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'''
Region of a complex plane ranging from -1 to +1 in both real
and imaginary axes is rpresented using a 2 dimensional matrix
having X x Y elements.For X and Y equal to 200, the stepsize
in the complex plane is 2.0/200 = 0.01.
The nature of the pattern depends very much on the value of c.
'''
from pylab import *
X = 200
Y = 200
rlim = 1.0
ilim = 1.0
rscale = 2*rlim / X
iscale = 2*ilim / Y
MAXIT = 100
MAXABS = 2.0
c = 0.02 - 0.8j # The constant in equation z**2 + c
m = zeros([X,Y],dtype=uint8) # A two dimensional array
def numit(x,y): # number of iterations to diverge
z = complex(x,y)
for k in range(MAXIT):
if abs(z) <= MAXABS:
z = z**2 + c
else:
return k # diverged after k trials
return MAXIT # did not diverge,
for x in range(X):
for y in range(Y):
re = rscale * x - rlim # complex number represented
im = iscale * y - ilim # by the (x,y) coordinate
m[x][y] = numit(re,im) # get the color for (x,y)
imshow(m) # Colored plot using the two dimensional matrix
show()
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