```python import numpy as np import matplotlib.pyplot as plt

def logistic_map(x, r):

   return r * x * (1 - x)

def function_iter(f, n, x, **kwargs):

   for _ in range(n):
       x = f(x, **kwargs)
   return x

r = 3.45 highest_exponent = 8 fig, axes = plt.subplots(nrows=highest_exponent, ncols=1, figsize=(40, 5 * highest_exponent))

x_values = np.linspace(0, 1, 10000) y_values = x_values last_n_iter = 0

for n in range(highest_exponent):

   ax = axes[n]
   n_iter = 2**n
   y_values = function_iter(logistic_map, n_iter - last_n_iter, y_values, r=r)
   last_n_iter = n_iter

   ax.plot(x_values, y_values, label=f'iteration = {2**n}', color='blue')
   ax.plot(x_values, x_values, linewidth=0.5, color='green')
   ax.hlines(0.5, 0, 1, linewidth=0.3, alpha=0.8, linestyle='--', color='black')
   ax.legend()

fig.suptitle(f'Iterates of the Logistic map with r = {r}',y=1.0) plt.tight_layout()

plt.savefig(f'logistic_iterates_{r}.svg') plt.show()