Fibonacci word/fractal

Fibonacci word/fractal is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

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

For F_word₃₇ 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

For this task create and display a fractal similar to Fig 1.

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>

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.