Conway’s Game of Life

unsorted — cgrand, 19 August 2011 @ 20 h 01 min

APL is famous for having a 1-liner for Conway’s game of life.
Being very efficient at implementing a matrix-based solution of Conway’s game of life should come to no suprise from an array-oriented language.

The way you model data determines your code. Clojure encourages what I call relational-oriented programming. That is modeling with sets, natural identifiers (thanks to composite values) and maps-as-indexes.

If you pick the right representation for the state of the board, you end up with a succinct implementation:

(defn neighbours [[x y]]
  (for [dx [-1 0 1] dy (if (zero? dx) [-1 1] [-1 0 1])] 
    [(+ dx x) (+ dy y)]))

(defn step [cells]
  (set (for [[loc n] (frequencies (mapcat neighbours cells))
             :when (or (= n 3) (and (= n 2) (cells loc)))]
         loc)))

Let’s see how it behaves with the “blinker” configuration:

(def board #{[1 0] [1 1] [1 2]})
; #'user/board
(take 5 (iterate step board))
; (#{[1 0] [1 1] [1 2]} #{[2 1] [1 1] [0 1]} #{[1 0] [1 1] [1 2]} #{[2 1] [1 1] [0 1]} #{[1 0] [1 1] [1 2]})

Great, it oscillates as expected!

From this step can be distilled a generic topology-agnostic life-like automatons stepper factory (phew!) but this is a subject for another post or — shameless plug — a book.

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