# -*- coding: utf-8 -*-
"""
logistic_iterator.py

finds values of the logistic map, f[i](x) = ax(1-x), 
for repeated iterations as i becomes large, approximates 
period doubling points, and finds said period points for
a between 2.9 and values close to 4.0

I'm trying to do something like this:
    en.wikipedia.org/wiki/File:LogisticMap_BifurcationDiagram.png

Created on Sun Oct  6 12:48:35 2013
@author: coriander
"""

import numpy as np
import matplotlib.pyplot as plt

def iterated_logistic(a_val, x, n=1000):
    for i in xrange(0, n):
        x = a_val*x*(1-x)
    return x


def logi_loop(a_0=2.95, x_0=0.25):
    x_i = x_0 # for clarity
    for a in np.arange(a_0, 3.98, 0.01): #start, (up to) end, step (rationals),
        x_i = iterated_logistic(a, x_i) 
        print "For a = {:.3f}: x_n = {:.4f}".format(a, x_i)   
        plt.plot(a, x_i)
    plt.show()
    #return x_n

def main():
    logi_loop()
    pass



main()