Conway's Game of Life

From Rosetta Code
Task
Conway's Game of Life
You are encouraged to solve this task according to the task description, using any language you may know.

The Game of Life is a   cellular automaton   devised by the British mathematician   John Horton Conway   in 1970.   It is the best-known example of a cellular automaton.

Conway's game of life is described   here:

A cell   C   is represented by a   1   when alive,   or   0   when dead,   in an   m-by-m   (or m×m)   square array of cells.

We calculate   N   - the sum of live cells in C's   eight-location neighbourhood,   then cell   C   is alive or dead in the next generation based on the following table:

   C   N                 new C
   1   0,1             ->  0  # Lonely
   1   4,5,6,7,8       ->  0  # Overcrowded
   1   2,3             ->  1  # Lives
   0   3               ->  1  # It takes three to give birth!
   0   0,1,2,4,5,6,7,8 ->  0  # Barren

Assume cells beyond the boundary are always dead.

The "game" is actually a zero-player game, meaning that its evolution is determined by its initial state, needing no input from human players.   One interacts with the Game of Life by creating an initial configuration and observing how it evolves.


Task

Although you should test your implementation on more complex examples such as the   glider   in a larger universe,   show the action of the blinker   (three adjoining cells in a row all alive),   over three generations, in a 3 by 3 grid.


References


Related task



11l

Translation of: Python
V cellcountx = 6
V cellcounty = 5
V celltable = [(1, 2) = 1,
               (1, 3) = 1,
               (0, 3) = 1]
DefaultDict[(Int, Int), Int] universe
universe[(1, 1)] = 1
universe[(2, 1)] = 1
universe[(3, 1)] = 1
universe[(1, 4)] = 1
universe[(2, 4)] = 1
universe[(3, 4)] = 1

L(i) 4
   print("\nGeneration "i‘:’)
   L(row) 0 .< cellcounty
      print(‘  ’(0 .< cellcountx).map(col -> [‘. ’, ‘O ’][:universe[(@row, col)]]).join(‘’))

   DefaultDict[(Int, Int), Int] nextgeneration
   L(row) 0 .< cellcounty
      L(col) 0 .< cellcountx
         nextgeneration[(row, col)] = celltable.get(
              (universe[(row, col)],
              -universe[(row, col)] + sum(multiloop(row-1..row+1,
                                                    col-1..col+1, (r, c) -> :universe[(r, c)]))
              ), 0)
   universe = nextgeneration

More optimal solution

V cellcountx = 6
V cellcounty = 5
V universe = [[0B] * cellcountx] * cellcounty
universe[1][1] = 1B
universe[2][1] = 1B
universe[3][1] = 1B
universe[1][4] = 1B
universe[2][4] = 1B
universe[3][4] = 1B
V nextgeneration = [[0B] * cellcountx] * cellcounty

L(i) 4
   print("\nGeneration "i‘:’)
   L(row) 0 .< cellcounty
      print(‘  ’, end' ‘’)
      L(col) 0 .< cellcountx
         print(I universe[row][col] {‘O ’} E ‘. ’, end' ‘’)
      print()

   L(row) 0 .< cellcounty
      L(col) 0 .< cellcountx
         V s = 0
         I row > 0
            s = universe[row-1][col]
            I col > 0
               s += universe[row-1][col-1]
            I col < cellcountx-1
               s += universe[row-1][col+1]
         I col > 0
            s += universe[row][col-1]
         I col < cellcountx-1
            s += universe[row][col+1]
         I row < cellcounty-1
            s += universe[row+1][col]
            I col > 0
               s += universe[row+1][col-1]
            I col < cellcountx-1
               s += universe[row+1][col+1]
         nextgeneration[row][col] = I universe[row][col] {s C 2..3} E s == 3
   universe = nextgeneration
Output:
Generation 0:
  . . . . . .
  . O . . O .
  . O . . O .
  . O . . O .
  . . . . . .

Generation 1:
  . . . . . .
  . . . . . .
  O O O O O O
  . . . . . .
  . . . . . .

Generation 2:
  . . . . . .
  . O O O O .
  . O O O O .
  . O O O O .
  . . . . . .

Generation 3:
  . . O O . .
  . O . . O .
  O . . . . O
  . O . . O .
  . . O O . .

6502 Assembly

Works with: [6502asm.com] version 1.2
randfill:   stx $01          ;$200 for indirect
            ldx #$02         ;addressing
            stx $02
randloop:   lda $fe          ;generate random
            and #$01         ;pixels on the
            sta ($01),Y      ;screen
            jsr inc0103
            cmp #$00
            bne randloop
            lda $02
            cmp #$06
            bne randloop


clearmem:   lda #$df         ;set $07df-$0a20
            sta $01          ;to $#00
            lda #$07
            sta $02
clearbyte:  lda #$00
            sta ($01),Y
            jsr inc0103
            cmp #$20
            bne clearbyte
            lda $02
            cmp #$0a
            bne clearbyte


starttick:
copyscreen: lda #$00         ;set up source
            sta $01          ;pointer at
            sta $03          ;$01/$02 and
            lda #$02         ;dest pointer
            sta $02          ;at $03/$04
            lda #$08
            sta $04
            ldy #$00
copybyte:   lda ($01),Y      ;copy pixel to
            sta ($03),Y      ;back buffer
            jsr inc0103      ;increment pointers
            cmp #$00         ;check to see
            bne copybyte     ;if we're at $600
            lda $02          ;if so, we've
            cmp #$06         ;copied the
            bne copybyte     ;entire screen


conway:     lda #$df         ;apply conway rules
            sta $01          ;reset the pointer
            sta $03          ;to $#01df/$#07df
            lda #$01         ;($200 - $21)
            sta $02          ;($800 - $21)
            lda #$07
            sta $04
onecell:    lda #$00         ;process one cell
            ldy #$01         ;upper cell
            clc
            adc ($03),Y
            ldy #$41         ;lower cell
            clc
            adc ($03),Y
chkleft:    tax              ;check to see
            lda $01          ;if we're at the
            and #$1f         ;left edge
            tay
            txa
            cpy #$1f
            beq rightcells
leftcells:  ldy #$00         ;upper-left cell
            clc
            adc ($03),Y
            ldy #$20         ;left cell
            clc
            adc ($03),Y
            ldy #$40         ;lower-left cell
            clc
            adc ($03),Y
chkright:   tax              ;check to see
            lda $01          ;if we're at the
            and #$1f         ;right edge
            tay
            txa
            cpy #$1e
            beq evaluate
rightcells: ldy #$02         ;upper-right cell
            clc
            adc ($03),Y
            ldy #$22         ;right cell
            clc
            adc ($03),Y
            ldy #$42         ;lower-right cell
            clc
            adc ($03),Y
evaluate:   ldx #$01         ;evaluate total
            ldy #$21         ;for current cell
            cmp #$03         ;3 = alive
            beq storex
            ldx #$00
            cmp #$02         ;2 = alive if
            bne storex       ;c = alive
            lda ($03),Y
            and #$01
            tax
storex:     txa              ;store to screen
            sta ($01),Y
            jsr inc0103      ;move to next cell
conwayloop: cmp #$e0         ;if not last cell,
            bne onecell      ;process next cell
            lda $02
            cmp #$05
            bne onecell
            jmp starttick    ;run next tick


inc0103:    lda $01          ;increment $01
            cmp #$ff         ;and $03 as 16-bit
            bne onlyinc01    ;pointers
            inc $02
            inc $04
onlyinc01:  inc $01
            lda $01
            sta $03
            rts

68000 Assembly

I went a little further and created a 40x30 grid, but this implementation is accurate and does have a blinker in it. As always, thanks to Keith of Chibiakumas for the cartridge header and hardware routines. This is the source code for a Sega Genesis game that you can compile with VASM. (It was tested in the Fusion emulator but it should work anywhere.)

Explanation of the implementation:

  • I'm using the Genesis's foreground tilemap to create the graphics.
  • Grid boundaries are handled by using the classic trick of padding all sides with a value that's not used in the "real" grid, and always counts as a dead cell.
  • Every iteration of the main loop does the same thing: check neighbors of each cell in the grid, write the next generation to a buffer, copy that buffer over the original, and display the output. This way, updates don't impact the outcome of the rest of the cells down the line (which would go against the rules of the game, as all cell births/deaths happen simultaneously.)

Explanation of macros:

  • pushRegs = MOVEM.L ___,-(SP)
  • popRegs = MOVEM.L (SP)+,___
  • pushLong = MOVE.L ___,-(SP)
  • popLong = MOVE.L (SP)+,___
include "\SrcALL\68000_Macros.asm"
;Ram Variables
Cursor_X equ $00FF0000		;Ram for Cursor Xpos
Cursor_Y equ $00FF0000+1	;Ram for Cursor Ypos

conwayTilemapRam equ $00FF1000
conwayBackupTilemapRam equ $00FF2000
;Video Ports
VDP_data	EQU	$C00000	; VDP data, R/W word or longword access only
VDP_ctrl	EQU	$C00004	; VDP control, word or longword writes only

;constants
ROWLENGTH equ 40

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; 					Traps
	DC.L	$FFFFFE00		;SP register value
	DC.L	ProgramStart	;Start of Program Code
	DS.L	7,IntReturn		; bus err,addr err,illegal inst,divzero,CHK,TRAPV,priv viol
	DC.L	IntReturn		; TRACE
	DC.L	IntReturn		; Line A (1010) emulator
	DC.L	IntReturn		; Line F (1111) emulator
	DS.L	4,IntReturn		; Reserverd /Coprocessor/Format err/ Uninit Interrupt
	DS.L	8,IntReturn		; Reserved
	DC.L	IntReturn		; spurious interrupt
	DC.L	IntReturn		; IRQ level 1
	DC.L	IntReturn		; IRQ level 2 EXT
	DC.L	IntReturn		; IRQ level 3
	DC.L	IntReturn		; IRQ level 4 Hsync
	DC.L	IntReturn		; IRQ level 5
	DC.L	IntReturn		; IRQ level 6 Vsync
	DC.L	IntReturn		; IRQ level 7 
	DS.L	16,IntReturn	; TRAPs
	DS.L	16,IntReturn	; Misc (FP/MMU)

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;					Header
	DC.B	"SEGA GENESIS    "	;System Name
	DC.B	"(C)CHBI "			;Copyright
 	DC.B	"2019.JAN"			;Date
	DC.B	"ChibiAkumas.com                                 " ; Cart Name
	DC.B	"ChibiAkumas.com                                 " ; Cart Name (Alt)
	DC.B	"GM CHIBI001-00"	;TT NNNNNNNN-RR T=Type (GM=Game) N=game Num  R=Revision
	DC.W	$0000				;16-bit Checksum (Address $000200+)
	DC.B	"J               "	;Control Data (J=3button K=Keyboard 6=6button C=cdrom)
	DC.L	$00000000			;ROM Start
	DC.L	$003FFFFF			;ROM Length
	DC.L	$00FF0000,$00FFFFFF	;RAM start/end (fixed)
	DC.B	"            "		;External RAM Data
	DC.B	"            "		;Modem Data
	DC.B	"                                        " ;MEMO
	DC.B	"JUE             "	;Regions Allowed

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;					Generic Interrupt Handler
IntReturn:
	rte
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;					Program Start
ProgramStart:
	;initialize TMSS (TradeMark Security System)
	move.b ($A10001),D0		;A10001 test the hardware version
	and.b #$0F,D0
	beq	NoTmss				;branch if no TMSS chip
	move.l #'SEGA',($A14000);A14000 disable TMSS 
NoTmss:

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;					Set Up Graphics

	lea VDPSettings,A5		;Initialize Screen Registers
	move.l #VDPSettingsEnd-VDPSettings,D1 ;length of Settings
	
	move.w (VDP_ctrl),D0	;C00004 read VDP status (interrupt acknowledge?)
	move.l #$00008000,d5	;VDP Reg command (%8rvv)
	
NextInitByte:
	move.b (A5)+,D5			;get next video control byte
	move.w D5,(VDP_ctrl)	;C00004 send write register command to VDP
		;   8RVV - R=Reg V=Value
	add.w #$0100,D5			;point to next VDP register
	dbra D1,NextInitByte	;loop for rest of block


;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;					Set up palette and graphics
	
	move.l #$C0000000,d0	;Color 0
	move.l d0,VDP_Ctrl
	MOVE.W #$0A00,VDP_Data		;BLUE
	
	move.l #$C01E0000,d0	;Color 0
	move.l d0,VDP_Ctrl
	MOVE.W #$00EE,VDP_Data		;YELLOW
	
	lea Graphics,a0						;background tiles
	move.w #(GraphicsEnd-Graphics)-1,d1	;data size
	CLR.L D2							;start loading at tile 0 of VRAM
	jsr DefineTiles	
	
	clr.b Cursor_X			;Clear Cursor XY
	clr.b Cursor_Y
	
	;Turn on screen
	move.w	#$8144,(VDP_Ctrl);C00004 reg 1 = 0x44 unblank display
	
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;	
; TESTING AREA

	;load the tilemaps
	LEA Conway_Tilemap,a3
	LEA ConwayTilemapRam,A2
	move.l #(Conway_Backup_Tilemap-Conway_Tilemap),d1
	JSR LDIR
	
	LEA Conway_Backup_Tilemap,a3
	LEA conwayBackupTilemapRam,A2
	move.l #(Conway_Backup_Tilemap-Conway_Tilemap),d1
	JSR LDIR	
	
	CLR.B Cursor_X
	CLR.B Cursor_Y
	;print the tilemap once
	LEA ConwayTilemapRam,A3
	JSR Conway_Print
	
main:
	
	;do the behavior
	jsr Conway_CheckTilemap
	
	;copy the tilemap
	lea conwayBackupTilemapRam,A3
	LEA ConwayTilemapRam,A2
	move.l #(Conway_Backup_Tilemap-Conway_Tilemap),d1
	jsr LDIR
	
	CLR.B Cursor_X
	CLR.B Cursor_Y
	;print the tilemap
	LEA ConwayTilemapRam,A3
	JSR Conway_Print
	
	;repeat
	JMP main

Conway_CheckTilemap:
	
	;since we don't want the partial results of the checks to mess with later ones, we'll copy the changes to a buffer, and then 
	;have that buffer clobber the original. That way, all changes to the ecosystem are effectively atomic.
	
