Here's a rough draft that has tons of room for improvement:
#lang racket
(define glider
(string->number "#x\
010000\
001000\
111000\
000000\
000000\
000000\
"))
(define (life s)
(define (c s n)
(if (= -1 n)
0
(+ (if (bitwise-bit-set? 3080 (arithmetic-shift s (* -4 n)))
(expt 16 n)
0)
(c (modulo s (expt 16 n)) (sub1 n)))))
(c (* s #x111000181000111/10000000)
36))
;; helper functions: run (step) repeatedly to watch
(define current glider)
(define (show s)
(define str1 (format "~x" s))
(define str (string-append (make-string (- 6 (modulo (string-length
str1) 6)) #\0) str1))
(for ([i (in-range 0 (string-length str) 6)])
(displayln (substring str i (+ i 6)))))
(define (step)
(set! current (life current))
(show current))
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