Essays/Game of Life

Conway's Game of Life is well known to programmers, mathematicians, and devotees of Scientific American of a certain age.

J programs to implement the Game of Life:

pattern =: _10 {."1 (7) {."1 (_10) {. 7 {. '.O'&i.;._2 (0 : 0)
.O
..O
OOO
)

NB. Game Of Life - one step
lifeprog =: 2 10 $ 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0
life =: (_2 ]\ 1 1 3 3) (lifeprog {~ ([: < (<1 1)&{ , +/@:,));._3 (0)&([ , [ ,~ [ ,. [ ,.~ ])

   NB. Run 4 iterations
   ' *' {~ life^:(<5) pattern
          
          
          
    *     
     *    
   ***    
          
          
          
          

          
          
          
          
   * *    
    **    
    *     
          
          
          

          
          
          
          
     *    
   * *    
    **    
          
          
          

          
          
          
          
    *     
     **   
    **    
          
          
          

          
          
          
          
     *    
      *   
    ***   
          

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Contributed by Henry Rich.