	LEA ConwayTilemapRam,A0
	LEA conwayBackupTilemapRam,A6
	LEA (ROWLENGTH+3,A0),A0	;actual data starts here
	LEA (ROWLENGTH+3,A6),A6	;actual data starts here
.loop:
	MOVE.B (A0),D2
	CMP.B #255,D2
	BEQ .done
	CMP.B #2,D2
	BEQ .overhead
	JSR Conway_CheckNeighbors

	pushLong D0
		JSR popcnt_8
		MOVE.B D0,D3
	popLong D0
	
	;now implement the table here.
	;neighbor bits in D0
	;current state in D2
	;popcnt in D3
	;pointer to where we are in A0
	
	;the only time the current state is relevant to the output, is when popcnt = 2. Otherwise, it's entirely determined by popcnt.
	CMP.B #4,D3
	BCC .DeadCell
	CMP.B #1,D3
	BLS .DeadCell
	CMP.B #3,D3
	BEQ .LiveCell
	;else, must be 2.
	MOVE.B D2,(A6)	;store current value into backup table.
	bra .overhead
.LiveCell:
	MOVE.B #1,(A6)
	BRA .overhead
.DeadCell:	
	MOVE.B #0,(A6)	;store in backup table.
.overhead:
	ADDA.L #1,A0
	ADDA.L #1,A6
	JMP .loop
.done:
	RTS

popcnt_8:
	pushRegs D2-D5
		MOVEQ #8-1,D5
		MOVEQ #0,D3
.loop:
		ROR.B #1,D0
		BCC .overhead
			ADDQ.B #1,D3
.overhead:
		dbra d5,.loop
	MOVE.B D3,D0
	popRegs D2-D5
	RTS

Conway_CheckNeighbors:
	;A0 = pointer to where we are in the tilemap.
	;returns: D0.B = uUrRdDlL
	;u = top left
	;U = top
	;r = top Right
	;R = Right
	;d = bottom right
	;D = bottom
	;l = bottom Left
	;L = Left
	pushRegs D2-D5/A0
	MOVEQ #0,D0
	MOVE.L A0,A1
	MOVE.L A1,A2
	SUBA.L #ROWLENGTH+2,A1		;POINTS ABOVE
	ADDA.L #ROWLENGTH+2,A2		;POINTS BELOW
	
	MOVE.B (A1),D1
	MOVE.B (A2),D2
	
	CMP.B #1,D1
	BNE .noUpper
	BSET #6,D0
	bra .next
.noUpper:
	BCLR #6,D0
.next:
CheckLower:
	CMP.B #1,D2
	BNE .noLower
	BSET #2,D0
	bra .next
.noLower:
	BCLR #2,D0
.next:	

	SUBA.L #1,A0	;left
	SUBA.L #1,A1	;upper-left
	SUBA.L #1,A2	;lower-left
	
	MOVE.B (A1),D1
	MOVE.B (A2),D2
	MOVE.B (A0),D3
CheckUpperLeft:
	CMP.B #1,D1
	BNE .noUpperLeft
	BSET #7,D0
	bra .next
.noUpperLeft:
	BCLR #7,D0
.next:

CheckLowerLeft:
	CMP.B #1,D2
	BNE .noLowerLeft
	BSET #1,D0
	bra .next
.noLowerLeft:
	BCLR #1,D0
.next:	

CheckLeft:
	CMP.B #1,D3
	BNE .noLeft
	BSET #0,D0
	bra .next
.noLeft:
	BCLR #0,D0
.next:	


	addA.L #2,A0
	addA.L #2,A1
	addA.L #2,A2
	
	MOVE.B (A1),D1
	MOVE.B (A2),D2
	MOVE.B (A0),D3
	
CheckUpperRight:
	CMP.B #1,D1
	BNE .noUpperRight
	BSET #5,D0
	bra .next
.noUpperRight:
	BCLR #5,D0
.next:

CheckLowerRight:
	CMP.B #1,D2
	BNE .noLowerRight
	BSET #3,D0
	bra .next
.noLowerRight:
	BCLR #3,D0
.next:	

CheckRight:
	CMP.B #1,D3
	BNE .noRight
	BSET #4,D0
	bra .next
.noRight:
	BCLR #4,D0
.next:	
	popRegs D2-D5/A0
	rts
	
Conway_Print:
	;input: A3 = base address of tilemap
	MOVE.B (A3)+,D0
	CMP.B #255,D0
	BEQ .done
	CMP.B #2,D0
	BEQ .skip
	;else, print
	JSR Conway_PrintChar
.skip
	BRA Conway_Print
.done
	rts
	
Conway_PrintChar:				;Show D0 to screen
	moveM.l d0-d7/a0-a7,-(sp)
		and.l #$FF,d0			;Keep only 1 byte
		Move.L  #$40000003,d5	;top 4=write, bottom $3=Cxxx range
		MOVEQ #0,D4				;Tilemap at $C000+

		Move.B (Cursor_Y),D4	
		rol.L #8,D4				;move $-FFF to $-FFF----
		rol.L #8,D4
		rol.L #7,D4				;2 bytes per tile * 64 tiles per line
		add.L D4,D5				;add $4------3
		
		Move.B (Cursor_X),D4
		rol.L #8,D4				;move $-FFF to $-FFF----
		rol.L #8,D4
		rol.L #1,D4				;2 bytes per tile
		add.L D4,D5				;add $4------3
		
		MOVE.L	D5,(VDP_ctrl)	; C00004 write next character to VDP
		MOVE.W	D0,(VDP_data)	; C00000 store next word of name data

		addq.b #1,(Cursor_X)	;INC Xpos
		move.b (Cursor_X),d0
		cmp.b #39,d0
		bls .nextpixel_Xok
		jsr NewLine			;If we're at end of line, start newline
.nextpixel_Xok:
	moveM.l (sp)+,d0-d7/a0-a7
	rts
	
;don't forget, these are in ROM so we can't write to them directly.
;instead, they will be copied to ram and worked with from there.
Conway_Tilemap:	;(screenwidth + 2) by (screenheight+2)
	DC.B $02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02
	DC.B $02,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$02
	DC.B $02,$00,$00,$01,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$01,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$02
	DC.B $02,$00,$00,$00,$01,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$01,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$02
	DC.B $02,$00,$01,$01,$01,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$01,$01,$01,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$02
	DC.B $02,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$02
	DC.B $02,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$02
	DC.B $02,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$02
	DC.B $02,$00,$00,$00,$00,$00,$00,$00,$00,$00,$01,$01,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$02
	DC.B $02,$00,$00,$00,$00,$00,$00,$00,$00,$01,$00,$00,$01,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$02
	DC.B $02,$00,$01,$01,$00,$00,$00,$00,$00,$00,$01,$01,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$02
	DC.B $02,$00,$01,$01,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$02
	DC.B $02,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$02
	DC.B $02,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$02
	DC.B $02,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$02
	DC.B $02,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$02
	DC.B $02,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$02
	DC.B $02,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$02
	DC.B $02,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$02
	DC.B $02,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$02
	DC.B $02,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$02
	DC.B $02,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$02
	DC.B $02,$00,$00,$00,$00,$01,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$02
	DC.B $02,$00,$00,$00,$00,$01,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$02
	DC.B $02,$00,$00,$00,$00,$01,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$02
	DC.B $02,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$02
	DC.B $02,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$02
	DC.B $02,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$02
	DC.B $02,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$02
	DC.B $02,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$02
	DC.B $02,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$02
	DC.B $02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02
	DC.B 255
	EVEN
Conway_Backup_Tilemap:	;(screenwidth + 2) by (screenheight+2)
	DC.B $02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02
	rept 30
	DC.B $02,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$02
	endr
	DC.B $02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02,$02
	DC.B 255
	EVEN
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
NewLine:
	addq.b #1,(Cursor_Y)		;INC Y
	clr.b (Cursor_X)			;Zero X
	rts	
	

LDIR:	;COPY D1 BYTES FROM A3 TO A2
	move.b (a3)+,(a2)+
	DBRA D1,LDIR
	rts
	
DefineTiles:						;Copy D1 bytes of data from A0 to VDP memory D2 
	jsr prepareVram					;Calculate the memory location we want to write
.again:								; the tile pattern definitions to
		move.l (a0)+,(VDP_data)				
		dbra d1,.again
	rts
			
prepareVram:							;To select a memory location D2 we need to calculate 
										;the command byte... depending on the memory location
	pushall								;$7FFF0003 = Vram $FFFF.... $40000000=Vram $0000
		move.l d2,d0
		and.w #%1100000000000000,d0		;Shift the top two bits to the far right 
		rol.w #2,d0
		
		and.l #%0011111111111111,d2	    ; shift all the other bits left two bytes
		rol.l #8,d2		
		rol.l #8,d2
		
		or.l d0,d2						
		or.l #$40000000,d2				;Set the second bit from the top to 1
										;#%01000000 00000000 00000000 00000000
		move.l d2,(VDP_ctrl)
popallRTS:
	popall
	rts
	
Graphics:
	DC.L $0000000F,$0000000F,$0000000F,$0000000F,$0000000F,$0000000F,$0000000F,$FFFFFFFF
	DC.L $FFFFFFFF,$FFFFFFFF,$FFFFFFFF,$FFFFFFFF,$FFFFFFFF,$FFFFFFFF,$FFFFFFFF,$FFFFFFFF
GraphicsEnd:

VDPSettings:
	DC.B $04 ; 0 mode register 1											---H-1M-
	DC.B $04 ; 1 mode register 2											-DVdP---
	DC.B $30 ; 2 name table base for scroll A (A=top 3 bits)				--AAA--- = $C000
	DC.B $3C ; 3 name table base for window (A=top 4 bits / 5 in H40 Mode)	--AAAAA- = $F000
	DC.B $07 ; 4 name table base for scroll B (A=top 3 bits)				-----AAA = $E000
	DC.B $6C ; 5 sprite attribute table base (A=top 7 bits / 6 in H40)		-AAAAAAA = $D800
	DC.B $00 ; 6 unused register											--------
	DC.B $00 ; 7 background color (P=Palette C=Color)						--PPCCCC
	DC.B $00 ; 8 unused register											--------
	DC.B $00 ; 9 unused register											--------
	DC.B $FF ;10 H interrupt register (L=Number of lines)					LLLLLLLL
	DC.B $00 ;11 mode register 3											----IVHL
	DC.B $81 ;12 mode register 4 (C bits both1 = H40 Cell)					C---SIIC
	DC.B $37 ;13 H scroll table base (A=Top 6 bits)							--AAAAAA = $FC00
	DC.B $00 ;14 unused register											--------
	DC.B $02 ;15 auto increment (After each Read/Write)						NNNNNNNN
	DC.B $01 ;16 scroll size (Horiz & Vert size of ScrollA & B)				--VV--HH = 64x32 tiles
	DC.B $00 ;17 window H position (D=Direction C=Cells)					D--CCCCC
	DC.B $00 ;18 window V position (D=Direction C=Cells)					D--CCCCC
	DC.B $FF ;19 DMA length count low										LLLLLLLL
	DC.B $FF ;20 DMA length count high										HHHHHHHH
	DC.B $00 ;21 DMA source address low										LLLLLLLL
	DC.B $00 ;22 DMA source address mid										MMMMMMMM
	DC.B $80 ;23 DMA source address high (C=CMD)							CCHHHHHH
VDPSettingsEnd:
	even
Output:

