"""
Animation recipe 3.
This is the most advanced approach, using the
FuncAnimation tool from matplotlib to create the plot. 
It supports both viewing the plot and creating a movie file
directly, but creating the movie file still 
depends on external software (ImageMagick).
"""

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

def f(x, m, s):
    return (1.0/(np.sqrt(2*np.pi)*s))*np.exp(-0.5*((x-m)/s)**2)

m = 0; s_start = 2; s_stop = 0.2
s_values = np.linspace(s_start,s_stop,30)

x = np.linspace(-3*s_start,3*s_start, 1000)

max_f = f(m,m,s_stop)

plt.axis([x[0],x[-1],0,max_f])
plt.xlabel('x')
plt.ylabel('y')

y = f(x,m,s_start)
lines = plt.plot(x,y) # Initial plot to create the lines object

#function to update the plot, the core of the FuncAnimation approach:
def next_frame(frame):
    y = f(x, m, frame)
    lines[0].set_ydata(y)
    return lines

ani = FuncAnimation(plt.gcf(), next_frame, frames=s_values, interval=50)

ani.save('movie.mp4',fps = 20) #this line may not work unless you have installed additional software
plt.show()