MySQL Functional Index on a Varchar column with multi decimal sequence

Question

So I have a table where we store a sequence value of what we call a "tree". Sort of looks like this

1
1.1
1.1.1
1.1.2
2
2.1
2.2
3
3.1
3.1.1
3.1.1.1
3.1.1.2
3.1.1.3
etc
etc
etc

Our application searches this tree, rebuilds the tree. Performs operations on it. What I am asking is if it would make sense to make a functional index on this column? If so, what would be ideal? Each number within the sequence? Cast it to number from the string? Any thoughts or idea would be much appreciated.