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

I know, I know. I should have started with the introduction. But doesn’t it introduce itself rather well? You can see for yourself that it’s ultimately concise, expressive and utterly alien to all the mainstream computer languages.