pi.py

#!/usr/bin/python
# -*- coding: utf-8 -*-

"""
Estimation of Pi using the Mandlebrot set

http://en.wikipedia.org/wiki/Mandelbrot_set
http://code.activestate.com/recipes/577584-amazing-estimation-of-pi-using-the-mandlebrot-set/
https://home.comcast.net/%7Edavejanelle/mandel.pdf
"""

def pi(err, abs=abs):
    """Approximation of pi +/- err using the Mandlebrot set"""
    n = 0
    z = c = complex(-0.75, err)
    while abs(z) < 2.0:
        n += 1
        z = z * z + c
    return n * err

if __name__ == '__main__':
    for i in range(1, 8):
        err_bound = 10 ** (-i)
        print(pi(err_bound), 'within', err_bound)