Screenshot of emulator

ABAP

Works with: ABAP version 7.4 SP05 or Above only

For the proposed task use 10,9;10,10;10,11 on screen field P_POS. Can be left blank for random filling

*&---------------------------------------------------------------------*
*& Report ZCONWAYS_GAME_OF_LIFE
*&---------------------------------------------------------------------*
*& by Marcelo Bovo
*&---------------------------------------------------------------------*
report zconways_game_of_life line-size 174 no standard page heading
                             line-count 40.

parameters: p_char type c default '#',
            p_pos  type string.

class lcl_game_of_life definition.

  public section.

    data: x_max      type i value 174,
          y_max      type i value 40,
          character  type c value abap_true,
          x          type i,
          y          type i,
          pos        type string,
          offlimits  type i value 9998,
          grid(9999) type c. " every X_MAX characters on grid equals one line on screen

    data: o_random_y type ref to cl_abap_random_int,
          o_random_x type ref to cl_abap_random_int.

    methods: constructor,
      play,
      initial_position,
      initial_grid,
      write,
      change_grid.

endclass.

class lcl_game_of_life implementation.
  method constructor.
    o_random_y = cl_abap_random_int=>create( seed = cl_abap_random=>create( conv i( sy-uzeit ) )->intinrange( low = 1 high = 999999 )
                                             min  = 1
                                             max = y_max ).

    o_random_x = cl_abap_random_int=>create( seed = cl_abap_random=>create( conv i( |{ sy-datum(4) }{ sy-uzeit }| ) )->intinrange( low = 1 high = 999999 )
                                             min  = 1
                                             max = x_max ).

  endmethod.

  method play.

    "fill initial data ramdonly if user hasnt typed any coordenates
    if pos is initial.
      initial_position( ).
    endif.

    initial_grid( ).

    write( ).

  endmethod.

  method initial_position.
    do cl_abap_random_int=>create( "seed = conv i( sy-uzeit )
                                   min  = 50
                                   max = 800 )->get_next( ) times.
      data(lv_index) = sy-index.

      x = o_random_x->get_next( ).
      y = o_random_y->get_next( ).

      p_pos = |{ p_pos }{ switch char1( lv_index when '1' then space else ';' ) }{ y },{ x }|.
    enddo.
  endmethod.

  method initial_grid.

    "Split coordenates
    split p_pos at ';' into table data(lt_pos_inicial) .

    "Sort By Line(Easy to read)
    sort lt_pos_inicial.

    loop at lt_pos_inicial assigning field-symbol(<pos_inicial>).

      split <pos_inicial> at ',' into data(y_char) data(x_char).

      x = x_char.
      y = y_char.

      "Ensure maximum coordenates are not surpassed
      x = cond #( when x <= x_max then x
                   else o_random_x->get_next( ) ).

      y = cond #( when y <= y_max then y
                   else o_random_y->get_next( ) ).

      "Write on string grid
      "Every x_max lines represent one line(Y) on the grid
      data(grid_xy) = ( x_max * y ) + x - x_max - 1.
      grid+grid_xy(1) = character.

    endloop.

  endmethod.

  method write.

    skip to line 1.

    "Write every line on screen
    do y_max times.
      data(lv_index) = sy-index - 1.

      "Write whole line(current line plus number of maximum X characters)
      data(grid_xy) = ( lv_index * x_max ).

      write / grid+grid_xy(x_max) no-gap.

      if grid+grid_xy(x_max) is initial.
        skip.
      endif.

    enddo.

    change_grid( ).

  endmethod.

  method change_grid.

    data(grid_aux) = grid.
    clear grid_aux.
    data(grid_size) = strlen( grid ).

    "Validate neighbours based on previous written grid
    "ABC
    "D.F
    "GHI
    do grid_size + x_max times.

      "Doens't write anything beyond borders
      check sy-index <= x_max * y_max.

      data(grid_xy) = sy-index - 1.

      data(neighbours) = 0.

      "Current Line neighbours
      data(d) = grid_xy - 1.
      data(f) = grid_xy + 1.

      "Line above neighbours
      data(b) = grid_xy - x_max.
      data(a) = b - 1.
      data(c) = b + 1.

      "Line Bellow neighbours
      data(h) = grid_xy + x_max.
      data(g) = h - 1.
      data(i) = h + 1.

      "Previous Neighbours
      neighbours += cond #( when a < 0 then 0 else cond #( when grid+a(1) is not initial then 1 else 0 )   ).
      neighbours += cond #( when b < 0 then 0 else cond #( when grid+b(1) is not initial then 1 else 0 )   ).
      neighbours += cond #( when c < 0 then 0 else cond #( when grid+c(1) is not initial then 1 else 0 )   ).
      neighbours += cond #( when d < 0 then 0 else cond #( when grid+d(1) is not initial then 1 else 0 )   ).

      "Next Neighbours
      neighbours += cond #( when f > grid_size then 0 else cond #( when grid+f(1) is not initial then 1 else 0 )   ).
      neighbours += cond #( when g > grid_size then 0 else cond #( when grid+g(1) is not initial then 1 else 0 )   ).
      neighbours += cond #( when h > grid_size then 0 else cond #( when grid+h(1) is not initial then 1 else 0 )   ).
      neighbours += cond #( when i > grid_size then 0 else cond #( when grid+i(1) is not initial then 1 else 0 )   ).

      grid_aux+grid_xy(1) = cond #( when  neighbours = 3 or (  neighbours = 2  and grid+grid_xy(1) = character )
                                     then character
                                    else space ).

    enddo.

    grid = grid_aux.

  endmethod.
endclass.

start-of-selection.

  set pf-status 'STANDARD_FULLSCREEN'. "Use &REFRESH button with F8 Shortcut to go to next generation

  data(lo_prog) = new lcl_game_of_life( ).
  lo_prog->character = p_char.
  lo_prog->pos = p_pos.
  lo_prog->play( ).

at user-command.

  case sy-ucomm.
    when 'REFR' or '&REFRESH'.
      sy-lsind = 1. "Prevents LIST_TOO_MANY_LEVELS DUMP
      lo_prog->write( ).
    when others.
      leave list-processing.
  endcase.

ACL2

(defun print-row (row)
   (if (endp row)
       nil
       (prog2$ (if (first row)
                   (cw "[]")
                   (cw "  "))
               (print-row (rest row)))))

(defun print-grid-r (grid)
   (if (endp grid)
       nil
       (progn$ (cw "|")
               (print-row (first grid))
               (cw "|~%")
               (print-grid-r (rest grid)))))

(defun print-line (l)
   (if (zp l)
       nil
       (prog2$ (cw "-")
               (print-line (1- l)))))

(defun print-grid (grid)
   (progn$ (cw "+")
           (print-line (* 2 (len (first grid))))
           (cw "+~%")
           (print-grid-r grid)
           (cw "+")
           (print-line (* 2 (len (first grid))))
           (cw "+~%")))

(defun neighbors-row-r (row)
   (if (endp (rest (rest row)))
       (list (if (first row) 1 0))
       (cons (+ (if (first row) 1 0)
                (if (third row) 1 0))
             (neighbors-row-r (rest row)))))

(defun neighbors-row (row)
   (cons (if (second row) 1 0)
         (neighbors-row-r row)))

(defun zip+ (xs ys)
   (if (or (endp xs) (endp ys))
       (append xs ys)
       (cons (+ (first xs) (first ys))
             (zip+ (rest xs) (rest ys)))))

(defun counts-row (row)
   (if (endp row)
       nil
       (cons (if (first row) 1 0)
             (counts-row (rest row)))))

(defun neighbors-r (grid prev-counts curr-counts next-counts
                         prev-neighbors curr-neighbors
                         next-neighbors)
   (if (endp (rest grid))
       (list (zip+ (zip+ prev-counts
                         prev-neighbors)
                   (neighbors-row (first grid))))
       (cons (zip+ (zip+ (zip+ prev-counts next-counts)
                         (zip+ prev-neighbors next-neighbors))
                   curr-neighbors)
             (neighbors-r (rest grid)
                          curr-counts
                          next-counts
                          (counts-row (third grid))
                          curr-neighbors
                          next-neighbors
                          (neighbors-row (third grid))))))

(defun neighbors (grid)
   (neighbors-r grid
                nil
                (counts-row (first grid))
                (counts-row (second grid))
                nil
                (neighbors-row (first grid))
                (neighbors-row (second grid))))

(defun life-rules-row (life neighbors)
   (if (or (endp life) (endp neighbors))
       nil
       (cons (or (and (first life)
                      (or (= (first neighbors) 2)
                          (= (first neighbors) 3)))
                 (and (not (first life))
                      (= (first neighbors) 3)))
             (life-rules-row (rest life) (rest neighbors)))))

(defun life-rules-r (grid neighbors)
   (if (or (endp grid) (endp neighbors))
       nil
       (cons (life-rules-row (first grid) (first neighbors))
             (life-rules-r (rest grid) (rest neighbors)))))

(defun conway-step (grid)
   (life-rules-r grid (neighbors grid)))

(defun conway (grid steps)
   (if (zp steps)
       nil
       (progn$ (print-grid grid)
               (conway (conway-step grid) (1- steps)))))
Output:
+------+
|  []  |
|  []  |
|  []  |
+------+
+------+
|      |
|[][][]|
|      |
+------+
+------+
|  []  |
|  []  |
|  []  |
+------+

Ada

WITH Ada.Text_IO;  USE Ada.Text_IO;
 
PROCEDURE Life IS
   SUBTYPE Cell IS Natural RANGE 0 .. 1;

   TYPE Petri_Dish IS ARRAY (Positive RANGE <>, Positive RANGE <>) OF Cell;

   PROCEDURE Step (Gen : IN OUT Petri_Dish) IS
      Above       : ARRAY (Gen'Range (2)) OF Cell := (OTHERS => 0);
      Left, This  : Cell;
   BEGIN
      FOR I IN Gen'First (1) + 1 .. Gen'Last (1) - 1 LOOP
         Left := 0;
         FOR J IN Gen'First (2) + 1 .. Gen'Last (2) - 1 LOOP
            This := (CASE Above (J - 1) + Above (J) + Above (J + 1) +
                          Left			    + Gen (I, J + 1) +
                          Gen (I + 1, J - 1) + Gen (I + 1, J) 	+ Gen (I + 1, J + 1) IS
                        WHEN 2      => Gen (I, J),
                        WHEN 3      => 1,
                        WHEN OTHERS => 0);
            Above (J - 1):= Left;
            Left         := Gen (I, J);
            Gen (I, J) 	 := This;
         END LOOP;
         Above (Above'Last - 1) := Left;
      END LOOP;
   END Step;
 
   PROCEDURE Put (Gen : Petri_Dish) IS
   BEGIN
      FOR I IN Gen'Range (1) LOOP
         FOR J IN Gen'Range (2) LOOP
            Put ( if Gen (I, J) = 0 then " " else "#");
         END LOOP;
         New_Line;
      END LOOP;
   END Put;
 
   Blinker : Petri_Dish := (2 .. 4 => (0, 0, 1, 0, 0), 1 | 5 => (0, 0, 0, 0, 0));
   Glider  : Petri_Dish (1..6,1..11):= (2 => (3 => 1, others => 0),
                                        3 => (4 => 1, others => 0),
                                        4 => (2|3|4=>1, others => 0),
                                        others => (others => 0));
   PROCEDURE Put_And_Step_Generation (N : Positive; Name : String; P : IN OUT Petri_Dish) IS
   BEGIN
      FOR Generation IN 1 .. N LOOP
         Put_Line (Name & Generation'Img);
         Put (P);
         Step (P);
      END LOOP;
   END Put_And_Step_Generation;

BEGIN
   Put_And_Step_Generation (3, "Blinker", Blinker);
   Put_And_Step_Generation (5, "Glider", Glider);
END Life;

The solution uses one cell thick border around square Petri dish as uninhabited dire land. This simplifies computations of neighborhood. Sample output contains 3 generations of the blinker and 5 of the glider:

Output:
Blinker 1

  #
  #
  #

Blinker 2


 ###


Blinker 3

  #
  #
  #

Glider 1

  #
   #
 ###


Glider 2


 # #
  ##
  #

Glider 3


   #
 # #
  ##

Glider 4


  #
   ##
  ##

Glider 5


   #
    #
  ###

ALGOL 68

See Conway's Game of Life/ALGOL 68

Amazing Hopper

El programa genera el algoritmo en modo texto.

