Some graphical explorations of the Julia sets with python and pyreport
#!/usr/bin/env python
from scipy import *
from pylab import *
#from pylab import imshow
def J(c):
return lambda z : z**2 + c
[x,y] = ogrid[ -1:1:0.002, -1:1:0.002 ]
z = x + y *1j
If we study the divergence of function J under repeated iteration depending on its inital conditions we get a very pretty graph
threshTime = zeros_like(z)
for i in range(40):
z = J(0.285)(z)
threshTime += z*conj(z) > 4
figure(0)
axes([0,0,1,1])
axis('off')
imshow(threshTime)
bone()
show()
We can also do that systematicaly for other values of c:
axes([0,0,1,1])
axis('off')
rcParams.update({'figure.figsize': [10.5,5]})
c_values = (0.285 + 0.013j, 0.45 - 0.1428j, -0.70176 -0.3842j,
-0.835-0.2321j, -0.939 +0.167j, -0.986+0.87j)
for i,c in enumerate(c_values):
threshTime = zeros_like(z)
z = x + y *1j
for n in range(40):
z = J(c)(z)
threshTime += z*conj(z) > 4
subplot(2,3,i+1)
imshow(threshTime)
axis('off')
show()
