Question

Please provide this solution in PYTHON. Thanks in advance.

Plot the Julia set for C=0.285+0.01i

Answer 1

import numpy as np

import matplotlib.pyplot as plt

import matplotlib.cm as cm

# Image width and height; parameters for the plot

im_width, im_height = 500, 500

c = complex(0.285, 0.01)

zabs_max = 10

nit_max = 1000

xmin, xmax = -1.5, 1.5

xwidth = xmax - xmin

ymin, ymax = -1.5, 1.5

yheight = ymax - ymin

julia = np.zeros((im_width, im_height))

for ix in range(im_width):

for iy in range(im_height):

nit = 0

# Map pixel position to a point in the complex plane

z = complex(ix / im_width * xwidth + xmin,

iy / im_height * yheight + ymin)

# Do the iterations

while abs(z) <= zabs_max and nit < nit_max:

z = z**2 + c

nit += 1

shade = 1-np.sqrt(nit / nit_max)

ratio = nit / nit_max

julia[ix,iy] = ratio

fig, ax = plt.subplots()

ax.imshow(julia, interpolation='nearest', cmap=cm.hot)

plt.show()