Animation

You can use animation class of matplotlib to show animations.

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

After downloading the code, please uncomment the line %matplotlib notebook to see animations.

%matplotlib inline
#%matplotlib notebook

FuncAnimation

It is often helpful to visualize the data while they are computed, rather than after all computations are done.
For that, you can define a function to draw each frame, and pass the function to FuncAnimation.

def pendulum(i, clear=True, dt=0.05):
    """swinging pendulum. i:frame number"""
    # clear previous plot
    if clear:
        plt.cla()
    # swinging pendulum
    l = 1  # length
    th = np.sin(np.pi*i*dt)  # angle, 2 sec period
    x = np.sin(th)
    y = -np.cos(th)
    # draw a new plot
    pl = plt.plot([0, x], [0, y], 'b')
    plt.axis('square')
    plt.xlim(-1.2*l, 1.2*l)
    plt.ylim(-1.2*l, 1.2*l)
    return pl   # for saving

fig = plt.figure()
anim = animation.FuncAnimation(fig, pendulum, frames=40, interval=50)

ArtistAnimation

You can alternatively save all frames in an array and animate at once.

fig = plt.figure()
frames = []  # prepare frames
for i in range(40):
    art = pendulum(i, False)
    # append to the frame
    frames.append(art)
anim = animation.ArtistAnimation(fig, frames, interval=50)

You can save the movie in a motion gif file.

anim.save("pend.gif", writer='pillow')

Here is the saved file pend.gif: