Reducing

      cantor ← { , ⊃ ∘.×/ ⍵ ⍴ ⊂1 0 1 }

Power and Reduce can both express "the outer product of ⍵ copies of 1 0 1".

      3 ⍴ ⊂1 0 1  ⍝ The normal Cantor rule
┌─────┬─────┬─────┐
│1 0 1│1 0 1│1 0 1│
└─────┴─────┴─────┘

      ⊢l ← {⊂1,(⍵⍴0),1}⍤0 ⍳3  ⍝ A list of different rules
┌───┬─────┬───────┐
│1 1│1 0 1│1 0 0 1│
└───┴─────┴───────┘

      , ⊃ ∘.×/ l
1 0 0 1 0 0 0 0 1 0 0 1 1 0 0 1 0 0 0 0 1 0 0 1