Fractal Picture With Newton-Raphson
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- # -*- coding: utf-8 -*-
- '''
- calculate the root of f=z**3-1 and plot fractal picture
- with Newton-Raphson method
- '''
- import matplotlib.pyplot as plt
- import time
- start=time.time()
- X1,X2,X3,Y1,Y2,Y3=[],[],[],[],[],[]
- a=1.732 #np.sqrt(3)
- z=-1-1j
- #Newton-Raphson
- for i in range(0,2000):
- z=z+0.001-z.imag*1j-1j
- for j in range(0,2000):
- z=z+0.001j
- r=z
- for k in range(0,15):
- r2=r-(r**3-1)/(3*r*r)
- r=r2
- if abs(r-1)<0.0001:
- X1[len(X1):]=[z.real]
- Y1[len(Y1):]=[z.imag]
- elif abs(r+1/2-a/2*1j)<0.0001:
- X2[len(X2):]=[z.real]
- Y2[len(Y2):]=[z.imag]
- elif abs(r+1/2+a/2*1j)<0.0001:
- X3[len(X3):]=[z.real]
- Y3[len(Y3):]=[z.imag]
- plt.figure('frctal')
- plt.plot(X1,Y1,'r.',X2,Y2,'b.',X3,Y3,'g.')
- plt.show()
- stop=time.time()
- print("time=",stop-start)
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