绘制peaks函数曲面并且将它绕Z轴旋转。写出编写的程序，并将旋转后的图形进行也复制上。

在Python中，我们可以使用matplotlib库来绘制三维图形，结合numpy库计算peaks函数的值，然后利用mpl_toolkits.mplot3d模块中的Axes3D类进行旋转。下面是一个简单的示例：

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

# Peaks function (also known as Ricker or Mexican hat wavelet)
def peaks(x, y):
    return (1 - x**2 - y**2)**2 * np.exp(-(x**2 + y**2))

# Generate a grid of points
X, Y = np.meshgrid(np.linspace(-5, 5, 100), np.linspace(-5, 5, 100))
Z = peaks(X, Y)

# Create a figure and an axes object for 3D plotting
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')

# Plot the surface and set some properties
surf = ax.plot_surface(X, Y, Z, cmap='viridis', linewidth=0, antialiased=False)

# Rotate the surface around the z-axis
for angle in range(0, 360, 10):  # For each rotation step
    ax.view_init(elev=30, azim=angle)  # Set elevation and azimuth
    plt.draw()  # Update the plot
    plt.pause(.01)  # Pause for a short time to see the rotation

# Save the rotated plot
plt.savefig('rotated_peaks.png')
plt.close()

# Copy the original plot for comparison
ax.view_init(elev=30, azim=0)  # Reset to initial view
plt.title("Original Peaks Function")
surf_original = ax.plot_surface(X, Y, Z, cmap='viridis', label="Original Peaks", alpha=0.7)
ax.legend()
plt.show()