spiral.py

# Right turn directions
TURN_DIR = {
    'u': 'r',
    'r': 'd',
    'd': 'l',
    'l': 'u',
}

# Right turn coordinate math
TURN_FN = {
    'u': lambda x, y: (x, y + 1),
    'r': lambda x, y: (x + 1, y),
    'd': lambda x, y: (x, y - 1),
    'l': lambda x, y: (x - 1, y),
}


def spiral(steps):
    """
    # `prev` is the previous step's direction
    # `dir is a direction, one of:
    # - 'r' - right
    # - 'l' - left
    # - 'd' - down
    # - 'u' - up
    `pos` is the current coordinate position
    `history` is a set of previously visited positions
    """
    yield (0, 0)
    yield (0, 1)
    pos = (0, 1)
    dir = 'u'
    history = set(("0:0", "0:1"))
    for _ in range(steps):
        right_dir = TURN_DIR[dir]
        # Test the turn to the right
        (rightx, righty) = TURN_FN[right_dir](*pos)
        right_key = f"{rightx}:{righty}"
        if right_key in history:
            # We already visited the node to the right, so continue forward
            pos = TURN_FN[dir](*pos)
            history.add(f"{pos[0]}:{pos[1]}")
        else:
            # Turn right!
            pos = (rightx, righty)
            history.add(right_key)
            dir = right_dir
        yield pos


if __name__ == '__main__':
    for pair in spiral(10):
        print(pair)