import numpy as np
import matplotlib.pyplot as plt

## 1) setting up the plotting area
plt.ion()  # interactive is on
fig = plt.figure(1, figsize=(7, 5))
plt.suptitle("A sequence of functions with unbounded norm",
             fontsize=13, c='b')
axes = fig.add_subplot(111, aspect='equal')
axes.set(xlim=(0, 1), ylim=(-.05, .85))


## 2) defining the data to animate
nbOfPoints = 800
N = 70  # number of functions
X = np.linspace(0, 1, nbOfPoints)
cst = 1.15

def F(x, n): return n**cst*x*np.exp(-n*x)

Y_list = []
for n in range(1, N+1):
    Y_list.append(F(X, n))


## 3) plotting the first functions
curve = axes.plot(X, Y_list[1], color='blue', lw=1.15,
                 label='current function')[0]
curveR1 = axes.plot(X, Y_list[1], color='dodgerblue', lw=.75)[0]
curveR1.set_alpha(.7)
curveR0 = axes.plot(X, Y_list[0], color='dodgerblue', lw=.75)[0]
curveR0.set_alpha(.4)
axes.plot(X, F(X, 150), color='red', lw=1.15,
         label=f"function with n = {150}")
axes.legend()
"""
We are setting up three polygonal line objects with some desired 
attributes: curve will be the current curve of the sequence (with
color blue); curveR* will be the old current curve with a lesser 
opacity and a lesser line weight. 

Note the [0] at the end.  This is necessary because the plot command 
returns a list of polygonal line objects.  We need the zeroth
entrance in this list.
"""

## 4) looping for an elementary animation
k = 1
for Y in Y_list[1:]:
    curveR0.set_ydata(curveR1.get_ydata())
    curveR1.set_ydata(curve.get_ydata())
    curve.set_ydata(Y)
    axes.set_title(f"n^{1.15} x exp(-nx)  with index n = {k}")
    fig.show()
    plt.pause(0.2)
    k = k + 1

    
plt.show()