local function vPath(width, height, depth)
    local dirs = {"forward", "left", "right", "up", "back"}
    local depthTravelled = 1
    local widthTravelled = 1
    local heightTravelled = 1
    local shiftRight = false
    local shiftLeft = false
    local goBack = false
    return function()
        --the turtle has been through every block
        if heightTravelled == height and widthTravelled == width and depthTravelled == depth then
            return nil
        end

        --if either of these flags are true, the turtle is in the middle of shifting columns
        --that means the turtle will turn, then move forward along the depth axis
        --therefore, dt must be incremented by 1
        if shiftRight == true then
            depthTravelled = depthTravelled + 1
            shiftRight = false
            return dirs[3]
        elseif shiftLeft == true then
            depthTravelled = depthTravelled + 1
            shiftLeft = false
            return dirs[2]
        elseif goBack == true then
            depthTravelled = depthTravelled + 1
            goBack = false
            return dirs[5]
        end

        --if the turtle has reached the end of a column
        if depthTravelled == depth then
            --reset dt; the turtle is starting on a new column
            depthTravelled = 1
            --if the turtle has reached the end of a layer
            if widthTravelled == width then
                goBack = true
                --reset the width travelled
                widthTravelled = 1
                --go to the next layer
                heightTravelled = heightTravelled + 1
                return dirs[4]
            end
            --if the turtle is in the middle of a layer, shift columns
            --if width is even, flip turn direction at every even height
            --if wt % 2 == 1, turn right, else turn left
            local flip = (width%2 == 0 and heightTravelled % 2 == 0)
            if (widthTravelled%2 == 0 and flip) or (widthTravelled%2 == 1 and not flip) then
                shiftRight = true
                widthTravelled = widthTravelled + 1
                return dirs[3]
            else
                shiftLeft = true
                widthTravelled = widthTravelled + 1
                return dirs[2]
            end
        end
        depthTravelled = depthTravelled + 1
        return dirs[1]
    end
end