File:Fibonacci word fractal, order 18.svg

Drawn in python.

```python from itertools import count, islice, groupby from math import floor, sqrt import matplotlib.pyplot as plt def sturm_word(ratio):

 xs = count(1)
 ys = map(lambda x : x * ratio, xs)
 fw = islice(groupby(map(floor, ys)), 1, None)
 return map(lambda x : 2 - len(list(x[1])), fw)

1. If the word is 1, then draw a line forward.
2. If the word is 0, then first draw a line forward

 # if the symbol 0 is in an even position then turn left, else turn right

def fib_line(fib_word, origin=(0, 0), length=1, angle=0):

 angle_dict = {
     0: (1, 0),
     90: (0, 1),
     180: (-1, 0),
     270: (0, -1)
 }
 is_even = True
 x0, y0 = origin
 current_angle=angle
 while True:
   dx, dy = angle_dict[current_angle]
   x1, y1 = x0 + dx, y0 + dy
   yield (x0, y0, x1, y1)
   if next(fib_word) == 0:
     if is_even:
       current_angle += 90
     else:
       current_angle -= 90
   current_angle %= 360
   x0, y0 = x1, y1
   is_even = not is_even

golden_ratio = (sqrt(5) - 1)/2 fib_word = sturm_word(golden_ratio)

def fibs(n):

 f0, f1 = 0, 1
 for _ in range(n):
   f0, f1 = f1, f0+f1
 return f0

xfirst, yfirst, xlast, ylast = 0, 0, 0, 0 golden_ratio = (sqrt(5) - 1)/2 fib_word = sturm_word(golden_ratio) i = 0 fib_i = fibs(i) limit_i = 18 plt.figure (figsize= (20, 32)) for line_i, (x0, y0, x1, y1) in enumerate(fib_line(fib_word, origin=(0, 0), length=0.1, angle=0)):

   plt.plot([x0, x1], [y0, y1], 'k')
   if line_i > fib_i - 2:
     i, fib_i = i+1, fibs(i+1)
     xfirst, yfirst, xlast, ylast = xlast, ylast, x1, y1
     color = 'blue' if i % 2 == 0 else 'green'
     r = plt.Rectangle((xfirst, yfirst), xlast-xfirst, ylast-yfirst, fc=color, ec='black', alpha=0.3)
     plt.gca().add_patch(r)
     if i > limit_i:
       break

plt.gca().set_aspect('equal') plt.axis('off') plt.savefig('fib_word.svg', bbox_inches=0, transparent=True)