periodic doubling https://pbs.twimg.com/media/BYKrHfpCEAABToE.png:large

periodic doubling.py

#! /usr/bin/python3.3
#-*- coding:utf-8 -*-

import matplotlib.pyplot as plt
import numpy as np
import random
from timeit import Timer
import time

def recur(n, x, func):
  y = x
  for _ in [0]*n:
    if not -100000 <= y <= 100000: return y
    y = func(y)
  return y

def recur_list(n, x, func, initp=1):
  y = initp
  for i in range(n):
    y = func(y)
    yield y

# y = μx(1-x)
# 0 < x < 1
# 各μを一つ決め、適当なxをfunctionに対してiterateさせる
# iterateの最初100回程度は切り捨て、残りをプロットする

def quadratic(mu, x):
  return mu * x * (1 - x)

def fix_mu(mu, func):
  def run(x):
    return func(mu, x)
  return run

def main():
  mu = np.arange(1.0, 5.0, 0.005)
  #x = np.arange(0.0, 1.01, 0.01)
  x = 0.483281

  for m in np.nditer(mu):
    q = fix_mu(m, quadratic)

    start_point = recur(100, x, q)
  #  print(x,m,start_point)
    for p in recur_list(10, x, q, initp=start_point):
      if not 0 <= p <= 1: break
      plt.plot(m, p, 'b,')

  plt.xlabel('mu')
  plt.ylabel('y(100-1000 times)')
  plt.show()

if __name__ == "__main__":
  main()