Adaptado del programa "Conway's Game of Life" de Vishal Nagda, en Hithub

https://github.com/vishalnagda1/CONWAYs-Game-of-Life-C/blob/master/game_of_life.c

#include <jambo.h>

#define SIZER   90
#define SIZEC   120

Main
   
    Dim (SIZER, SIZEC) as zeros 'grid, neighbour_count'
    Dim (SIZER, SIZEC) as fill '" ",disp grid'
    
    c=0, Let( c := Utf8(Chr(254)))
    
    moi=0, moj=0, poi=0, poj=0

    m={}
    Set ' 0,1,1 ' Apnd row 'm'
    Set ' 1,1,0 ' Apnd row 'm'
    Set ' 0,1,0 ' Apnd row 'm'
    [44:46, 59:61] Set 'm', Put 'grid'
    Clr all marks
    
    i=0, j=0
    Tok sep '""'
    Locate (1,1)
    Loop 
       i=1
       Iterator ( ++i, Less equal(i,SIZER),\
                  j=1, Iterator ( ++j, Less equal(j,SIZEC), \
                          Set 'i,j', Gosub 'Count NBR', [i,j], Put 'neighbour_count' ) )

       i=1
       Loop if( Less equal(i,SIZER) )
          j=1
          Loop if( Less equal(j,SIZEC) )
             [i,j]
             If ( Get 'grid' )
                Get 'neighbour_count'
                When ( Out of range including '1,4' ) {
                   Set '0," "', Put 'disp grid', Put 'grid'
                }
             Else
                Get 'neighbour_count'
                When ( Is equal to '3' ) {
                   Set '1,c', Put 'disp grid', Put 'grid'
                }
             End If
             ++j
          Back
          ++i
       Back 
       
       Clr all marks
       Print table 'disp grid'
       Break if ( Key pressed )

    Back 
    Pause
End

Subrutines

Define 'Count NBR, i, j'
    n_count = 0

    When ( Must be( Minus one 'i' ---Backup to 'moi'---, Minus one 'j' ---Backup to 'moj'--- ) ) {

       When ( [moi,moj]Get 'grid' ) {
          ++n_count
       }
    }

    Plus one 'j', Move to 'poj'

    When ( moi ) { 
       When ( [ moi, j ] Get 'grid' ) {
          ++n_count
       }
       When ( Less equal( poj, SIZEC )) {
          When ( [ moi, poj] Get 'grid' ) {
             ++n_count
          }
       }
    }

    When ( moj ) { 
       When( [i, moj] Get 'grid' )  {
          ++n_count
       }
    }

    When ( Less equal ( poj, SIZEC ) ){
  
       When( [i, poj] Get 'grid' ) {
          ++n_count
       }
    }

    When ( Less equal (Plus one 'i' ---Backup to 'poi'---, SIZER ) ) {

       When ( [ poi, j] Get 'grid' ) {
          ++n_count
       }
       
       When ( Less equal ( poj, SIZEC) ) {
          When ( [poi, poj] Get 'grid' ) {
             ++n_count
          }
       }
       
       When ( moj ){
          When ([poi, moj] Get 'grid' ){
             ++n_count
          }
       }
    }
Return 'n_count'
Output:
La llamada se realiza desde terminal, con el programa "rxvt" de Linux, para adaptar la terminal a los pixeles y dimensiones adecuados.

Llamada:
rxvt -g 270x100 -fn "xft:FantasqueSansMono-Regular:pixelsize=3" -e hopper jm/gamelife.jambo

Version 2

Me di cuenta de que la subrutina "Count NBR" era un poco lenta, y además, una función que cuente los vecinos en un radio dado, me es útil para hacer juegos, por lo que incluí esa función dentro de las funciones de HOPPER.

Además, reescribí el programa "a la Hopper", como debió ser desde un principio.

#include <jambo.h>
#define SIZER   90
#define SIZEC   120

Main
    Cls
    Hide cursor

    Dim (SIZER, SIZEC), as zeros 'grid, neighbour_count'
    Dim (SIZER, SIZEC), as fill '" ",disp grid'
 
    c=0 , Let( c := Utf8(Chr(254)))

    m={}
    Set ' 0,1,1 ' Apend row to 'm'
    Set ' 1,1,0 ' Apend row to 'm'
    Set ' 0,1,0 ' Apend row to 'm'
 
    [44:46, 59:61] Set 'm', Put 'grid'
    
    Clr all marks
    
    radio=1, r=0

    Tok sep '""'

    Locate (1,1)
    Loop
       i=1
       Iterator ( ++i, Less equal(i,SIZER),\
                  j=1, Iterator ( ++j, Less equal(j,SIZEC), \
                           [i,j], Neighbour count (grid,radio), Put 'neighbour_count' ) )
       
       Cartesian ( Greater equal(grid, 1)---Back up to 'r'--- Mul by 'neighbour_count';\
                                                          Out of range including '1,4' )
       Get range, Set '0," "', Put 'disp grid', Put 'grid', Forget

       Cartesian ( Not( r ); Mul by 'neighbour_count'; Is equal to '3' )
       Get range, Set '1,c', Put 'disp grid', Put 'grid', Forget
       Clr range

       Clr all marks
       Print table 'disp grid'
       
       Break if ( Key pressed )
    Back 
    Pause
    Show cursor
End
Output:

La salida es la misma, pero ahora va mucho más rápido... parecen estrellitas explotando :D

APL

GNU APL (from Wikipedia: https://aplwiki.com/wiki/John_Scholes%27_Conway%27s_Game_of_Life#Translations)
      Life{↑↑1 .3 4=+/,¯1 0 1∘.¯1 0 1∘.⌽⊂}
      m  5 5(0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0)
      m
0 0 0 0 0
0 0 0 0 0
0 1 1 1 0
0 0 0 0 0
0 0 0 0 0
      Life m
0 0 0 0 0
0 0 1 0 0
0 0 1 0 0
0 0 1 0 0
0 0 0 0 0
      Life Life m
0 0 0 0 0
0 0 0 0 0
0 1 1 1 0
0 0 0 0 0
0 0 0 0 0


APL2 (Dyalog) Example in one line

APL \ 1130 example (very old APL dialect via simulator)
https://web.archive.org/web/20160313204013/http://www.farnik.com/wiki/uploads/lifeAPL1130.jpg

From: APL \ 1130 Samples

The following APL \ 1130 code will need APL385 font installed to display correctly.
See Download APL TT Font

      ∇LIFE[⎕]∇
[0]   NG←LIFE CG;W
[1]   W←CG+(¯1⊖CG)+(1⊖CG)+(¯1⌽CG)+(1⌽CG)
[2]   W←W+(1⊖1⌽CG)+(¯1⊖1⌽CG)+(1⊖¯1⌽CG)+(¯1⊖¯1⌽CG)
[3]   NG←(3=W)+(CG∧4=W)
      ∇
      RP←5 5⍴0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 1 0 0
      RP
0 0 0 0 0
0 0 1 1 0
0 1 1 0 0
0 0 1 0 0
0 0 0 0 0
      LIFE RP
0 0 0 0 0
0 1 1 1 0
0 1 0 0 0
0 1 1 0 0
0 0 0 0 0
      LIFE LIFE RP
0 0 1 0 0
0 1 1 0 0
1 0 0 1 0
0 1 1 0 0
0 0 0 0 0

AppleScript

This handler creates and returns a "universe" script object initialised with given "seed" text and dimensions. For convenience, the seed text's visible characters can be anything, the set-up code itself replacing them with "■" characters. The use of the returned universe is demo'd later.

use AppleScript version "2.4" -- OS X 10.10 (Yosemite) or later
use framework "Foundation" -- For the regex at the top of newUniverse()
use scripting additions

-- The characters to represent the live and dead cells.
property live : "■" -- character id 9632 (U+25A0).
property dead : space
-- Infinite universes are expensive to maintain, so only a local region of universe is represented here.
-- Its invisible border is a wall of "dead" cells one cell deep, lined with a two-cell buffer layer into which
-- objects nominally leaving the region can disappear without being seen to hit the wall or bouncing back.
property borderThickness : 3

on newUniverse(seed, {w, h})
    -- Replace every visible character in the seed text with "■" and every horizontal space with a space.
    set seed to current application's class "NSMutableString"'s stringWithString:(seed)
    set regex to current application's NSRegularExpressionSearch
    tell seed to replaceOccurrencesOfString:("\\S") withString:(live) options:(regex) range:({0, its |length|()})
    tell seed to replaceOccurrencesOfString:("\\h") withString:(dead) options:(regex) range:({0, its |length|()})
    -- Ensure the universe dimensions are at least equal to the number of lines and the length of the longest.
    set seedLines to paragraphs of (seed as text)
    set lineCount to (count seedLines)
    if (lineCount > h) then set h to lineCount
    set seedWidth to 0
    repeat with thisLine in seedLines
        set lineLength to (count thisLine)
        if (lineLength > seedWidth) then set seedWidth to lineLength
    end repeat
    if (seedWidth > w) then set w to seedWidth
    
    -- Get a new universe.
    script universe
        -- State lists. These will contain or be lists of 0s and 1s and will include the border cells.
        property newState : {}
        property previousState : {}
        property currentRow : {}
        property rowAbove : {}
        property rowBelow : {}
        property replacementRow : {}
        -- Equivalent text lists. These will only cover what's in the bounded region.
        property lineList : {}
        property characterGrid : {}
        property currentLineCharacters : {}
        -- Precalculated border cell indices.
        property rightInnerBuffer : borderThickness + w + 1
        property rightOuterBuffer : rightInnerBuffer + borderThickness - 2
        property bottomInnerBuffer : borderThickness + h + 1
        property bottomOuterBuffer : bottomInnerBuffer + borderThickness - 2
        -- Generation counter.
        property counter : 0
        -- Temporary lists used in the set-up.
        property rowTemplate : {}
        property lineCharacterTemplate : {}
        
        -- Built-in handlers. Both return text representing a universe state and
        -- a boolean indicating whether or not the state's the same as the previous one.
        on nextState()
            set astid to AppleScript's text item delimiters
            set AppleScript's text item delimiters to ""
            copy newState to previousState
            set currentRow to beginning of my previousState
            set rowBelow to item 2 of my previousState
            -- Check each occupiable cell in each occupiable row of the 'previousState' grid, including the buffer cells.
            -- If warranted by the number of live neighbours, edit the equivalent cell in 'newState' and,
            -- if within the region's bounds, change the corresponding text character too.
            repeat with r from 2 to bottomOuterBuffer
                set rowAbove to currentRow
                set currentRow to rowBelow
                set rowBelow to item (r + 1) of my previousState
                set replacementRow to item r of my newState
                set rowCrossesRegion to ((r comes after borderThickness) and (r comes before bottomInnerBuffer))
                if (rowCrossesRegion) then set currentLineCharacters to item (r - borderThickness) of my characterGrid
                set lineChanged to false
                repeat with c from 2 to rightOuterBuffer
                    set liveNeighbours to ¬
                        (item (c - 1) of my rowAbove) + (item c of my rowAbove) + (item (c + 1) of my rowAbove) + ¬
                        (item (c - 1) of my currentRow) + (item (c + 1) of my currentRow) + ¬
                        (item (c - 1) of my rowBelow) + (item c of my rowBelow) + (item (c + 1) of my rowBelow)
                    if (item c of my currentRow is 1) then
                        if ((liveNeighbours < 2) or (liveNeighbours > 3)) then
                            set item c of my replacementRow to 0
                            if ((c comes after borderThickness) and (c comes before rightInnerBuffer) and (rowCrossesRegion)) then
                                set item (c - borderThickness) of my currentLineCharacters to dead
                                set lineChanged to true
                            else if ((c is 3) or (c is rightOuterBuffer) or (r is 3) or (r is bottomOuterBuffer)) then
                                -- This is a fudge to dissolve "bombers" entering the buffer zone.
                                set item (c - 1) of my replacementRow to -1
                                set item c of item (r - 1) of my newState to -1
                            end if
                        end if
                    else if (liveNeighbours is 3) then
                        set item c of my replacementRow to 1
                        if ((c comes after borderThickness) and (c comes before rightInnerBuffer) and (rowCrossesRegion)) then
                            set item (c - borderThickness) of my currentLineCharacters to live
                            set lineChanged to true
                        end if
                    end if
                end repeat
                if (lineChanged) then set item (r - borderThickness) of my lineList to currentLineCharacters as text
            end repeat
            set AppleScript's text item delimiters to astid
            set counter to counter + 1
            set last item of my lineList to "Generation " & counter
            
            return currentState()
        end nextState
        
        on currentState()
            set noChanges to (newState = previousState)
            if (noChanges) then ¬
                set last item of my lineList to (last item of my lineList) & " (all dead, still lifes, or left the universe)"
            set astid to AppleScript's text item delimiters
            set AppleScript's text item delimiters to return
            set stateText to lineList as text
            set AppleScript's text item delimiters to astid
            
            return {stateText, noChanges}
        end currentState
    end script
    
    -- Set the universe's start conditions.
    -- Build a row template list containing w + 2 * borderThickness zeros
    -- and a line character template list containing w 'dead' characters.
    repeat (borderThickness * 2) times
        set end of universe's rowTemplate to 0
    end repeat
    repeat w times
        set end of universe's rowTemplate to 0
        set end of universe's lineCharacterTemplate to dead
    end repeat
    set astid to AppleScript's text item delimiters
    set AppleScript's text item delimiters to ""
    set blankLine to universe's lineCharacterTemplate as text
    
