⍝ Conway's Game of Life — toroidal one-liner
⍝
⍝ Roger Hui formulation (without leading ⊃, since our inner-product
⍝ already produces a clean 2D board from a heterogeneous strand):
⍝   life ← {1 ⍵ ∨.∧ 3 4 = +/ +/ ¯1 0 1 ∘.⊖ ¯1 0 1 ⌽¨ ⊂⍵}
⍝
⍝ Read right-to-left:
⍝   ⊂⍵                : enclose the board (so it's a single scalar item)
⍝   ¯1 0 1 ⌽¨ ⊂⍵      : produce 3 horizontally-shifted copies
⍝   ¯1 0 1 ∘.⊖ …      : outer-product with vertical shifts → 3×3 = 9 shifts
⍝   +/ +/ …           : sum the 9 boards element-wise → neighbor-count + self
⍝   3 4 = …           : leading-axis-extended boolean — count is 3 (born) or 4 (survive)
⍝   1 ⍵ ∨.∧ …         : "alive next" iff (count=3) or (alive AND count=4)
⍝
⍝ Rules in plain language:
⍝   - dead cell + 3 live neighbors → born
⍝   - live cell + 2 or 3 live neighbors → survives
⍝   - all else → dies
⍝
⍝ Toroidal: edges wrap (rotate is cyclic).

life ← {1 ⍵ ∨.∧ 3 4 = +/ +/ ¯1 0 1 ∘.⊖ ¯1 0 1 ⌽¨ ⊂⍵}