'''

mandelbrot.py

Draw a Mandelbrot set

Using "Escape time algorithm" from:

http://en.wikipedia.org/wiki/Mandelbrot_set#Computer_drawings

Thanks to http://www.vallis.org/salon/summary-10.html for some important

ideas for implementation.

'''

import matplotlib.pyplot as plt

import matplotlib.cm as cm

# Subset of the complex plane we are considering

x0, x1 = -2.5, 1

y0, y1 = -1, 1

def initialize_image(x_p, y_p):

image = []

for i in range(y_p):

x_colors = []

for j in range(x_p):

x_colors.append(0)

image.append(x_colors)

return image

def mandelbrot_set():

# Number of divisions along each axis

n = 400

# Maximum iterations

max_iteration=1000

image = initialize_image(n, n)

# Generate a set of equally spaced points in the region

# above

dx = (x1-x0)/(n-1)

dy = (y1-y0)/(n-1)

x_coords = [x0 + i*dx for i in range(n)]

y_coords = [y0 + i*dy for i in range(n)]

for i, x in enumerate(x_coords):

for k, y in enumerate(y_coords):

z1 = complex(0, 0)

iteration = 0

c = complex(x, y)

while (abs(z1) < 2 and iteration < max_iteration):

z1 = z1**2 + c

iteration += 1

image[k][i] = iteration

return image

if __name__ == '__main__':

image = mandelbrot_set()

plt.imshow(image, origin='lower', extent=(x0, x1, y0,y1),

cmap=cm.Greys_r, interpolation='nearest')

plt.show()