File:Folded-towel map attractor.png

```python import numpy as np

def dynamical_system(x, y, z, a, b, n_iter):

   x_values = np.empty(n_iter)
   y_values = np.empty(n_iter)
   z_values = np.empty(n_iter)

   x_values[0] = x
   y_values[0] = y
   z_values[0] = z

   for i in range(1, n_iter):
       x, y, z = x_values[i], y_values[i], z_values[i] = a * x * (1 - x) - 0.05 * (y + 0.35) * (1 - 2 * z), 0.1 * ((y + 0.35) * (1 + 2 * z) - 1) * (1 - 1.9 * x), 3.78 * z * (1 - z) + b * y

   return x_values, y_values, z_values

1. Parameters

a = 3.8 b = 0.2 x_init = 0.085 y_init = -0.121 z_init = 0.075 n_iter = 1000000

x, y, z = dynamical_system(x_init, y_init, z_init, a, b, n_iter)

from sklearn.preprocessing import normalize x = normalize([x])[0] y = normalize([y])[0] z = normalize([z])[0]

import matplotlib.pyplot as plt fig, ax = plt.subplots(figsize=(30, 30)) init_time = 1000 ax.scatter(y[init_time:], x[init_time:], color='k', s=0.005) ax.axis("off") plt.show()