# Fibonacci word/fractal

Fibonacci word/fractal
You are encouraged to solve this task according to the task description, using any language you may know.

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

For F_wordm start with F_wordCharn=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.

## AutoHotkey

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

Library: GDIP
Also see the Gdip examples.
#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

## C

Writes an EPS file that has the 26th fractal. This is probably cheating.

#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;
}

## 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" );
}

## D

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

Translation of: Python
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");
}

It prints the level 25 word as the Python entry.

## Elixir

Translation of: Ruby
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)

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
Seq.unfold(fun (f1, f2) -> Some(f1, (f2, f2+f1))) ("1", "0")
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)
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>
<html><body><svg height="
100%%" width="100%%" viewbox="0 0 %d %d">
<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
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

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 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. ' 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 Next ' we need to set screen in order to create image buffer in memory Screen 21 scr_ptr = ScreenPtr() If (scr_ptr = 0) Then 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 ## Go Library: Go Graphics Translation of: Kotlin 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") } 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. 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 ## J Plotting the fractal as a parametric equation, this looks reasonably nice: require 'plot' plot }:+/\ 0,*/\(^~ 0j_1 0j1$~ #)'0'=_1{::F_Words 20

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

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

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
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);
});
}
}

## JavaScript

Translation of: PARI/GP
File:FiboWFractal2.png
Output FiboWFractal2.png
File:FiboWFractal1.png
Output FiboWFractal1.png

// 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)
}

Executing:

<!-- FiboWFractal2.html -->
<html>
<head>
<title>Fibonacci word/fractal</title>
<script src="FiboWFractal.js"></script>
</head>
<body onload="pFibowFractal(31,2,'canvid','red')">
<h3>Fibonacci word/fractal: n=31, len=2</h3>
<canvas id="canvid" width="850" height="1150" style="border: 2px inset;"></canvas>
</body>
</html>

<!-- FiboWFractal1.html -->
<html>
<head>
<title>Fibonacci word/fractal</title>
<script src="FiboWFractal.js"></script>
</head>
<body onload="pFibowFractal(31,1,'canvid','navy')">
<h3>Fibonacci word/fractal: n=31, len=1</h3>
<canvas id="canvid" width="1400" height="1030" style="border: 2px inset;"></canvas>
</body>
</html>

Output:
Page with FiboWFractal2.png
Page with FiboWFractal1.png

## Julia

Works with: Julia version 0.6
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()

## Kotlin

Translation of: Java
// 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
}
}
}

## 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
; 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

## Lua

Needs LÖVE 2D Engine

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

## Mathematica / Wolfram Language

(*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}] = [email protected][Pi/2];
step["0", {_?OddQ}] = [email protected][-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]]]]];

## 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.

Output Fibofrac1.png
Output Fibofrac2.png
Translation of: C++
Works with: PARI/GP version 2.7.4 and above

\\ 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
}

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 Fibofrac3.png
Output Fibofrac4.png
Translation of: Java
Works with: PARI/GP version 2.7.4 and above

\\ 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
}

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.

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;

## Perl 6

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

## Phix

Output matches Fig 1 (at the top of the page)

Library: pGUI
--
-- demo\rosetta\FibonacciFractal.exw
--
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*/, integer /*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

function esc_close(Ihandle /*ih*/, atom c)
if c=K_ESC then return IUP_CLOSE end if
return IUP_CONTINUE
end function

procedure main()
IupOpen()

canvas = IupCanvas(NULL)
IupSetAttribute(canvas, "RASTERSIZE", "620x450")
IupSetCallback(canvas, "MAP_CB", Icallback("map_cb"))

dlg = IupDialog(canvas, "RESIZE=NO")
IupSetAttribute(dlg, "TITLE", "Fibonacci Fractal")
IupSetCallback(dlg, "K_ANY", Icallback("esc_close"))
IupSetCallback(canvas, "ACTION", Icallback("redraw_cb"))

IupMap(dlg)
IupShowXY(dlg,IUP_CENTER,IUP_CENTER)
IupMainLoop()
IupClose()
end procedure

main()

## Python

Translation of: Unicon

Note that for Python 3, functools.lru_cache could be used instead of the memoize decorator below.

