hilbert.py

# $ python3 --version
# Python 3.10.1
# $ python3 hilbert.py 
# [(0, 0), (1, 0), (1, 1), (2, 1), (2, 2), (2, 3), (3, 3), (3, 4), (4, 4), (4, 5), (5, 5), (5, 6), (5, 7), (6, 7), (6, 8), (7, 8)]

import math


def hilbert_iter(n):
    (i, j) = (0, 0)
    size = n * n
    h = 0
    d = 3

    while h < size:
        yield (i, j)
        h += 1
        l = math.floor(0.5 * math.log2(h & -h))
        a = math.floor(h / (4**l)) % 4
        is_odd = bool(l & 1)
        d ^= 3 * (is_odd != (a == 3))
        j += (d - 1) % 2
        i += (d - 2) % 2
        d ^= is_odd != (a == 1)


print(list(hilbert_iter(4)))