# Plot the Feigenbaum tree
from __future__ import division
from scipy import *
import pylab

def compute_x(r, N=1000):
    x0 = 0.2
    x = [x0]
    for i in range(N):
        x.append(r*x[-1]*(1-x[-1]))
    return x

R = []
X = []
for r in linspace(0, 4, 1000):
    x = compute_x(r)
    X += x[-100:]
    R += [r] * 100

pylab.plot(R, X, ',')
pylab.axis([0, 4, 0.2, 0.8])
pylab.title('Feigenbaum tree')

pylab.show()