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()

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

## Fibonacci word/fractal 2/20/17 aev
## 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)
}
## Plot Fibonacci word/fractal:
## 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
}

## Executing:
pfibofractal(23, 1000, 1000, 1, "navy")
pfibofractal(25, 2300, 1000, 1, "red")

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

## 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.

The output of this REXX program is written to the screen as well as a disk file.

/*REXX program generates a  Fibonacci word,  then displays the  fractal curve.          */
parse arg ord . /*obtain optional arguments from the CL*/
if ord=='' then ord=23 /*Not specified? Then use the default*/
s=FibWord(ord) /*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='│'; if dx\==0 then c="─"; if n==1 then c='┌' /*is this the first plot?*/
@.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; z=substr(s,n,1) /*save old x,y; assign plot character.*/
if z==1 then iterate /*Is Z equal to unity? Then ignore it.*/
ox=dx; oy=dy; dx=0; dy=0 /*save DX,DY as the old versions. */
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 to maxX; _=_ || @.c.r; end /*c*/; _=strip(_, 'T') /*build a line.*/
if _=='' then iterate /*if the line is blank, then ignore it.*/
say _; call lineout "FIBFRACT.OUT", _ /*display the line; also write to disk.*/
end /*r*/ /* [↑] only display the non-blank rows*/
exit /*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; k1=k-1; k2=k-2 /*generate the Kth " " */
!.k=!.k1 || !.k2 /*construct the next " " */
end /*k*/ /* [↑] generate a " " */
return !.x /*return the Xth " " */

output   when using the input:   17

(The output is shown 1/2 size.)

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

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

## 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
(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)))))

## 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
area[[x,y]] = "S"
word.each_char.with_index(1) do |c,n|
area[[x+dx, y+dy]] = dx.zero? ? "|" : "-"
x, y = x+2*dx, y+2*dy
area[[x, 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| area[[x,y]]}.join
end
end