    -- Use the templates to populate lists representing the universe's conditions.
    -- Firstly the top border rows ('newState' list only).
    repeat borderThickness times
        copy universe's rowTemplate to end of universe's newState
    end repeat
    -- Then enough rows and text lines to centre the input roughly halfway down the grid.
    set headroom to (h - lineCount) div 2
    repeat headroom times
        copy universe's rowTemplate to end of universe's newState
        copy universe's lineCharacterTemplate to end of universe's characterGrid
        set end of universe's lineList to blankLine
    end repeat
    -- Then the rows and lines representing the input itself, centring it roughly halfway across the grid.
    set textInset to (w - seedWidth) div 2
    set stateInset to textInset + borderThickness
    repeat with thisLine in seedLines
        copy universe's rowTemplate to universe's currentRow
        copy universe's lineCharacterTemplate to universe's currentLineCharacters
        repeat with c from 1 to (count thisLine)
            set thisCharacter to character c of thisLine
            set item (textInset + c) of universe's currentLineCharacters to thisCharacter
            set item (stateInset + c) of universe's currentRow to (thisCharacter is live) as integer
        end repeat
        set end of universe's newState to universe's currentRow
        set end of universe's characterGrid to universe's currentLineCharacters
        set end of universe's lineList to universe's currentLineCharacters as text
    end repeat
    set AppleScript's text item delimiters to astid
    -- Then the rows and lines beneath and the bottom border.
    repeat (h - (headroom + lineCount)) times
        copy universe's rowTemplate to end of universe's newState
        copy universe's lineCharacterTemplate to end of universe's characterGrid
        set end of universe's lineList to blankLine
    end repeat
    repeat borderThickness times
        copy universe's rowTemplate to end of universe's newState
    end repeat
    -- Add a generation counter display line to the end of the line list.
    set end of universe's lineList to "Generation 0"
    -- Lose the no-longer-needed template lists.
    set universe's rowTemplate to missing value
    set universe's lineCharacterTemplate to universe's rowTemplate
    
    return universe
end newUniverse

In conjunction with the above, this fulfills the task as set:

on RCTask(seed, dimensions, maxGenerations)
    -- Create a universe and start a list with its initial state.
    set universe to newUniverse(seed, dimensions)
    set {stateText} to universe's currentState()
    set output to {stateText}
    -- Add successive states to the list.
    repeat maxGenerations times
        set {stateText, noChanges} to universe's nextState()
        set end of output to stateText
        if (noChanges) then exit repeat
    end repeat
    -- Coerce the states to a single text, each followed by a short line of dashes.
    set astid to AppleScript's text item delimiters
    set AppleScript's text item delimiters to linefeed & "-----" & linefeed & linefeed
    set output to (output as text) & linefeed & "-----"
    set AppleScript's text item delimiters to astid
    
    return output
end RCTask

-- Return text containing the original and three generations of a "blinker" in a 3 x 3 grid.
return RCTask("***", {3, 3}, 3)
Output:
"   
■■■
   
Generation 0
-----




Generation 1
-----

   
■■■
   
Generation 2
-----




Generation 3
-----"

This alternative to the task code runs an animation of a "Gosper glider gun" in TextEdit, the AppleScriptable text editor included with macOS. The animation's achieved by replacing the entire text of a document with successive universe states. It's faster than it sounds, but the universe size specified shouldn't be much greater than 150 x 150 with current machines.

on runGame(seed, dimensions, maxGenerations)
    -- Create an RTF file set up for Menlo-Regular 12pt, half spacing, and a reasonable window size.
    set fontName to "Menlo-Regular"
    set fontSize to 12
    set viewScale to fontSize * 12.4 -- Seems to work well.
    set {w, h} to dimensions
    
    set RTFHeaders to "{\\rtf1\\ansi\\ansicpg1252\\cocoartf1671\\cocoasubrtf600
{\\fonttbl\\f0\\fnil\\fcharset0 " & fontName & ";}
{\\colortbl;\\red255\\green255\\blue255;}
{\\*\\expandedcolortbl;;}
\\margl1440\\margr1440\\vieww" & (w * viewScale as integer) & "\\viewh" & ((h + 1) * viewScale as integer) & "\\viewkind0
\\pard\\sl120\\slmult1\\pardirnatural\\partightenfactor0
\\f0\\fs" & (fontSize * 2) & " \\cf0  }" -- Contains a space as body text for TextEdit to see as an 'attribute run'.
    set RTFFile to ((path to temporary items as text) & "Conway's Game of Life.rtf") as «class furl»
    set fRef to (open for access RTFFile with write permission)
    try
        set eof fRef to 0
        write RTFHeaders as «class utf8» to fRef
        close access fRef
    on error errMsg number errNum
        close access fRef
        error errMsg number errNum
    end try
    -- Open the file as a document in TextEdit.
    tell application "TextEdit"
        activate
        tell document "Conway's Game of Life.rtf" to if (it exists) then close saving no
        set CGoLDoc to (open RTFFile)
    end tell
    
    -- Create a universe and display its initial state in the document window.
    set universe to newUniverse(seed, dimensions)
    set {stateText} to universe's currentState()
    tell application "TextEdit" to set CGoLDoc's first attribute run to stateText
    -- Get and display successive states.
    repeat maxGenerations times
        set {stateText, noChanges} to universe's nextState()
        tell application "TextEdit" to set CGoLDoc's first attribute run to stateText
        if (noChanges) then exit repeat
    end repeat
end runGame

set GosperGliderGun to "                        *
                      * *
            **      **            ** 
           *   *    **            **
**        *     *   **
**        *   * **    * *
          *     *       *
           *   *
            **"
-- Run for 500 generations in a 100 x 100 universe.
runGame(GosperGliderGun, {100, 100}, 500)

ARM Assembly

Works with: TI-Nspire
	.string "PRG"

	lcd_ptr .req r4
	active_fb .req r5
	inactive_fb .req r6
	offset_r .req r7
	backup_fb .req r8

	@ start
	push {r4-r10, r12, lr}
	
	ldr lcd_ptr, =0xC0000000 @ address of the LCD controller
	adr offset_r, offsets
	ldrh r0, [offset_r, #6] @ 0xffff is already in memory because -1 is in the offsets table
	str r0, [lcd_ptr, #0x200] @ set up paletted colors: 1 is black, 0 is white
	
	ldr r2, [lcd_ptr, #0x18] @ load lcd configuration
	bic r2, #14
	orr r2, #6 @ Set color mode to 8 bpp, paletted
	str r2, [lcd_ptr, #0x18]
	
	ldr backup_fb, [lcd_ptr, #0x10] @ Save address of OS framebuffer
	
	@ allocate a buffer for game state / framebuffer
	ldr r0, =153600 @ 320 * 240 * 2
	add r0, #8
	svc #5 @ malloc
	push {r0}
	orr inactive_fb, r0, #7
	add inactive_fb, #1
	add active_fb, inactive_fb, #76800
	
	@ fill buffer with random ones and zeroes
	ldr r10, =76800
	mov r9, #0
1:	subs r10, r10, #1
	strb r9, [active_fb, r10] @ zero other framebuffer
	svc #206 @ rand syscall
	and r0, r0, #1
	strb r0, [inactive_fb, r10]
	bne 1b
	
	@ set first and last rows to zero
	mov r2, #320
	mov r1, #0
	mov r0, inactive_fb
	push {r1,r2}
	svc #7 @ memset
	pop {r1,r2}
	ldr r3, =76480
	add r0, r0, r3
	svc #7
	
	@ beginning of main loop, swap framebuffers
3:	ldr r0, =76480 @ 320 * 239
	str inactive_fb, [lcd_ptr, #0x10]
	mov inactive_fb, active_fb
	ldr active_fb, [lcd_ptr, #0x10]
	
	@ per-pixel loop
2:	mov r1, #16 @ 8 * 2
	mov r2, #0
	sub r0, #1
	
	@ loop to count up neighboring living cells
1:	subs r1, #2
	ldrsh r3, [offset_r, r1] @ cant use lsl #1
	add r3, r3, r0
	ldrb r3, [active_fb, r3]
	add r2, r2, r3
	bne 1b @ at end of loop, r1 and r3 can be discarded
	
	@ decides whether the cell should live or die based on neighbors
	ldrb r1, [active_fb, r0]
	add r2, r2, r1
	teq r2, #3
	moveq r1, #1
	teqne r2, #4
	movne r1, #0
	strb r1, [inactive_fb, r0]
	teq r0, #320
	bne 2b
	
	@ checks if the escape key is pressed
	ldr r0, =0x900E001C
	ldr r1, [r0]
	tst r1, #0x80
	beq 3b
	
	str backup_fb, [lcd_ptr, #0x10] @ restores OS framebuffer
	
	pop {r0}
	svc #6 @ free buffer
	pop {r4-r10, r12, pc}
offsets:
	.hword -321, -320, -319, -1, 1, 319, 320, 321

http://i.imgur.com/kV9RirP.gif

AutoHotkey

ahk discussion

rows := cols := 10                               ; set grid dimensions
i = -1,0,1, -1,1, -1,0,1                         ; neighbors' x-offsets
j = -1,-1,-1, 0,0, 1,1,1                         ; neighbors' y-offsets
StringSplit i, i, `,                             ; make arrays
StringSplit j, j, `,

Loop % rows {                                    ; setup grid of checkboxes
   r := A_Index, y := r*17-8                     ; looks good in VISTA
   Loop % cols {
      c := A_Index, x := c*17-5
      Gui Add, CheckBox, x%x% y%y% w17 h17 vv%c%_%r% gCheck
   }
}
Gui Add, Button, % "x12 w" x+2, step             ; button to step to next generation
Gui Show
Return

Check:
   GuiControlGet %A_GuiControl%                  ; manual set of cells
Return

ButtonStep:                                      ; move to next generation
   Loop % rows {
      r := A_Index
      Loop % cols {
         c := A_Index, n := 0
         Loop 8                                  ; w[x,y] <- new states
            x := c+i%A_Index%, y := r+j%A_Index%, n += 1=v%x%_%y%
         GuiControl,,v%c%_%r%,% w%c%_%r% := v%c%_%r% ? n=2 || n=3 : n=3
      }
   }
   Loop % rows {                                 ; update v[x,y] = states
      r := A_Index
      Loop % cols
         v%A_Index%_%r% := w%A_Index%_%r%
   }
Return

GuiClose:                                        ; exit when GUI is closed
ExitApp

AWK

50x20 grid (hardcoded) with empty border, filled with random cells, running for 220 generations, using ANSI escape-codes for output to terminal:

BEGIN {
 c=220; d=619; i=10000; 
 printf("\033[2J");      # Clear screen
 while(i--) m[i]=0;
 while(d--) m[int(rand()*1000)]=1;

 while(c--){
  for(i=52; i<=949; i++){
   d=m[i-1]+m[i+1]+m[i-51]+m[i-50]+m[i-49]+m[i+49]+m[i+50]+m[i+51];
   n[i]=m[i];
   if(m[i]==0 && d==3) n[i]=1;
   else if(m[i]==1 && d<2) n[i]=0;
        else if(m[i]==1 && d>3) n[i]=0;
  }
  printf("\033[1;1H");   # Home cursor
  for(i=1;i<=1000;i++)   # gridsize 50x20
  {
   if(n[i]) printf("O"); else printf(".");
   m[i]=n[i];
   if(!(i%50)) printf("\n");
  }
  printf("%3d\n",c);     # Countdown
  x=30000; while(x--) ;  # Delay
 }
}
Output:
Finally
..................................................
..........................................OO......
..........................................O.O.....
...........................................O......
......................................OOO.......OO
................................................OO
....................................O.....O.......
....................................O.....O.......
....................................O.....O.......
..................................................
......................................OOO.........
..................................................
..................................................
..................................................
..O...............................................
.O.O..............................................
O.O...........OO...........OO.....................
.O............OO.........O..O.....................
.........................OOO......................
..................................................
  0

Axe

This example is in need of improvement:
Improve performance and add a way to interactively seed the map.

