Devils Staircase

cantor.py

import numpy as np
from matplotlib import pyplot as plt
from matplotlib import animation

fig = plt.figure()
ax = plt.axes(xlim=(0, 1), ylim=(0, 1))
line, = ax.plot([], [], lw=2)

def init():
    line.set_data([], [])
    return line,

# C_n in the Cantor set definition
def c(n):
	if n == 0:
		return [(0,1)]
	else:
		h = c(n-1)
		k = []
		for i in h:
			k.append((i[0]/3, i[1]/3))
			k.append((i[0]/3 + 2/3, i[1]/3 + 2/3)) 
		return k

def complement(n):
	h = c(n)
	h = sorted(h, key = lambda x: x[1])
	k = []
	for i in range(len(h) - 1):
		k.append((h[i][1], h[i+1][0]))
	return k

def k(n):
	h = []
	for i in range(0,n+1):
		for l in complement(i):
			if (l,i-1) not in h:
				h.append(l)
	return sorted(set(h), key = lambda x : x[0])

def line_between(x1, x2, y1, y2, x):
	m = (y2-y1)/(x2-x1)
	b = (x1*y1-x2*y1)/(x2-x1)
	return ((y2-y1)/(x2-x1))*x + (x1*y2-x2*y1)/(x1-x2)

def f(x, n):
	intervals = k(n)
	if x >= 0 and x < intervals[0][0]:	
		return line_between(0, intervals[0][0], 0, 1/2**(n), x)
	if x <= 1 and x > intervals[-1][1]:
		return line_between(intervals[-1][1], 1, (len(intervals))/(2**(n)), 1, x)
	for i in range(len(intervals)):
		if x >= intervals[i][0] and x <= intervals[i][1]:
			return (i+1)/2**(n)
		elif x < intervals[i][0]:
			if intervals[i-1][1] < x:
				return min(1,line_between(round(intervals[i-1][1],5), round(intervals[i][0],5), ((i)/2**(n)), ((i+1)/(2**(n))), x))
		
def connectpoints(x,y,p1,p2):
    x1, x2 = x[p1], x[p2]
    y1, y2 = y[p1], y[p2]
    plt.plot([x1,x2],[y1,y2],'k-')	

def animate(n):
    print(n)
    x = np.linspace(0, 1, 100)
    h = k(n)
    y = [f(i, n+1) for i in x]
    line.set_data(x, y)
    return line,
anim = animation.FuncAnimation(fig, animate, init_func=init,
                               frames=10, interval=200, blit=True)

'''
# In case you just want to plot the function itself.
x = np.linspace(0, 1, 100)
y = [f(i,4) for i in x]
plt.plot(x,y)
plt.show()
'''

# Saves the animation as a .gif. Used imagemagick since I'm on a linux distribution.
anim.save('cantor.gif', fps=1, writer='imagemagick')