# -*- 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
"""

from scipy import arange

def logistic(a, x):
    value = a*x*(1-x)
    return value

def iterated_logistic(a_val, x_n, out_len=1, n=1000):
    ''' Iterates the logistic map
        Returns a list of varying length with the last iterates of f(x)
    '''
    out_list = [0]*out_len
    for i in xrange(0, n):
        x_n = logistic(a_val, x_n)
    xn1 = logistic(a_val, x_n)    
    if xn1 != x_n:
        # return a list of twice the previous size
    else:
        # return current sized list
    return out_list


def logi_loop(a_0=2.95, x_0=0.25):
    array_list = []
    for a in arange(a_0, 3.98, 0.01): #start, (up to) end, step (rationals),
        x_array = iterated_logistic(a, x_0, out_len=out_length)
        #lists of lists, oh my!
        array_list.append(x_list) #the list of the lists of x values for large n
                
        
        # change to print list:
        print "For a = {:.3f}: x_n = {:.4f}".format(a, x_i)   
    #return x_n

def main():
    logi_loop()
    pass



main()