```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 = 3.56994567 alpha = 2.502907875 highest_exponent = 8 fig, ax = plt.subplots(figsize=(30, 10))

x_values = np.linspace(0, 1, 100000) y_values = x_values last_n_iter = 0

for n in range(highest_exponent):

   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(0.5+(x_values-0.5)*(-alpha)**(n), 0.5+(y_values-0.5)*(-alpha)**(n), label=f'iteration = {2**n}', 
           alpha=0.1, color='black', linewidth=4)

ax.hlines(0.5, 0, 1, linewidth=0.3, alpha=0.8, linestyle='--', color='black')

1. ax.legend(

l_x = 5 ax.set_xlim(0.5-l_x, 0.5+l_x) ax.set_ylim(-6, 4)

fig.suptitle(f'Up to {2**(highest_exponent-1)} iterates of the Logistic map with r = {r}, each iterate scaled up',y=1.0) plt.tight_layout() plt.savefig(f"./logistic_scaling_limit_{r}.svg") plt.show()