This implementation uses the full screen buffer instead of a 3x3 grid. This naive, unoptimized version gets less than 1 FPS.

Full

While getKey(0)
End

ClrDraw
.BLINKER
Pxl-On(45,45)
Pxl-On(46,45)
Pxl-On(47,45)

.GLIDER
Pxl-On(1,1)
Pxl-On(2,2)
Pxl-On(2,3)
Pxl-On(3,1)
Pxl-On(3,2)

Repeat getKey(0)
 DispGraph
 EVOLVE()
 RecallPic
 ClrDrawʳ
End
Return

Lbl EVOLVE
For(Y,0,63)
 For(X,0,95)
  0→N
  For(B,Y-1,Y+1)
   For(A,X-1,X+1)
    pxl-Test(A,B)?N++
   End
  End
  pxl_Test(X,Y)?N--
  If N=3??(N=2?pxl-Test(X,Y))
   Pxl-On(X,Y)ʳ
  Else
   Pxl-Off(X,Y)ʳ
  End
 End
End
Return

BASIC

BASIC256

"Thunderbird" methuselah evolution in the Game of Life (created with BASIC-256)

Saving to PNG files function is omited. You can find it in the Galton box animation example.

# Conway's_Game_of_Life

X = 59 : Y = 35 : H = 4

fastgraphics
graphsize X*H,Y*H

dim c(X,Y) : dim cn(X,Y) : dim cl(X,Y)
# Thunderbird methuselah
c[X/2-1,Y/3+1] = 1 : c[X/2,Y/3+1] = 1 : c[X/2+1,Y/3+1] = 1	
c[X/2,Y/3+3] = 1 : c[X/2,Y/3+4] = 1 : c[X/2,Y/3+5] = 1

s = 0
do
	color black
	rect 0,0,graphwidth,graphheight
	alive = 0 : stable = 1
	s = s + 1
	for y = 0 to Y-1 
		for x = 0 to X-1
			xm1 = (x-1+X)%X : xp1 = (x+1+X)%X
			ym1 = (y-1+Y)%Y : yp1 = (y+1+Y)%Y
			cn[x,y] = c[xm1,y] + c[xp1,y]
			cn[x,y] = c[xm1,ym1] + c[x,ym1] + c[xp1,ym1] + cn[x,y]
			cn[x,y] = c[xm1,yp1] + c[x,yp1] + c[xp1,yp1] + cn[x,y]
			if c[x,y] = 1 then
				if cn[x,y] < 2 or cn[x,y] > 3 then 
					cn[x,y] = 0
				else 
					cn[x,y] = 1
					alive = alive + 1
				end if
			else 
				if cn[x,y] = 3 then 
					cn[x,y] = 1
					alive = alive + 1
				else
					cn[x,y] = 0
				end if
			end if
			if c[x,y] then
				if cn[x,y] then
					if cl[x,y] then color purple		# adult
					if not cl[x,y] then color green	        # newborn
				else 
					if cl[x,y] then color red		# old
					if not cl[x,y] then color yellow	# shortlived
				end if 
				rect x*H,y*H,H,H
			end if
		next x
	next y
	refresh
	pause 0.06
	# Copy arrays
	for i = 0 to X-1
		for j = 0 to Y-1
			if cl[i,j]<>cn[i,j] then stable = 0
			cl[i,j] = c[i,j]
			c[i,j] = cn[i,j]
		next j
	next i	
until not alive or stable

if not alive then
	print "Died in "+s+" iterations"
	color black
	rect 0,0,graphwidth,graphheight
	refresh
else 
	print "Stabilized in "+(s-2)+" iterations"	
end if
Output:
 Stabilized in 243 iterations

BBC BASIC

      dx% = 64
      dy% = 64
      DIM old&(dx%+1,dy%+1), new&(dx%+1,dy%+1)
      VDU 23,22,dx%*4;dy%*4;16,16,16,0
      OFF
      
      REM Set blinker:
      old&(50,50) = 1 : old&(50,51) = 1 : old&(50,52) = 1
      REM Set glider:
      old&(5,7) = 1 : old&(6,7) = 1 : old&(7,7) = 1 : old&(7,6) = 1 : old&(6,5) = 1
      
      REM Draw initial grid:
      FOR X% = 1 TO dx%
        FOR Y% = 1 TO dy%
          IF old&(X%,Y%) GCOL 11 ELSE GCOL 4
          PLOT 69, X%*8-6, Y%*8-4
        NEXT
      NEXT X%
      
      REM Run:
      GCOL 4,0
      REPEAT
        FOR X% = 1 TO dx%
          FOR Y% = 1 TO dy%
            S% = old&(X%-1,Y%) + old&(X%,Y%-1) + old&(X%-1,Y%-1) + old&(X%+1,Y%-1) + \
            \    old&(X%+1,Y%) + old&(X%,Y%+1) + old&(X%-1,Y%+1) + old&(X%+1,Y%+1)
            O% = old&(X%,Y%)
            N% = -(S%=3 OR (O%=1 AND S%=2))
            new&(X%,Y%) = N%
            IF N%<>O% PLOT X%*8-6, Y%*8-4
          NEXT
        NEXT X%
        SWAP old&(), new&()
        WAIT 30
      UNTIL FALSE
Output:


CASIO BASIC

Filename:JG VIDA 
Cls 
20→D 
D+2→F 
1→E 
{F,F}→Dim Mat A 
{F,F}→Dim Mat B 
{F,F}→Dim Mat C 
Fill(0,Mat A) 
Fill(0,Mat B) 
Fill(0,Mat C) 
"PONDERACION 1"?→G 
"PONDERACION 2"?→H 
For 1→I To D 
For 1→J To D 
RanInt#(1,G)→R 
If R≦H:Then  
0→Mat A[I+1,J+1] 
Else  
1→Mat A[I+1,J+1] 
IfEnd 
Next 
Next 
Goto 2 
Lbl 1 
Mat A→Mat C 
Mat B→Mat A 
Lbl 2 
For 1→I To D 
For 1→J To D 
I+1→K 
J+1→L 
K→M 
L+20→N 
If Mat C[K,L]=0:Then  
If Mat A[K,L]=1:Then For 0→R To 2 
For 0→S To 2 
PxlOn 3I+R-2,3J+S-2 
Next 
Next 
IfEnd 
IfEnd 
If Mat C[K,L]=1:Then  
If Mat A[K,L]=0:Then For 0→R To 2 
For 0→S To 2 
PxlOff 3I+R-2,3J+S-2 
Next 
Next 
IfEnd 
IfEnd 
Next 
Next
For 1→I To D 
For 1→J To D 
0→C 
I+1→K 
J+1→L 
Mat A[I,J]=1⇨C+1→C 
Mat A[I+1,J]=1⇨C+1→C 
Mat A[I+2,J]=1⇨C+1→C 
Mat A[I+2,J+1]=1⇨C+1→C 
Mat A[I+2,J+2]=1⇨C+1→C 
Mat A[I+1,J+2]=1⇨C+1→C 
Mat A[I,J+2]=1⇨C+1→C 
Mat A[I,J+1]=1⇨C+1→C 
If Mat A[K,L]=1:Then  
C<2⇨0→Mat B[K,L] 
C>3⇨0→Mat B[K,L] 
IfEnd 
If Mat A[K,L]=0:Then  
C=3⇨1→Mat B[K,L] 
IfEnd 
Next 
Next 
Goto 1

FreeBASIC

' FreeBASIC Conway's Game of Life
' May 2015
' 07-10-2016 cleanup/little changes
' moved test inkey outside the ScreenLock - ScreenUnLock block
' compile: fbc -s gui

Const As UInteger grid  = 300  '480 by 480
Const As UInteger gridy = grid
Const As UInteger gridx = grid
Const As UInteger pointsize = 5 'pixels
Const As UInteger steps = 10
Dim As UInteger gen, n, neighbours, x, y, was

Dim As String press

Const As UByte red   = 4  'red is color 6
Const As UByte white = 15 'color
Const As UByte black = 0  'color

'color 0 normaly is black
'color 1 normaly is dark blue
'color 2 normaly is green
Const As UInteger bot = 35 'this is 35 lines from the top of the page
Dim As UByte old( grid + 10, grid +10), new_( grid +10, grid +10)

'Set blinker:
' old( 160, 160) =1: old( 160, 170) =1 : old( 160, 180) =1

'Set blinker:
' old( 160, 20) =1: old( 160, 30) =1 : old( 160, 40) =1

'Set blinker:
' old( 20, 20) =1: old( 20, 30) =1 : old( 20, 40) =1

'Set glider:
'  old(  50,  70) =1: old(  60,  70) =1: old(  70,  70) =1
' old(  70,  60) =1: old(  60,  50) =1

' http://en.wikipedia.org/wiki/Conway%27s_Game_of_Life
' Thunderbird methuselah
'X = 59 : Y = 35 : H = 4
'c[X/2-1,Y/3+1] = 1 : c[X/2,Y/3+1] = 1 : c[X/2+1,Y/3+1] = 1
'c[X/2,Y/3+3] = 1 : c[X/2,Y/3+4] = 1 : c[X/2,Y/3+5] = 1

'xb = 59 : yb = 35
' old( Xb/2-1,Yb/3+1) =1: old(Xb/2,Yb/3+1) =1: old(Xb/2+1,Yb/3+1) =1
' old( Xb/2,Yb/3+3) =1: old(Xb/2,Yb/3+4) =1 :old(Xb/2,Yb/3+5) = 1
'r-pentomino
'  old( 150,140) =1: old( 160,140) =1
'  old( 140,150) =1 :old( 150,150) =1
'  old( 150,160) =1

'Die Hard  around 150 generations
' old( 150,140) =1: old(160,140) =1 : old(160,150) =1
' old( 200,150) =1: old(210,150) =1 : old(210,130) = 1 : old(220,150) = 1

'Acorn  around 450 generations
' it looks like this:
'   0X
'   000X
'   XX00XXX
old( 180,200) =1
old( 200,210) =1
old( 170,220) =1 : old( 180,220) =1 : old( 210,220) =1 : old( 220,220) =1 : old( 230,220) =1

Screen 20 'Resolution 800x600 with at least 256 colors

Color white
Line (10, 10) - (gridx + 10, gridy + 10),,B  'box from top left to bottom right

Locate bot, 1  'Use a standard place on the bottom of the page
Color white
Print " Welcome to Conway's Game of Life"
Print " Using a constrained playing field (300x300), the Acorn seed runs"
Print " for about 450 generations before it becomes stable (or stale)."
Print " Enter any key to start"
Beep
Sleep

Do      ' flush the key input buffer
  press = Inkey
Loop Until press = ""
'Print "                       "

'Draw initial grid
For x = 10 To gridX Step steps
  For y = 10 To gridY Step steps
    Color white 'old(x,y)
    If old(x,y) = 1 Then Circle (x + pointsize, y + pointsize), pointsize,,,,, F
  Next y
Next x
'
Locate bot, 1
Color white
Print " Welcome to Conway's Game of Life"
Print " Using a constrained playing field, the Acorn seed runs for      "
Print " about 450 generations before it becomes stable (or stale).    "
Color red
Print " Enter spacebar to continue or pause, ESC to stop"
Sleep
'
Do      ' flush the key input buffer
  press = Inkey
Loop Until press = ""

Do
  gen = gen + 1
  Locate bot+5,1
  Color white
  Print " Gen = "; gen
  ScreenLock
  For x = 10 To gridX Step steps
    For y = 10 To gridY Step steps
      'find number of live neighbours
      neighbours = old( x - steps, y - steps) +old( x , y - steps)
      neighbours = neighbours + old( x + steps, y -steps)
      neighbours = neighbours + old( x - steps, y) + old( x + steps, y)
      neighbours = neighbours + old( x - steps, y + steps)
      neighbours = neighbours + old( x, y + steps) +old( x + steps, y + steps)
      was =old( x, y)
      If was =0 Then
        If neighbours =3 Then N =1 Else N =0
      Else
        If neighbours =3  Or neighbours =2 Then N =1 Else N =0
      End If
      new_( x, y) = N
      If n = 2 Then Color white
      If n = 1 Then Color red
      If n = 0 Then Color black
      Circle (x + pointsize, y + pointsize), pointsize,,,,, F
    Next y
  Next x
  Color white
  Line (10, 10) - (gridx + 10, gridy + 10),,B  'box from top left to bottom right
  ' Locate bot,1
  '
  't = timer
  'do
  'loop until timer > t + .2
  ScreenUnlock
  ' might not be slow enough
  Sleep 70, 1  ' ignore key press

  press = Inkey
  If press = " " Then
    Do      ' flush the key input buffer
      press = Inkey
    Loop Until press = ""
    Do      ' wait until a key is pressed
      press = Inkey
    Loop Until press <> ""
  End If
  If press = Chr(27) Then Exit Do
  ' mouse click on close window "X"
  If press = Chr(255)+"k" Then End ' stop and close window

  For x =10 To gridX Step steps
    For y =10 To gridY Step steps
      old( x, y) =new_( x, y)
    Next y
  Next x

Loop ' UNTIL press = CHR(27) 'return to do loop up top until "esc" key is pressed.

