Spiral: Solution

def spiral_by_nested_boxes(matrix_size):
    """Spiral coordinates of a matrix of `matrix_size` size.

    This version works by drawing TRBL boxes until the entire matrix
    has been printed.
    """

    # Loop and create square nested boxes

    for box_number in range(0, matrix_size // 2):
        top = left = box_number
        bottom = right = matrix_size - box_number - 1

        for x in range(left, right):  # draw top line going >
            print((x, top))

        for y in range(top, bottom):  # draw right line going \/
            print((right, y))

        for x in range(right, left, -1):  # draw bottom line going <
            print((x, bottom))

        for y in range(bottom, top, -1):  # draw left line going /\
            print((left, y))

    # Odd-width matrices: print center point manually

    if matrix_size % 2 != 0:
        print((matrix_size // 2, matrix_size // 2))

def spiral_recursion(matrix_size):
    """Spiral matrix of `matrix_size` size.

    This version works by drawing TRBL boxes until the entire matrix
    has been printed. Rather than a loop, it uses recursion.
    """

    def spiral_inner(box_number):

        # By nesting this function, we have access to the enclosing
        # function's vars -- in this case, `matrix_size`. Alternately,
        # we could make this a top-level function & pass `matrix_size`
        # in -- but it is tidy to nest this, since it's not useful
        # outside of the outer function.

        top = left = box_number
        bottom = right = matrix_size - box_number - 1

        # If we're on the last ring, we've reached base case
        if box_number == matrix_size // 2:
            # Base case -- we've reached the innermost box
            if matrix_size % 2 != 0:
                # Print center dot in odd-sized matrices
                print((matrix_size // 2, matrix_size // 2))

            return

        for x in range(left, right):  # draw top line going >
            print((x, top))

        for y in range(top, bottom):  # draw right line going \/
            print((right, y))

        for x in range(right, left, -1):  # draw bottom line going <
            print((x, bottom))

        for y in range(bottom, top, -1):  # draw left line going /\
            print((left, y))

        # Now do the smaller box inside of us
        spiral_inner(box_number + 1)

    spiral_inner(0)

def spiral_by_points(matrix_size):
    """Spiral coordinates of a matrix of n size.

    This version works by looping over all of the points, changing
    directions at the corners.
    """

    min_x = min_y = 0  # Full matrix starts at top left
    max_x = max_y = matrix_size - 1  # ... and can go to bottom right
    curr_x = curr_y = 0  # We begin at top left
    vel_x, vel_y = +1, 0  # ... and are going east

    # Loop over each point, print point then move to the next point

    for i in range(matrix_size ** 2):
        print((curr_x, curr_y))
        curr_x += vel_x
        curr_y += vel_y

        # If going east and at edge, start going down & reduce box \/
        if vel_x == +1 and curr_x == max_x:
            vel_x, vel_y = 0, +1
            min_y += 1

        # If going south and at edge, start going west & reduce box <
        elif vel_y == +1 and curr_y == max_y:
            vel_x, vel_y = -1, 0
            max_x -= 1

        # If going west and at edge, start going up & reduce box /\
        elif vel_x == -1 and curr_x == min_x:
            vel_x, vel_y = 0, -1
            max_y -= 1

        # If going north and at edge, start going east & reduce box >
        elif vel_y == -1 and curr_y == min_y:
            vel_x, vel_y = +1, 0
            min_x += 1