Conway’s Game of Life
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.
I couldn’t believe that such a short solution could possibly work, so I copied it into my IDE to play around with it. I verified that a glider worked and that a 3 cell diagonal died off as expected.
Very cool!
Can’t wait for your book to come out.
You make your point with elegance. impressive!
[...] Otherwise here is a beautiful implementation of Conway’s Game of Life by Christophe Grand: [...]
[...] and Rupert decided to look at someone else’s solution in Clojure, to understand how a functional approach using list comprehensions can lead to a very concise [...]
[...] 另外，下面是一个由Christophe Grand实现的生命游戏的Clojure版本： [...]
[...] session se termine par une session de coding pré-enregistrée, montrant l’implémentation du jeu de la vie de Conway. Les résultats intermédiaires sont affichés après chaque fonction développée, ce qui [...]
I put together a screencast of building this solution interactively in Clojure for a presentation: check it out here if you’re interested… http://www.youtube.com/watch?v=lgsAztXDuH0
[...] Christophe’s Game of Life [...]
[...] 另外，下面是一个由Christophe Grand实现的生命游戏的Clojure版本： (defn neighbours [[x y]] (for [dx [-1 0 1] dy (if (zero? dx) [-1 1] [-1 0 1])] [(+ dx x) (+ dy y)])) [...]
I wrote an in-depth explanation of your solution. It should be understandable to non-Clojure programmers and newcomers.
http://programmablelife.blogspot.com/2012/08/conways-game-of-life-in-clojure.html