"""
Animate how a Gaussian curve changes as
we change the parameter 's'.

Recipe 3: This is the most advanced version, using a
'FuncAnimation' object from matplotlib. We define a function
'next_frame' which takes the s-value as input and creates
updates the plot for the new frame. This function is 
passed as an argument to the 'FuncAnimation' class to create
the animation. 
"""

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; #the midpoint of the curve (constant)

#create an array of s-values, one for each curve/frame:
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

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=100)
ani.save('movie.mp4', fps=20)
plt.show()