Color white
Locate bot+3,1
Print Space(55) 'clear instructions
Locate bot+6,1
Print " Press any key to exit                            "
Sleep
End

GFA Basic

'
' Conway's Game of Life
'
' 30x30 world held in an array size 32x32
' world is in indices 1->30, 0 and 31 are always false, for neighbourhoods
'
DIM world!(32,32)
DIM ns%(31,31) ! used to hold the neighbour counts
clock%=1
'
' run the world
'
@setup_world
@open_window
DO
  @display_world
  t$=INKEY$
  EXIT IF t$="q" ! need to hold key down to exit
  @update_world
  DELAY 0.5 ! delay of 0.5s needed in compiled version
LOOP
@close_window
'
' Setup the world, with a blinker in one corner and a glider in the other
'
PROCEDURE setup_world
  ARRAYFILL world!(),FALSE
  ' blinker in lower-right
  world!(25,25)=TRUE
  world!(26,25)=TRUE
  world!(27,25)=TRUE
  ' glider in top-left
  world!(2,2)=TRUE
  world!(3,3)=TRUE
  world!(3,4)=TRUE
  world!(2,4)=TRUE
  world!(1,4)=TRUE
RETURN
'
' Count the number of neighbours of the point i,j
' (Assume i/j +/- 1 will not fall out of world)
'
FUNCTION count_neighbours(i%,j%)
  LOCAL count%,l%
  count%=0
  FOR l%=-1 TO 1
    IF world!(i%+l%,j%-1)
      count%=count%+1
    ENDIF
    IF world!(i%+l%,j%+1)
      count%=count%+1
    ENDIF
  NEXT l%
  IF world!(i%-1,j%)
    count%=count%+1
  ENDIF
  IF world!(i%+1,j%)
    count%=count%+1
  ENDIF
  RETURN count%
ENDFUNC
'
' Update the world one step
'
PROCEDURE update_world
  LOCAL i%,j%
  ' compute neighbour counts and store
  FOR i%=1 TO 30
    FOR j%=1 TO 30
      ns%(i%,j%)=@count_neighbours(i%,j%)
    NEXT j%
  NEXT i%
  ' update the world cells
  FOR i%=1 TO 30
    FOR j%=1 TO 30
      IF world!(i%,j%)
        SELECT ns%(i%,j%)
        CASE 0,1
          world!(i%,j%)=FALSE ! LONELY
        CASE 2,3
          world!(i%,j%)=TRUE ! LIVES
        CASE 4,5,6,7,8
          world!(i%,j%)=FALSE ! OVERCROWDED
        ENDSELECT
      ELSE
        IF ns%(i%,j%)=3
          world!(i%,j%)=TRUE ! BIRTH
        ELSE
          world!(i%,j%)=FALSE ! BARREN
        ENDIF
      ENDIF
    NEXT j%
  NEXT i%
  ' update the clock
  clock%=clock%+1
RETURN
'
' Display the world in window
'
PROCEDURE display_world
  LOCAL offsetx%,offsety%,i%,j%,x%,y%,scale%
  @clear_window
  ' show clock
  VSETCOLOR 2,0,0,0
  DEFTEXT 2
  PRINT AT(5,1);"Clock: ";clock%
  ' offset from top-left of display
  offsetx%=10
  offsety%=10
  ' colour to display active cell
  VSETCOLOR 1,15,0,0
  DEFFILL 1
  ' scale of display
  scale%=9
  ' display each cell in world
  FOR i%=1 TO 30
    FOR j%=1 TO 30
      IF world!(i%,j%)
        ' display active cell
        x%=offsetx%+scale%*i%
        y%=offsety%+scale%*j%
        PBOX x%,y%,x%+scale%,y%+scale%
      ENDIF
    NEXT j%
  NEXT i%
RETURN
'
' Manage window for display
'
PROCEDURE open_window
  OPENW 1
  CLEARW 1
RETURN
'
PROCEDURE clear_window
  VSETCOLOR 0,15,15,15
  DEFFILL 0
  PBOX 0,0,300,300
RETURN
'
PROCEDURE close_window
  CLOSEW 1
RETURN

GW-BASIC

Allows a blinker to be loaded. It also has a routine for randomising the grid; common objects like blocks, gliders, etc turn up semi-frequently so it won't take long to verify that these all work.

10 REM Conway's Game of Life
20 REM 30x30 grid, padded with zeroes as the boundary
30 DIM WORLD(31,  31, 1)
40 RANDOMIZE TIMER
50 CUR = 0 : BUF = 1
60 CLS
70 SCREEN 2
80 LOCATE 5,10: PRINT "Press space to perform one iteration"
90 LOCATE 6,10: PRINT "B to load a blinker"
100 LOCATE 7,10: PRINT "R to randomise the world"
110 LOCATE 8,10: PRINT "Q to quit"
120 K$ = INKEY$
130 IF K$=" " THEN GOSUB 250: GOSUB 180
140 IF K$="B" OR K$="b" THEN GOSUB 400: GOSUB 180
150 IF K$="R" OR K$="r" THEN GOSUB 480: GOSUB 180
160 IF K$="Q" OR K$="q" THEN SCREEN 0: END
170 GOTO 120
180 REM draw the world
190 FOR XX=1 TO 30
200 FOR YY=1 TO 30
210 PSET (XX, YY), 15*WORLD(XX, YY, CUR)
220 NEXT YY
230 NEXT XX
240 RETURN
250 REM perform one iteration
260 FOR XX=1 TO 30
270 FOR YY=1 TO 30
280 SM=0
290 SM = SM + WORLD(XX-1, YY-1, CUR) + WORLD(XX, YY-1, CUR) + WORLD(XX+1, YY-1, CUR)
300 SM = SM + WORLD(XX-1, YY, CUR) + WORLD(XX+1, YY, CUR)
310 SM = SM + WORLD(XX-1, YY+1, CUR) + WORLD(XX, YY+1, CUR) + WORLD(XX+1, YY+1, CUR)
320 IF SM<2 OR SM>3 THEN WORLD(XX, YY, BUF) = 0
330 IF SM=3 THEN WORLD(XX, YY, BUF) = 1
340 IF SM=2 THEN WORLD(XX,YY,BUF) = WORLD(XX,YY,CUR)
350 NEXT YY
360 NEXT XX
370 CUR = BUF : REM exchange identities of current and buffer
380 BUF = 1 - BUF
390 RETURN
400 REM produces a vertical blinker at the top left corner, and blanks the rest
410 FOR XX=1 TO 30
420 FOR YY=1 TO 30
430 WORLD(XX,YY,CUR) = 0
440 IF XX=2 AND YY<4 THEN WORLD(XX, YY, CUR) = 1
450 NEXT YY
460 NEXT XX
470 RETURN
480 REM randomizes the world with a density of 1/2
490 FOR XX = 1 TO 30
500 FOR YY = 1 TO 30
510 WORLD(XX, YY, CUR) = INT(RND*2)
520 NEXT YY
530 NEXT XX
540 RETURN

Liberty BASIC

It will run slow for grids above say 25!

      nomainwin

      gridX = 20
      gridY = gridX

      mult      =500 /gridX
      pointSize =360 /gridX

      dim old( gridX +1, gridY +1), new( gridX +1, gridY +1)

'Set blinker:
      old( 16, 16) =1: old( 16, 17) =1 : old( 16, 18) =1

'Set glider:
      old(  5,  7) =1: old(  6,  7) =1: old(  7,  7) =1
      old(  7,  6) =1: old(  6,  5) =1

      WindowWidth  =570
      WindowHeight =600

      open "Conway's 'Game of Life'." for graphics_nsb_nf as #w

      #w "trapclose [quit]"
      #w "down ; size "; pointSize
      #w "fill black"

'Draw initial grid
      for x = 1 to gridX
        for y = 1 to gridY
          '#w "color "; int( old( x, y) *256); " 0 255"
          if old( x, y) <>0 then #w "color red" else #w "color darkgray"
          #w "set "; x *mult +20; " "; y *mult +20
        next y
      next x
'   ______________________________________________________________________________
'Run
      do
        for x =1 to gridX
          for y =1 to gridY
            'find number of live Moore neighbours
            neighbours =old( x -1, y -1) +old( x, y -1) +old( x +1, y -1)+_
                        old( x -1, y)                   +old( x +1, y   )+_
                        old( x -1, y +1) +old( x, y +1) +old( x +1, y +1)
            was =old( x, y)
            if was =0 then
                if neighbours =3 then N =1 else N =0
            else
                if neighbours =3  or neighbours =2 then N =1 else N =0Tail Recursive
            end if
            new( x, y) = N
            '#w "color "; int( N /8 *256); " 0 255"
            if N <>0 then #w "color red" else #w "color darkgray"
            #w "set "; x *mult +20; " "; y *mult +20
          next y
        next x
        scan
'swap
        for x =1 to gridX
          for y =1 to gridY
            old( x, y) =new( x, y)
          next y
        next x
'Re-run until interrupted...
      loop until FALSE
'User shutdown received
    [quit]
    close #w
    end

MSX Basic

10 DEFINT A-Z
20 DIM L(16,16), N(16,16)
30 M = 16
40 CLS
50 PRINT "PRESS A KEY TO START...";
60 W = RND(1)
70 IF INKEY$ = "" THEN 60
80 CLS
100 FOR I=1 TO M
110   FOR J=1 TO M
120     IF RND(1)>=.7 THEN N(I,J) = 1 ELSE N(I,J) = 0
130   NEXT J
140 NEXT I
1000 FOR I=0 TO M+1
1010   LOCATE I,0 : PRINT "+";
1020   LOCATE I,M+1 : PRINT "+";
1030   LOCATE 0,I : PRINT "+";
1040   LOCATE M+1,I : PRINT "+";
1050 NEXT I
1080 G=0
1090 LOCATE 1,M+3 : PRINT USING "#####";G
1100 FOR I=1 TO M
1110   FOR J=1 TO M
1115     W = N(I,J) : L(I,J) = W
1120     LOCATE I,J 
1130     IF W=0 THEN PRINT " "; ELSE PRINT "*";
1160   NEXT J
1170 NEXT I
1180 FOR I=1 TO M
1190   FOR J=1 TO M
1200     NC=0
1210     FOR K=I-1 TO I+1
1215       IF K=0 OR K>M THEN 1260
1220       FOR W=J-1 TO J+1
1230         IF W=0 OR W>M OR (K=I AND W=J) THEN 1250
1240         NC = NC + L(K,W)
1250       NEXT W
1260     NEXT K
1270     IF NC=2 THEN N(I,J)=L(I,J) : GOTO 1300
1280     IF NC=3 THEN N(I,J)=1 ELSE N(I,J)=0
1300   NEXT J
1310 NEXT I
1350 G=G+1
1360 GOTO 1090

PureBasic

EnableExplicit
Define.i x, y ,Xmax ,Ymax ,N
Xmax = 13 : Ymax = 20
Dim     world.i(Xmax+1,Ymax+1)
Dim Nextworld.i(Xmax+1,Ymax+1)  

; Glider test
;------------------------------------------
 world(1,1)=1 : world(1,2)=0 : world(1,3)=0
 world(2,1)=0 : world(2,2)=1 : world(2,3)=1
 world(3,1)=1 : world(3,2)=1 : world(3,3)=0
;------------------------------------------
 
OpenConsole()
EnableGraphicalConsole(1)
ClearConsole()
Print("Press any key to interrupt")
Repeat
  ConsoleLocate(0,2)
  PrintN(LSet("", Xmax+2, "-"))
 ;---------- endless world ---------
  For y = 1 To Ymax
    world(0,y)=world(Xmax,y)
    world(Xmax+1,y)=world(1,y)  
  Next
  For x = 1 To Xmax
    world(x,0)=world(x,Ymax)
    world(x,Ymax+1)=world(x,1)
  Next
  world(0     ,0     )=world(Xmax,Ymax)
  world(Xmax+1,Ymax+1)=world(1   ,1   )
  world(Xmax+1,0     )=world(1   ,Ymax)
  world(     0,Ymax+1)=world(Xmax,1   )
 ;---------- endless world ---------
  For y = 1 To Ymax
    Print("|") 
    For x = 1 To Xmax
      Print(Chr(32+world(x,y)*3))
      N = world(x-1,y-1)+world(x-1,y)+world(x-1,y+1)+world(x,y-1)
      N + world(x,y+1)+world(x+1,y-1)+world(x+1,y)+world(x+1,y+1)
      If (world(x,y) And (N = 2 Or N = 3))Or (world(x,y)=0 And N = 3)
        Nextworld(x,y)=1      
      Else
        Nextworld(x,y)=0
      EndIf
    Next
    PrintN("|")
  Next
  PrintN(LSet("", Xmax+2, "-"))
  Delay(100) 
  ;Swap world() , Nextworld()    ;PB  <4.50
  CopyArray(Nextworld(), world());PB =>4.50
  Dim Nextworld.i(Xmax+1,Ymax+1) 
Until Inkey() <> ""
 
PrintN("Press any key to exit"): Repeat: Until Inkey() <> ""

Sample output:


QBasic

El código es de Ben Wagner (bwgames.org)
The code is from Ben Wagner (bwgames.org)
Yo solo lo transcrito y comento al español.
I just transcribed it and comment it in Spanish.