word = fibonacci_word(16)
print_fractal(word)
Output:
+-+-+   +-+-+       +-+-+   +-+-+               +-+-+   +-+-+       +-+-+   +-+-+                                   +-+-+   +-+-+       +-+-+   +-+-+               +-+-+   +-+-+       +-+-+   +-+-+
|   |   |   |       |   |   |   |               |   |   |   |       |   |   |   |                                   |   |   |   |       |   |   |   |               |   |   |   |       |   |   |   |
+   +-+-+   +       +   +-+-+   +               +   +-+-+   +       +   +-+-+   +                                   +   +-+-+   +       +   +-+-+   +               +   +-+-+   +       +   +-+-+   +
|           |       |           |               |           |       |           |                                   |           |       |           |               |           |       |           |
+-+       +-+       +-+       +-+               +-+       +-+       +-+       +-+                                   +-+       +-+       +-+       +-+               +-+       +-+       +-+       +-+
|       |           |       |                   |       |           |       |                                       |       |           |       |                   |       |           |       |
+       +   +-+-+   +       +                   +       +   +-+-+   +       +                                       +       +   +-+-+   +       +                   +       +   +-+-+   +       +
|       |   |   |   |       |                   |       |   |   |   |       |                                       |       |   |   |   |       |                   |       |   |   |   |       |
+-+       +-+-+   +-+-+       +-+               +-+       +-+-+   +-+-+       +-+                                   +-+       +-+-+   +-+-+       +-+               +-+       +-+-+   +-+-+       +-+
|                               |               |                               |                                   |                               |               |                               |
+   +-+-+               +-+-+   +               +   +-+-+               +-+-+   +                                   +   +-+-+               +-+-+   +               +   +-+-+               +-+-+   +
|   |   |               |   |   |               |   |   |               |   |   |                                   |   |   |               |   |   |               |   |   |               |   |   |
+-+-+   +               +   +-+-+               +-+-+   +               +   +-+-+                                   +-+-+   +               +   +-+-+               +-+-+   +               +   +-+-+
|               |                               |               |                                                   |               |                               |               |
+-+               +-+       +-+-+   +-+-+       +-+               +-+                                               +-+               +-+       +-+-+   +-+-+       +-+               +-+
|                   |       |   |   |   |       |                   |                                               |                   |       |   |   |   |       |                   |
+                   +       +   +-+-+   +       +                   +                                               +                   +       +   +-+-+   +       +                   +
|                   |       |           |       |                   |                                               |                   |       |           |       |                   |
+-+               +-+       +-+       +-+       +-+               +-+                                               +-+               +-+       +-+       +-+       +-+               +-+
|               |           |       |           |               |                                                   |               |           |       |           |               |
+-+-+   +               +   +-+-+   +       +   +-+-+   +               +   +-+-+                                   +-+-+   +               +   +-+-+   +       +   +-+-+   +               +   +-+-+
|   |   |               |   |   |   |       |   |   |   |               |   |   |                                   |   |   |               |   |   |   |       |   |   |   |               |   |   |
+   +-+-+               +-+-+   +-+-+       +-+-+   +-+-+               +-+-+   +                                   +   +-+-+               +-+-+   +-+-+       +-+-+   +-+-+               +-+-+   +
|                                                                               |                                   |                                                                               |
+-+       +-+-+   +-+-+                                   +-+-+   +-+-+       +-+                                   +-+       +-+-+   +-+-+                                   +-+-+   +-+-+       +-+
|       |   |   |   |                                   |   |   |   |       |                                       |       |   |   |   |                                   |   |   |   |       |
+       +   +-+-+   +                                   +   +-+-+   +       +                                       +       +   +-+-+   +                                   +   +-+-+   +       +
|       |           |                                   |           |       |                                       |       |           |                                   |           |       |
+-+       +-+       +-+                                   +-+       +-+       +-+                                   +-+       +-+       +-+                                   +-+       +-+       +-+
|           |       |                                       |       |           |                                   |           |       |                                       |       |           |
+   +-+-+   +       +                                       +       +   +-+-+   +                                   +   +-+-+   +       +                                       +       +   +-+-+   +
|   |   |   |       |                                       |       |   |   |   |                                   |   |   |   |       |                                       |       |   |   |   |
+-+-+   +-+-+       +-+                                   +-+       +-+-+   +-+-+                                   +-+-+   +-+-+       +-+                                   +-+       +-+-+   +-+-+
|                                   |                                                                               |                                   |
+-+-+   +                                   +   +-+-+               +-+-+   +-+-+       +-+-+   +-+-+               +-+-+   +                                   +   +-+-+
|   |   |                                   |   |   |               |   |   |   |       |   |   |   |               |   |   |                                   |   |   |
+   +-+-+                                   +-+-+   +               +   +-+-+   +       +   +-+-+   +               +   +-+-+                                   +-+-+   +
|                                                   |               |           |       |           |               |                                                   |
+-+                                               +-+               +-+       +-+       +-+       +-+               +-+                                               +-+
|                                               |                   |       |           |       |                   |                                               |
+                                               +                   +       +   +-+-+   +       +                   +                                               +
|                                               |                   |       |   |   |   |       |                   |                                               |
+-+                                               +-+               +-+       +-+-+   +-+-+       +-+               +-+                                               +-+
|                                                   |               |                               |               |                                                   |
+   +-+-+                                   +-+-+   +               +   +-+-+               +-+-+   +               +   +-+-+                                   +-+-+   +
|   |   |                                   |   |   |               |   |   |               |   |   |               |   |   |                                   |   |   |
+-+-+   +                                   +   +-+-+               +-+-+   +               +   +-+-+               +-+-+   +                                   +   +-+-+
|                                   |                               |               |                               |                                   |
+-+-+   +-+-+       +-+                                   +-+       +-+-+   +-+-+       +-+               +-+       +-+-+   +-+-+       +-+                                   +-+       +-+-+   +-+-+
|   |   |   |       |                                       |       |   |   |   |       |                   |       |   |   |   |       |                                       |       |   |   |   |
+   +-+-+   +       +                                       +       +   +-+-+   +       +                   +       +   +-+-+   +       +                                       +       +   +-+-+   +
|           |       |                                       |       |           |       |                   |       |           |       |                                       |       |           |
+-+       +-+       +-+                                   +-+       +-+       +-+       +-+               +-+       +-+       +-+       +-+                                   +-+       +-+       +-+
|       |           |                                   |           |       |           |               |           |       |           |                                   |           |       |
+       +   +-+-+   +                                   +   +-+-+   +       +   +-+-+   +               +   +-+-+   +       +   +-+-+   +                                   +   +-+-+   +       +
|       |   |   |   |                                   |   |   |   |       |   |   |   |               |   |   |   |       |   |   |   |                                   |   |   |   |       |
+-+       +-+-+   +-+-+                                   +-+-+   +-+-+       +-+-+   +-+-+               +-+-+   +-+-+       +-+-+   +-+-+                                   +-+-+   +-+-+       +-+
|                                                                                                                                                                                                   |
+   +-+-+               +-+-+   +-+-+       +-+-+   +-+-+                                                                                   +-+-+   +-+-+       +-+-+   +-+-+               +-+-+   +
|   |   |               |   |   |   |       |   |   |   |                                                                                   |   |   |   |       |   |   |   |               |   |   |
+-+-+   +               +   +-+-+   +       +   +-+-+   +                                                                                   +   +-+-+   +       +   +-+-+   +               +   +-+-+
|               |           |       |           |                                                                                   |           |       |           |               |
+-+               +-+       +-+       +-+       +-+                                                                                   +-+       +-+       +-+       +-+               +-+
|                   |       |           |       |                                                                                       |       |           |       |                   |
