Python: Butterfly effect graph 3D

import numpy as np
import matplotlib.pyplot as plt
from matplotlib.animation import FuncAnimation

# Constants
sigma = 10.0
rho = 28.0
beta = 8.0 / 3.0

# Time parameters
dt = 0.01
num_steps = 10000

# Initial conditions
x0, y0, z0 = 0.0, 1.0, 1.05

# Arrays to store trajectories
x = np.empty(num_steps + 1)
y = np.empty(num_steps + 1)
z = np.empty(num_steps + 1)
x[0], y[0], z[0] = x0, y0, z0

# Lorenz system equations
def lorenz(x, y, z, sigma, rho, beta):
    dx = sigma * (y - x)
    dy = x * (rho - z) - y
    dz = x * y - beta * z
    return dx, dy, dz

# Integrate the Lorenz equations
for i in range(num_steps):
    dx, dy, dz = lorenz(x[i], y[i], z[i], sigma, rho, beta)
    x[i + 1] = x[i] + dx * dt
    y[i + 1] = y[i] + dy * dt
    z[i + 1] = z[i] + dz * dt

# Animation setup
fig = plt.figure(figsize=(10, 7))
ax = fig.add_subplot(111, projection='3d')
ax.set_xlim(-20, 20)
ax.set_ylim(-30, 30)
ax.set_zlim(0, 50)
line, = ax.plot([], [], [], lw=2)
plt.title('Lorenz Attractor')

def init():
    line.set_data(np.array([]), np.array([]))
    line.set_3d_properties(np.array([]))
    return line,

def update(frame):
    line.set_data(x[:frame], y[:frame])
    line.set_3d_properties(z[:frame])
    return line,

ani = FuncAnimation(fig, update, frames=num_steps, init_func=init, blit=True, interval=1)
plt.show()