The source for this post is online at 2013-11-18-life.rkt.
I find Conway’s Game of Life to be a fascinating idea. I decided to try to make a very short and efficient implementation today in Racket.
The Game of Life involves an infinite two-dimensional grid where each grid cell just contains a boolean that is interpreted as whether the cell is "alive". There are very simple rules to determine how one grid configuration changes into the next configuration: a cell is dead unless in the previous state it has three living neighbors or was alive and had two living neighbors. A particular game is interesting if has an interesting seed. For instance, this is the Gosper glider gun:
(let-there-be-life (string-append "........................O..........." "......................O.O..........." "............OO......OO............OO" "...........O...O....OO............OO" "OO........O.....O...OO.............." "OO........O...O.OO....O.O..........." "..........O.....O.......O..........." "...........O...O...................." "............OO......................"))
The key to implementing the Game of Life is an efficient representation of the grid, which I call the "dish" vector. I chose to use a byte array stored in column major order:
(define (make-dishv rs cs) (make-bytes (* rs cs))) (define-inline (dishv-set! dv rs i j ?) (unsafe-bytes-set! dv (unsafe-fx+ i (unsafe-fx* rs j)) (if ? 1 0))) (define-inline (dishv-ref dv rs i j) (unsafe-fx= 1 (unsafe-bytes-ref dv (unsafe-fx+ i (unsafe-fx* rs j)))))
Once I have this framework, I represent the entire dish as two dish vectors plus the size of the grid. The reason to have two vectors is to limit allocation by constantly using the same two arrays, but you need at least two because you read one as you write the other. The parser for the string representation is pretty boring:
(struct dish (rows cols cur nxt) #:mutable) (define (string->dish s) (define rows (string-split s)) (define rs (* 2 (length rows))) (define cs (* 1 (apply max (map string-length rows)))) (define cur (make-dishv rs cs)) (define nxt (make-dishv rs cs)) (for ([i (in-naturals)] [r (in-list rows)]) (for ([j (in-naturals)] [c (in-string r)]) (dishv-set! cur rs i j (char=? #\O c)))) (dish rs cs cur nxt))
The next interesting thing is a way to figure out how many living neighbors a particular cell has. I made a highly optimized version, so it’s pretty ugly, but the basic premise is to sum up all the neighbors, while avoiding going off the screen or considering the cell itself:
(define-syntax-rule (unsafe-between min x max) (and (unsafe-fx<= min x) (unsafe-fx< x max))) (define-inline (neighbors gv rs cs i j) (let ([cnt 0]) (for ([di (in-range -1 2)]) (let ([ni (unsafe-fx+ di i)]) (when (unsafe-between 0 ni rs) (for ([dj (in-range -1 2)]) (unless (and (unsafe-fx= di 0) (unsafe-fx= dj 0)) (let ([nj (unsafe-fx+ dj j)]) (when (and (unsafe-between 0 nj cs) (dishv-ref gv rs ni nj)) (set! cnt (unsafe-fx+ 1 cnt))))))))) cnt))
After you can figure out how many neighbors there are, the actual transition is dirt simple. The only interesting thing is that I use the same structure to ensure that I don’t do any allocation.
(define (tick d) (match-define (dish rs cs cur nxt) d) (for* ([i (in-range rs)] [j (in-range cs)]) (define alive? (dishv-ref cur rs i j)) (define ns (neighbors cur rs cs i j)) (define new-alive? (or (and alive? (or (unsafe-fx= ns 2) (unsafe-fx= ns 3))) (and (not alive?) (unsafe-fx= ns 3)))) (dishv-set! nxt rs i j new-alive?)) (set-dish-cur! d nxt) (set-dish-nxt! d cur) d)
This code is a bit ugly because of all the "unsafe" stuff, but it is very fast, especially compared to the original version. I used this code to benchmark the Gosper gun to ten thousand generations:
(define (let-there-be-life s) (define seed (string->dish s)) (collect-garbage) (collect-garbage) (time (for ([i (in-range 10000)]) (tick seed))))
The original version was 1800 milliseconds. Once I optimized the dish vector code, I shaved off 200 milliseconds. The real speed came from optimizing neighbors, which dropped it down to 500 milliseconds.
However, the Game is mainly exciting when you get to watch it. So I wrote a small visualizer too:
(define (draw d) (match-define (dish rs cs cur _) d) (define SCALE 10) (define BOX (square SCALE "solid" "black")) (for*/fold ([img (empty-scene (* SCALE cs) (* SCALE rs))]) ([i (in-range rs)] [j (in-range cs)]) (if (dishv-ref cur rs i j) (place-image BOX (+ (/ SCALE 2) 0.5 (* j SCALE)) (+ (/ SCALE 2) 0.5 (* i SCALE)) img) img))) (define (let-there-be-life s) (big-bang (string->dish s) [on-tick tick] [on-draw draw]))
It was actually pretty important for the visualizer to be done this way, so that only live cells caused allocation and new images to be constructed. I originally wrote it as a fairly naive version were every cell contributed, but that ran incredibly slowly.
But first let’s remember what we learned today!
The Game of Life is cool and can be implemented in less than a hundred lines of efficient Racket code.
Through judicious use of unsafe operations and inlining, you can drastically improve your Racket code’s performance.
If you’d like to run this exact code at home, you should put it in this order:
Or just download the raw version.