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

Recipe 1: Run the animation "live" by 
drawing each curve as it is created. 
"""
import matplotlib.pyplot as plt
import numpy as np

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

for s in s_values:
    y = f(x, m, s)
    lines[0].set_ydata(y) #update plot data and redraw
    plt.draw()
    plt.pause(0.1)