</span><span style="color: #0000FF;">()</span>
-end procedure
+         <span style="color: #7060A8;">IupClose</span><span style="color: #0000FF;">()</span>
+     <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
-main()</lang>
+ <span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
+ <span style="color: #000000;">main</span><span style="color: #0000FF;">()</span>
+<!--</lang>-->
 =={{header|Processing}}==