Fractal Picture With Newton-Raphson

1. # -*- coding: utf-8 -*-
2. '''
3. calculate the root of f=z**3-1 and plot fractal picture
4. with  Newton-Raphson method
5. '''
6. import matplotlib.pyplot as plt
7. import time
8. start=time.time()
9. X1,X2,X3,Y1,Y2,Y3=[],[],[],[],[],[]
10. a=1.732  #np.sqrt(3)
11. z=-1-1j
12. #Newton-Raphson
13. for i in range(0,2000):
14.     z=z+0.001-z.imag*1j-1j
15.     for j in range(0,2000):
16.         z=z+0.001j
17.         r=z
18.         for k in range(0,15):
19.             r2=r-(r**3-1)/(3*r*r)
20.             r=r2
21.         if abs(r-1)<0.0001:
22.             X1[len(X1):]=[z.real]
23.             Y1[len(Y1):]=[z.imag]
24.         elif abs(r+1/2-a/2*1j)<0.0001:
25.              X2[len(X2):]=[z.real]
26.              Y2[len(Y2):]=[z.imag]
27.         elif abs(r+1/2+a/2*1j)<0.0001:
28.              X3[len(X3):]=[z.real]
29.              Y3[len(Y3):]=[z.imag]
30. plt.figure('frctal')
31. plt.plot(X1,Y1,'r.',X2,Y2,'b.',X3,Y3,'g.')
32. plt.show()
33. stop=time.time()
34. print("time=",stop-start)