/
chaos_Newton.py
44 lines (32 loc) · 1011 Bytes
/
chaos_Newton.py
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import numpy as np
import matplotlib.image as mpimg
def f(z):
return z**4 -1
def f_(z):
return 4*z**3
def iter_apply(funct, deriv, start, n):
res = start
for i in range(n):
if deriv(res) == 0:
return None
res = res - funct(res)/deriv(res)
return res
def color_for(comp_num):
nbs = [1, -1, 1j, -1j]
colors = [(0,0,1), (0,1,0),(1,0,0), (1,1,1)]
if comp_num is None:
return (0,0,0)
for i, c in enumerate(nbs):
if abs(c-comp_num) < 10**-3:
return colors[i]
return (0,0,0)
def Newton(nb_pixels, radius=1):
image = np.zeros((nb_pixels, nb_pixels, 3))
for i,x in enumerate(np.linspace(-radius, radius, nb_pixels)):
for j,y in enumerate(np.linspace(-radius, radius, nb_pixels)):
val = iter_apply(f, f_, complex(x,y), 100)
image[nb_pixels-1-i,j] = color_for(val)
return image
if __name__ == "__main__":
img = Newton(512, radius=1)
mpimg.imsave('tes.png', img)