Associating

      cantor  { , ((∘.×  1 0 1)  ) 1 }
      cantor 3
1 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1

Here's a Cantor set dfn. Notice that we only have to ravel once at the very end.

      (cantor 3)    , 1 0 1 ∘.× 1 0 1 ∘.× 1 0 1
1

But ∘.× is associative! Let's do these outer products starting at the other side:

      cantor  { , 1 0 1 (∘.×  ) 1 }
      cantor 3
1 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1