# -*- coding: utf-8 -*-
import matplotlib
#matplotlib.use('TkAgg')

from pylab import plot, show, text,  ion, ioff, draw, xlabel, ylabel,xlim,ylim
import numpy as np
from time import sleep

def fun(x,r):
    return r*x*(1-x)
    

    
t = 1
iter = 20 
u = np.zeros(iter)
u[0] = 0.29
r = 3.1#2.5
u_s = np.arange(0,1,0.01)
ion()
plot(u_s, fun(u_s,r))
plot(u_s, fun(fun(u_s,r),r))
plot(u_s, fun(fun(fun(u_s,r),r),r))
xlabel('N_t')
ylabel('N_{t+1}')
text(0.8,0.4, 'N_{t+1}=f(N_t)')
plot([0,1],[0,1])
u[1] = fun(u[0],r)
plot([u[0],u[0]],[0,u[1]],'r')
plot([u[0],u[1]],[u[1],u[1]],'r')


for t in range(iter-1):
    u[t+1]=fun(u[t],r)
    plot([u[t],u[t]],[u[t],u[t+1]],'r')
    plot([u[t],u[t+1]],[u[t+1],u[t+1]],'r')
    u[t]=u[t+1]
    draw

ioff()
xlim([0,1])
ylim([0,1])
show()