import numpy as np
import scipy.integrate as integr
import matplotlib.pyplot as plt

A = [0]
B = [1]
for k in range(99):
    B.append(4*np.sqrt(B[k])/(2+A[k]))
    A.append(1+A[k]/2)

plt.figure('suite A')
plt.plot(A)
plt.show()

plt.figure('suite B')
plt.plot(B)
plt.show()

X = np.arange(0,1,0.01)
for n in range(19) :
    Y = [B[n]*x**A[n] for x in X]
    plt.plot(X,Y)
    plt.pause(1)