+                   +       +   +-+-+   +       +                                                                                       +       +   +-+-+   +       +                   +
|                   |       |   |   |   |       |                                                                                       |       |   |   |   |       |                   |
+-+               +-+       +-+-+   +-+-+       +-+                                                                                   +-+       +-+-+   +-+-+       +-+               +-+
|               |                               |                                                                                   |                               |               |
+-+-+   +               +   +-+-+               +-+-+   +                                                                                   +   +-+-+               +-+-+   +               +   +-+-+
|   |   |               |   |   |               |   |   |                                                                                   |   |   |               |   |   |               |   |   |
+   +-+-+               +-+-+   +               +   +-+-+                                                                                   +-+-+   +               +   +-+-+               +-+-+   +
|                               |               |                                                                                                   |               |                               |
+-+       +-+-+   +-+-+       +-+               +-+                                                                                               +-+               +-+       +-+-+   +-+-+       +-+
|       |   |   |   |       |                   |                                                                                               |                   |       |   |   |   |       |
+       +   +-+-+   +       +                   +                                                                                               +                   +       +   +-+-+   +       +
|       |           |       |                   |                                                                                               |                   |       |           |       |
+-+       +-+       +-+       +-+               +-+                                                                                               +-+               +-+       +-+       +-+       +-+
|           |       |           |               |                                                                                                   |               |           |       |           |
+   +-+-+   +       +   +-+-+   +               +   +-+-+                                                                                   +-+-+   +               +   +-+-+   +       +   +-+-+   +
|   |   |   |       |   |   |   |               |   |   |                                                                                   |   |   |               |   |   |   |       |   |   |   |
+-+-+   +-+-+       +-+-+   +-+-+               +-+-+   +                                                                                   +   +-+-+               +-+-+   +-+-+       +-+-+   +-+-+
|                                                                                   |
+-+-+   +-+-+       +-+                                                                                   +-+       +-+-+   +-+-+
|   |   |   |       |                                                                                       |       |   |   |   |
+   +-+-+   +       +                                                                                       +       +   +-+-+   +
|           |       |                                                                                       |       |           |
+-+       +-+       +-+                                                                                   +-+       +-+       +-+
|       |           |                                                                                   |           |       |
+       +   +-+-+   +                                                                                   +   +-+-+   +       +
|       |   |   |   |                                                                                   |   |   |   |       |
+-+       +-+-+   +-+-+                                                                                   +-+-+   +-+-+       +-+
|                                                                                                                               |
+   +-+-+                                                                                                               +-+-+   +
|   |   |                                                                                                               |   |   |
+-+-+   +                                                                                                               +   +-+-+
|                                                                                                               |
+-+                                                                                                               +-+
|                                                                                                                   |
+                                                                                                                   +
|                                                                                                                   |
+-+                                                                                                               +-+
|                                                                                                               |
+-+-+   +                                                                                                               +   +-+-+
|   |   |                                                                                                               |   |   |
+   +-+-+                                                                                                               +-+-+   +
|                                                                                                                               |
+-+       +-+-+   +-+-+                                                                                   +-+-+   +-+-+       +-+
|       |   |   |   |                                                                                   |   |   |   |       |
+       +   +-+-+   +                                                                                   +   +-+-+   +       +
|       |           |                                                                                   |           |       |
+-+       +-+       +-+                                                                                   +-+       +-+       +-+
|           |       |                                                                                       |       |           |
+   +-+-+   +       +                                                                                       +       +   +-+-+   +
|   |   |   |       |                                                                                       |       |   |   |   |
+-+-+   +-+-+       +-+                                                                                   +-+       +-+-+   +-+-+
|                                                                                   |
+-+-+   +-+-+       +-+-+   +-+-+               +-+-+   +                                                                                   +   +-+-+               +-+-+   +-+-+       +-+-+   +-+-+
|   |   |   |       |   |   |   |               |   |   |                                                                                   |   |   |               |   |   |   |       |   |   |   |
+   +-+-+   +       +   +-+-+   +               +   +-+-+                                                                                   +-+-+   +               +   +-+-+   +       +   +-+-+   +
|           |       |           |               |                                                                                                   |               |           |       |           |
+-+       +-+       +-+       +-+               +-+                                                                                               +-+               +-+       +-+       +-+       +-+
|       |           |       |                   |                                                                                               |                   |       |           |       |
+       +   +-+-+   +       +                   +                                                                                               +                   +       +   +-+-+   +       +
|       |   |   |   |       |                   |                                                                                               |                   |       |   |   |   |       |
+-+       +-+-+   +-+-+       +-+               +-+                                                                                               +-+               +-+       +-+-+   +-+-+       +-+
|                               |               |                                                                                                   |               |                               |
+   +-+-+               +-+-+   +               +   +-+-+                                                                                   +-+-+   +               +   +-+-+               +-+-+   +
|   |   |               |   |   |               |   |   |                                                                                   |   |   |               |   |   |               |   |   |
+-+-+   +               +   +-+-+               +-+-+   +                                                                                   +   +-+-+               +-+-+   +               +   +-+-+
|               |                               |                                                                                   |                               |               |
+-+               +-+       +-+-+   +-+-+       +-+                                                                                   +-+       +-+-+   +-+-+       +-+               +-+
|                   |       |   |   |   |       |                                                                                       |       |   |   |   |       |                   |
+                   +       +   +-+-+   +       +                                                                                       +       +   +-+-+   +       +                   +
|                   |       |           |       |                                                                                       |       |           |       |                   |
+-+               +-+       +-+       +-+       +-+                                                                                   +-+       +-+       +-+       +-+               +-+
|               |           |       |           |                                                                                   |           |       |           |               |
+-+-+   +               +   +-+-+   +       +   +-+-+   +                                                                                   +   +-+-+   +       +   +-+-+   +               +   +-+-+
|   |   |               |   |   |   |       |   |   |   |                                                                                   |   |   |   |       |   |   |   |               |   |   |
S   +-+-+               +-+-+   +-+-+       +-+-+   +-+-+                                                                                   +-+-+   +-+-+       +-+-+   +-+-+               +-+-+   +-+

