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')
# 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()