import matplotlib.pyplot as plt
import numpy as np
#
#  Sample the unit interval.
#
t = np.linspace ( 0.0, 1.0, 101 )
#
#  Plot the function.
#
plt.plot ( t, np.cos ( t ), 'r', linewidth = 2 )
#
#  Plot the dotted line y = x.
#
plt.plot ( t, t, "g:", linewidth = 2 )
#   
#  Plot the iterates x, cos(x), cos(cos(x)), ...
#
x = 1.0
y = np.cos ( x )
for _ in range ( 20 ):
  fy = np.cos ( y )
  plt.plot ( [x, y], [y,  y], 'b', linewidth = 1 )
  plt.plot ( [y, y], [y, fy], 'b', linewidth = 1 )
  x = y
  y = fy
#
#  Give x and y axis the same scale.
#
plt.axis ( 'equal' )
#
#  Save a copy of the figure.
#
plt.savefig ( 'cos_cobweb.png' )
#
#  Show the figure.
#
plt.show ( )