# plot periodic orbits and iterations for the logistic map
#
import numpy as np
import matplotlib.pyplot as plt


# logistic map is f(x) = mu*x*(1-x)  with mu in (0,4)
def logistic(x, mu):
    y = mu * x * (1.0 - x)
    return y


# fill an array with iteration n1 to n2 of the logistic map starting with x0
# and with parameter mu
def fillit(n1, n2, x0, mu):
    x = x0  # initial x value
    z = np.linspace(0.0, 1.0, n2 - n1)  # create an array
    for i in range(0, n1):  # do n1 iterations
        x = logistic(x, mu)

    for i in range(0, n2 - n1):  # fill n2-n1 iterations
        x = logistic(x, mu)
        z[i] = x

    return z  # returning the array


# plot the iterated logistic map for nmu number of mu values
def mkplot(mu_min, nmu):  # nmu is number of mu values to use, mu_min range
    mu_max = 4.0  # maximum mu value
    muarr = np.linspace(mu_min, mu_max, nmu)
    n1 = 100  # specify iteration range
    n2 = 200
    x0 = 0.4  # initial x
    for i in range(0, nmu):
        mu = muarr[i]
        y = fillit(n1, n2, x0, mu)  # get the array of iterations
        x = y * 0.0 + mu  # dummy x value is all mu
        plt.plot(x, y, 'ko', markersize=1)  # k=black, plot small points


plt.figure()
plt.xlabel(r'$\mu$', fontsize=20)
mu_min = 2.9
plt.axis([mu_min, 4.0, 0, 1.0])
# this makes the plot!
mkplot(mu_min, 1000)
plt.show()