This generates a series of images that I turned into a logistic map. (link to gif in comment)

logisticmap.py

import sys
import matplotlib.pyplot as plt
import numpy as np

def f(a, x):
    return a*x*(1 - x)

n = 1000
imgs = 50
for k in np.arange(imgs):
    for j in np.arange(n+1):
        a = j / 250.0
        x = np.arange(n)/(1.0*n)
        for i in range(k):
            x = f(a, x)
            sys.stdout.write("Progress: %d%% - %d%% \r" % (100.0*j/n, 100.0*(k)/imgs))
            sys.stdout.flush()
        plt.plot(np.ones(len(x))*a, x, "b,")
    plt.savefig(("%03d" % (k,))+"_out.png")
    plt.clf()
# https://twitter.com/randompast/status/984569577697882112