You can do it:
abcdefghijklm...n..o..p..q..r..s..t..u..v..w..x..y..z..z.ab...z..c...z..d...z..e
etc.
i.e., `.` changes direction. Once you get to `z` you can continue appending additional `z`s to keep it going. I quit making the spiral here cos I realized the top comment is also a spiral, although theirs is in the other direction.