```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_min, r_max = 3.56994567, 4 delta = 4.6692 frames_per_delta = 1 total_deltas = 1 frames = frames_per_delta * total_deltas scaling_factor = delta**(1/frames_per_delta) rs = r_max + (r_min - r_max) / (scaling_factor ** np.array(range(frames)))

1. rs = np.flip(rs)

for r in rs:

   highest_exponent = 8
   fig, ax = plt.subplots(figsize=(30, 6))

   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(x_values, y_values, label=f'iteration = {2**n}', alpha=0.2, color='blue')

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

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