spiral.py

from math import sqrt, ceil


def shell(n):
    a = int(ceil(sqrt(n)))
    if a % 2 == 0:
        a += 1
    c = a - 1
    d = c / 2
    return d


def f(n):
    if n == 1:
        return (0, 0)
    d = shell(n)
    a = 2*d + 1
    c = 2*d
    b = n - (a-2)**2
    bm = (b-1) % c + 1
    #print d, b, int((b-1)/c)
    return [
        (d, bm-d),
        (d-bm, d),
        (-d, d-bm),
        (bm-d, -d),
    ][int((b-1)/c)]

for n in range(25):
    print f(n+1)