Creates a greyscale image of the Mandelbrot set.

mandelbrot.py

# Modified from http://forthescience.org/blog/2010/07/12/the-mandelbrot-set-in-python/

from PIL import Image

max_iteration = 100
x_center = -1.0
y_center =  0.0
size = 3000

im = Image.new("RGB", (size,size))
for i in xrange(size):
    for j in xrange(size):
        x,y = ( x_center + 4.0*float(i-size/2)/size,
                  y_center + 4.0*float(j-size/2)/size
                )

        a,b = (0.0, 0.0)
        iteration = 0

        while (a**2 + b**2 <= 4.0 and iteration < max_iteration):
            a,b = a**2 - b**2 + x, 2*a*b + y
            iteration += 1
        if iteration == max_iteration:
            color_value = 0
        else:
            color_value = 255 - (iteration*10 % 255)
        im.putpixel( (i,j), (color_value, color_value, color_value))

im.save("mandelbrot.png", "PNG")