## 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.

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")

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.

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');

## Sidef

Translation of: Perl 6
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)
Output:
$sidef fib_word_fractal.sf 12 3 ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⠀⡤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠃⠘⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣇⣸⠉⣇⣀⠀⣀⣸⠉⣇⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠼⠀⠧⢤⠀⡤⠼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢲⠀⡖⠚⠀⠓⢲⠀⡖⢲⠀⠀ ⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⡁⠀⠀⠀⢈⣉⡁⢈⣉⡇ ⠀⠀⠀⡤⠼⠀⠧⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠼⠀⠧⢤⠀⡤⠼⠀⠧⠼⠀⠀ ⠀⠀⠀⠓⢲⠀⡖⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢲⠀⡖⠚⠀⠓⢲⠀⠀⠀⠀⠀ ⠉⢹⣀⡏⠉⠀⠉⢹⣀⡏⢹⣀⡀⢀⣀⡏⢹⣀⡏⠉⠀⠉⢹⣀⡏⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠤⡄⢠⠤⠇⠸⠤⡄⢠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡖⠚⠀⠓⠚⠀⠀⠀⠀⠓⠚⠀⠓⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⢹⣀⡏⢹⣀⡀⢀⣀⡏⢹⣀⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠇⠸⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⡆⢰⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ## Tcl Library: Tk package require Tk # OK, this stripped down version doesn't work for n<2… proc fibword {n} { set fw {1 0} while {[llength$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]

## zkl

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

Translation of: D
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"));