Fixed point iteration and plotting in Python

def fixedpoint(f,x):
    while x != f(x):
        yield x
        x = f(x)
    yield x

Usage: fixedpoint(g,some_starting_value).

Vertical and horizontal bars depend on plotting library. Specify which one you use.

Your function looks fine. I am not familiar with vlines and hlines. I used your store arg to get the points, and plot them outside the function (it is generally better to separate problems like this).

I used only the plot function from matplotlib.pyplot, and the show function to display the graph.

from matplotlib import pyplot as plt
import numpy as np

def fixpt(f, x, epsilon=1.0E-4, N=500, store=False):
    y = f(x)
    n = 0
    if store: Values = [(x, y)]
    while abs(y-x) >= epsilon and n < N:
        x = f(x)
        n += 1
        y = f(x)
        if store: Values.append((x, y))
    if store:
        return y, Values
    else:
        if n >= N:
            return "No fixed point for given start value"
        else: 
            return x, n, y

# define f
def f(x):
    return 0.2*x*x

# find fixed point
res, points = fixpt(f, 3, store = True)

# create mesh for plots
xx = np.arange(0, 6, 0.1)

#plot function and identity
plt.plot(xx, f(xx), 'b')
plt.plot(xx, xx, 'r')

# plot lines
for x, y in points:
    plt.plot([x, x], [x, y], 'g')
    plt.plot([x, y], [y, y], 'g')

# show result
plt.show()

Here is how I thought it through :

from pylab import *

def f(x):
  return 8*x/(1 + 2*x)

def cobweb(x0, n, ax):
  xs = [x0]
  ys = [0]
  for i in range(1,n):
    if i % 2 == 0:
      xs.append(ys[-1])
      ys.append(ys[-1])
    else:
      xs.append(xs[-1])
      ys.append(f(xs[-1]))
  ax.plot(xs, ys, 'k--', lw=2.0)

x = linspace(0, 4, 100)

fig = figure()
ax  = fig.add_subplot(111)

ax.plot(x, x,    'k', lw=2.0)
ax.plot(x, f(x), 'r', lw=2.0)
cobweb(0.5, 50, ax)

ax.set_xlabel(r'$x$')
ax.set_ylabel(r'$f(x)$')

grid()
show()