plot-fibonacci.py

# http://junilyd.github.io/blog/2014/08/13/fibonacci-mystery-pythonified/

"""
Fibonacci squares and spirals by the use of artist, by Jacob Møller
http://matplotlib.org/examples/shapes_and_collections/artist_reference.html
"""
import matplotlib.pyplot as plt; plt.rcdefaults()
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.path as mpath
import matplotlib.lines as mlines
import matplotlib.patches as mpatches
from matplotlib.collections import PatchCollection

def fib(n):
	if n < 2:
		return n
	else:
		return fib(n-1) + fib(n-2)
		
def label(xy, text, j):
	y = xy[1] - 0.025 # shift y-value to center label
	plt.text(xy[0], y, text, ha="center", family='sans-serif', size=j)
	
fig, ax = plt.subplots(); patches = []

xy = np.array([0, 0]); c = xy; i=1; t = np.array([270, 0])
for j in range(1,7+4):
	t += 90;
	if i == 5: i=1;
	if i==1:
		xy = xy + [ -fib(j-2)    , fib(j-1) ];     c = c + [ -fib(j-2), 0         ];
	if i==2:
		xy = xy + [ -fib(j)      , -fib(j-2)];     c = c + [0         , -fib(j-2) ];
	elif i==3:
		xy = xy + [ 0            , -fib(j)  ];     c = c + [ fib(j-2) , 0         ];
	elif i==4:
		xy = xy + [ fib(j-1)     , 0        ];     c = c + [ 0        , fib(j-2)  ];
		
	# Add a wedge
	rect = mpatches.Wedge([c[0],c[1]], fib(j), t[0] , t[1]   , ec="none")
	patches.append(rect)
	
	# Add a rectangle
	rect = mpatches.Rectangle([xy[0],xy[1]], fib(j), fib(j), ec="none"); patches.append(rect); i+=1;
	label( xy+[0.5*fib(j),  0.5*fib(j)], "%s"%fib(j), j*2)
	
colors = np.linspace(0, 0, 0)
collection = PatchCollection(patches, cmap=plt.cm.hsv, alpha=0.9); collection.set_array(np.array(colors)); ax.add_collection(collection)
plt.axis('equal'); plt.axis('off'); plt.grid('off');plt.show();