Fibonacci word/fractal: Difference between revisions

{{task|Fractals}}

<langsyntaxhighlight AutoHotkeylang="autohotkey">#NoEnv

ExitApp</langsyntaxhighlight>

<langsyntaxhighlight lang="c">#include <stdio.h>

}</langsyntaxhighlight>

<langsyntaxhighlight lang="cpp">

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

}</langsyntaxhighlight>

<langsyntaxhighlight lang="elixir">defmodule Fibonacci do

Fibonacci.word_fractal(16)</langsyntaxhighlight>

<li>Rather than using the "usual" Fibonacci catamorphismen <langsyntaxhighlight lang="fsharp">Seq.unfold(fun (f1, f2) -> Some(f1, (f2, f2+f1))) ("1", "0")</langsyntaxhighlight> we use the morphism &sigma;: 0 &rarr; 01, 1 &rarr; 0, starting with a single 1, described in the referenced PDF in the task description.</li>

<langsyntaxhighlight lang="fsharp">let sigma s = seq {

0</langsyntaxhighlight>

<langsyntaxhighlight FreeBASIClang="freebasic">' version 23-06-2015

Loop</langsyntaxhighlight>

<langsyntaxhighlight lang="unicon">global width, height

end</langsyntaxhighlight>

<langsyntaxhighlight Jlang="j">require 'plot'

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

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

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,sum shift aof 0 ontofollowed the front ofby the list ofrunning products andof computethat the running sumlist. (Of course, this would translate to a rather simple loop, also, once you see the pattern.)

<langsyntaxhighlight lang="java">import java.awt.*;

}</langsyntaxhighlight>

<langsyntaxhighlight lang="javascript">

</langsyntaxhighlight>

<langsyntaxhighlight lang="html">

</langsyntaxhighlight>

<langsyntaxhighlight Logolang="logo">; Return the low 1-bits of :n

fibonacci.word.fractal 377</langsyntaxhighlight>

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

Graphics[Line[FoldList[Plus, {0, 0}, dirs]]]]];</langsyntaxhighlight>

<langsyntaxhighlight lang="parigp">

</langsyntaxhighlight>

<langsyntaxhighlight lang="parigp">

</langsyntaxhighlight>

<langsyntaxhighlight lang="perl">use strict;

my $im = new GD::Image->new($size,$size);

=={{header|Perl=Using 6}}Tk===

}</langsyntaxhighlight>

TheIf outputthe order of thisthe REXX programgraph is writtennegative, to&nbsp; the screengraph asisn't welldisplayed asto athe diskterminal filescreen.

s=FibWord(ord)parse arg order . /*obtain theoptional arguments orderfrom the of Fibonacci word.CL*/

tell= order>=0 y=0; /*Negative order? maxY=0;Then don't dy=1; @display.0.0=.; yp=0*/

s= FibWord( abs(order) ) do n=1 for length(s); x=x+dx; y=y+dy /*advanceobtain the plot fororder the nextof point.Fibonacci word.*/

c y='│' 0; if dx\= maxY= 0; then c dy="─" 1; if n==1 then c='┌' /*is@.0.0= this.; the first plot?*/ yp= 0

ifmaxX= @max(xp-1maxX,yp x)\==b; then if @maxY= max(xpmaxY,yp-1 y)\==b then call @ xp,yp,'┐'/*set the maximums /*fix─upfor adisplaying cornerplot.*/

if @(xp-1,yp)\==b then if @(xp,yp+1)\==b then call @ xp,yp, c= '┘│' /* " " " /*glyph (character) used for the plot. */

if @(xp+1,yp)dx\==b0 then ifc= "─" @(xp,yp+1)\==b then call @ xp,yp,'└' /* " " " /*if x+dx isn't zero, use this char.*/

if @(xp+1,yp)\n==b1 then if then @(xp,yp-1)\=c=b '┌' then call @ xp,yp,'┌' /* " " " /*is this the first part to be graphed?*/

xp=@.x;.y= c yp=y; z=substr(s,n,1) /*save old x,y; /*assign plota plotting character. for curve*/

ox= dx; oy= dy; dx=0; dy=0 /*save DX,DY as the old versions. */

ddx=-n//2 0; if d= dy= 0 then d=1 /*determinedefine DX,DY " " new " the sign for the chirality.*/

if oy\d==0 -n//2; then dx=-sign(oy)*d if d==0 then d= 1 /*Going north|south? Go /*determine the sign east|westfor the chirality.*/

if oxoy\==0 then dydx= -sign(oxoy) * d /*Going "north│south? Go east|west? " south|north */

do r=maxY to 0 by -1; _= /*show single row at a time, top first.*/

do c=0 tofor maxX+1; _= _ || @.c.r; end /*c*/;add a plot character _=strip(_, 'T'glyph) /*build ato line.*/

if _=='' thenend /*c*/ iterate /*if the[↑] line isconstruct blank,a thenline ignorechar itby char. */

say _;= strip(_, 'T') call lineout "FIBFRACT.OUT", _ /*displayconstruct thea line; alsoof writethe to diskgraph. */

end if _=='' /*r*/ then iterate /*Is the line blank? Then ignore it. /* [↑] only display the non-blank rows*/

exit if tell then say _ /*stickDisplay athe forkline into it,the terminal 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 1 /*obtain the order of Fibonacci word. */

do k=3 to x; k1=k-1; k2=k-2 /*generate the Kth " " */

!.k=!.k1 || !.k2 k1= k-1; k2= k - 2 /*constructcalculate the next K-1 & K-2 " " shortcut.*/

return !.x /*return the Xth " " */</langsyntaxhighlight>

'''{{out|output''' |text=&nbsp; when using the input of: &nbsp; &nbsp; <tt> 17 </tt>}}

<br><br>(The output is shown ¹/₂₈ size.)

<pre style="font-size:5013%">

<langsyntaxhighlight lang="ruby">def fibonacci_word(n)

print_fractal(word)</langsyntaxhighlight>

<langsyntaxhighlight lang="scala">

{{trans|Perl 6Raku}}

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

braille_graphics(world)</langsyntaxhighlight>

<langsyntaxhighlight lang="tcl">package require Tk

drawFW .c [fibword 23]</langsyntaxhighlight>

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

img.write(File("foo.ppm","wb"));</langsyntaxhighlight>