SCREEN 9, 0, 0, 1

RANDOMIZE TIMER

WINDOW (0, 0)-(80, 80)

'La matrizA es la actual, la matrizB es la siguiente iteración
'ArrayA is current, arrayB is next iteration
DIM matrizA(-1 TO 81, -1 TO 81)
DIM matrizB(-1 TO 81, -1 TO 81)

'Aleatorizar las celdas de matrizA, 
'Randomize cells in arrayA,
'y establecer las de matrizB a 0
'and set those of matrixB to 0
y = 0
DO
	x = 0  
	DO
		x = x + 1
		matrizA(x, y) = INT(RND + .5)
        matrizB(x, y) = 0
    LOOP UNTIL x > 80
    
    y = y + 1
LOOP UNTIL y > 80

''--- Bucle Principal ---
'' --- Main Loop ---
DO
    CLS   
    'Dibuja la matriz 
    'Draw the matrix
    y = 0
    DO
        x = 0			 
        DO
            IF matrizA(x, y) = 1 THEN LINE (x, y)-(x + 1, y + 1), 1, BF
            x = x + 1
        LOOP UNTIL x > 80
        
        y = y + 1
    LOOP UNTIL y > 80
    
    'Cuenta el recuento de la celda circundante
    'Counts the count of the surrounding cell
     'Luego aplica la operación a la celda
     'Then apply the operation to the cell
    y = 0
    DO
        x = 0
        DO
            'Cuenta las células circundantes
            'Count the surrounding cells
            cuenta = 0
            
            IF matrizA(x - 1, y + 1) = 1 THEN cuenta = cuenta + 1
            IF matrizA(x, y + 1) = 1 THEN cuenta = cuenta + 1
            IF matrizA(x + 1, y + 1) = 1 THEN cuenta = cuenta + 1
            IF matrizA(x - 1, y) = 1 THEN cuenta = cuenta + 1
            IF matrizA(x + 1, y) = 1 THEN cuenta = cuenta + 1
            IF matrizA(x - 1, y - 1) = 1 THEN cuenta = cuenta + 1
            IF matrizA(x, y - 1) = 1 THEN cuenta = cuenta + 1
            IF matrizA(x + 1, y - 1) = 1 THEN cuenta = cuenta + 1
            
            'Aplica las operaciones
            'Apply the operations
            'Muerte
            'Death
            IF matrizA(x, y) = 1 THEN
                IF cuenta = 2 OR cuenta = 3 THEN matrizB(x, y) = 1 ELSE matrizB(x, y) = 0
            END IF
            
            'Nacimiento
            'Birth
            IF matrizA(x, y) = 0 THEN
                IF cuenta = 3 THEN matrizB(x, y) = 1 ELSE matrizB(x, y) = 0
            END IF
            x = x + 1
        LOOP UNTIL x > 80
        
        y = y + 1
    LOOP UNTIL y > 80
    
    'Actualiza la matriz con la nueva matriz que hemos calculado.
    'Update the matrix with the new matrix that we have calculated.
    y = 0
    DO
        x = 0
        DO
            x = x + 1
            matrizA(x, y) = matrizB(x, y)
        LOOP UNTIL x > 80
        y = y + 1
        
    LOOP UNTIL y > 80
    PCOPY 0, 1
LOOP WHILE INKEY$ = ""

Sinclair ZX81 BASIC

Requires at least 2k of RAM. Expects to find a square array of "0" and "1" characters, L$(), giving the initial configuration. You can build this up by issuing commands in immediate mode and then run the program by entering GOTO 1000, but it's probably easier—assuming you can spare some RAM—to write the setup into the program using line numbers below 1000.

The graphics character in lines 1030 to 1060 can be obtained by typing SHIFT9 then SHIFTH, and the one in line 1130 by typing SHIFT9 then SPACE.

1000 LET M=LEN L$(1)
1010 DIM N$(M,M)
1020 FOR I=0 TO M+1
1030 PRINT AT I,0;"▩"
1040 PRINT AT I,M+1;"▩"
1050 PRINT AT 0,I;"▩"
1060 PRINT AT M+1,I;"▩"
1070 NEXT I
1080 LET G=0
1090 PRINT AT 1,M+3;G
1100 FOR I=1 TO M
1110 FOR J=1 TO M
1120 IF L$(I,J)="0" THEN GOTO 1150
1130 PRINT AT I,J;"■"
1140 GOTO 1160
1150 PRINT AT I,J;" "
1160 NEXT J
1170 NEXT I
1180 FOR I=1 TO M
1190 FOR J=1 TO M
1200 LET N=0
1210 FOR K=I-1 TO I+1
1220 FOR L=J-1 TO J+1
1230 IF K=0 OR K>M OR L=0 OR L>M OR (K=I AND L=J) THEN GOTO 1250
1240 LET N=N+VAL L$(K,L)
1250 NEXT L
1260 NEXT K
1270 LET N$(I,J)=L$(I,J)
1280 IF N<=1 OR N>=4 THEN LET N$(I,J)="0"
1290 IF N=3 THEN LET N$(I,J)="1"
1300 NEXT J
1310 NEXT I
1320 FOR I=1 TO M
1330 LET L$(I)=N$(I)
1340 NEXT I
1350 LET G=G+1
1360 GOTO 1090

To run the blinker, add this code:

10 DIM L$(3,3)
20 LET L$(1)="000"
30 LET L$(2)="111"
40 LET L$(3)="000"

A screenshot of it running can be found here.

To try a random starting configuration on a 16x16 grid, use this:

10 DIM L$(16,16)
20 FOR I=1 TO 16
30 FOR J=1 TO 16
40 LET L$(I,J)="0"
50 IF RND>=.7 THEN LET L$(I,J)="1"
60 NEXT J
70 NEXT I

A screenshot is here.

TI-83 BASIC

This implementation is loosely based on the Processing Version. It uses the home screen and draws cells as "X"s. It is extremely slow, and limited to a bounding box of 16 by 8. In order for it to work, you need to initialize arrays [A] and [B] to be 18x10.

 PROGRAM:CONWAY
:While 1
:For(X,2,9,1)
:For(Y,2,17,1)
:If [A](Y,X)
:Then
:Output(X-1,Y-1,"X")
:Else
:Output(X-1,Y-1," ")
:End
:[A](Y-1,X-1)+[A](Y,X-1)+[A](Y+1,X-1)+[A](Y-1,X)+[A](Y+1,X)+[A](Y-1,X+1)+[A](Y,X+1)+[A](Y+1,X+1)→N
:If ([A](Y,X) and (N=2 or N=3)) or (not([A](Y,X)) and N=3)
:Then
:1→[B](Y,X)
:Else
:0→[B](Y,X)
:End
:End
:End
:[B]→[A]
:End

Here is an additional, very simple program to input the top corner of the GRAPH screen into the starting array. Make sure to draw on pixels in the rectangle (1,1) to (8,16).

PROGRAM:PIC2LIFE
:For(I,0,17,1)
:For(J,0,9,1)
:pxl-Test(J,I)→[A](I+1,J+1)
:End
:End

TI-89 BASIC

This program draws its cells as 2x2 blocks on the graph screen. In order to avoid needing external storage for the previous generation, it uses the upper-left corner of each block to mark the next generation's state in all cells, then updates each cell to match its corner pixel.

A further improvement would be to have an option to start with the existing picture rather than clearing, and stop at a point where the picture has clean 2x2 blocks.

Define life(pattern) = Prgm
  Local x,y,nt,count,save,xl,yl,xh,yh
  Define nt(y,x) = when(pxlTest(y,x), 1, 0)
  
  {}→save
  setGraph("Axes", "Off")→save[1]
  setGraph("Grid", "Off")→save[2]
  setGraph("Labels", "Off")→save[3]
  FnOff
  PlotOff
  ClrDraw

  If pattern = "blinker" Then
    36→yl
    40→yh
    78→xl
    82→xh
    PxlOn  36,80
    PxlOn  38,80
    PxlOn  40,80
  ElseIf pattern = "glider" Then
    30→yl
    40→yh
    76→xl
    88→xh
    PxlOn  38,76
    PxlOn  36,78
    PxlOn  36,80
    PxlOn  38,80
    PxlOn  40,80
  ElseIf pattern = "r" Then
    38-5*2→yl
    38+5*2→yh
    80-5*2→xl
    80+5*2→xh
    PxlOn  38,78
    PxlOn  36,82
    PxlOn  36,80
    PxlOn  38,80
    PxlOn  40,80
  EndIf

  While getKey() = 0
    © Expand upper-left corner to whole cell
    For y,yl,yh,2
      For x,xl,xh,2
        If pxlTest(y,x) Then
          PxlOn y+1,x
          PxlOn y+1,x+1
          PxlOn y,  x+1
        Else
          PxlOff y+1,x
          PxlOff y+1,x+1
          PxlOff y,  x+1
        EndIf
      EndFor
    EndFor

    © Compute next generation
    For y,yl,yh,2
      For x,xl,xh,2
        nt(y-1,x-1) + nt(y-1,x) + nt(y-1,x+2) + nt(y,x-1) + nt(y+1,x+2) + nt(y+2,x-1) + nt(y+2,x+1) + nt(y+2,x+2) → count
        If count = 3 Then
          PxlOn y,x
        ElseIf count ≠ 2 Then
          PxlOff y,x
        EndIf
      EndFor
    EndFor
  EndWhile

  © Restore changed options
  setGraph("Axes", save[1])
  setGraph("Grid", save[2])
  setGraph("Labels", save[3])
EndPrgm

Batch File

This code takes three parameters: m chance iterations Where,
m - The length and width of the array of cells
chance - The percent chance of any cell within the set array initially being alive. Full numbers only.
iterations - The amount of iterations of evolution the array goes through to display.

If no parameters are parsed, it defaults to 5 iterations of the blinking example.

@echo off
setlocal enabledelayedexpansion

if "%1"=="" (
  call:_blinkerArray
) else (
  call:_randomArray %*
)

for /l %%i in (1,1,%iterations%) do (
  call:_setStatus
  call:_display
  
  for /l %%m in (1,1,%m%) do (
    for /l %%n in (1,1,%m%) do (
      call:_evolution %%m %%n
    )
  )
)
  
:_blinkerArray
for /l %%m in (0,1,4) do (
  for /l %%n in (0,1,4) do (
    set cell[%%m][%%n]=0
  )
)
set cell[2][1]=1
set cell[2][2]=1
set cell[2][3]=1
set iterations=5
set m=3
set cellsaddone=4

exit /b

:_randomArray
set cellsaddone=%1+1
for /l %%m in (0,1,%cellsaddone%) do for /l %%n in (0,1,%cellsaddone%) do set cell[%%m][%%n]=0
for /l %%m in (1,1,%1) do (
  for /l %%n in (1,1,%1) do (
    set /a cellrandom=!random! %% 101
    set cell[%%m][%%n]=0
    if !cellrandom! leq %2 set cell[%%m][%%n]=1
  )
)
set iterations=%3
set m=%1

exit /b

:_setStatus
for /l %%m in (0,1,%cellsaddone%) do (
  for /l %%n in (0,1,%cellsaddone%) do (
    if !cell[%%m][%%n]!==1 set cellstatus[%%m][%%n]=alive
    if !cell[%%m][%%n]!==0 set cellstatus[%%m][%%n]=dead
  )
)
exit /b


:_evolution
set /a lowerm=%1-1
set /a upperm=%1+1
set /a lowern=%2-1
set /a uppern=%2+1
set numm=%1
set numn=%2
set sum=0
for /l %%m in (%lowerm%,1,%upperm%) do (
  for /l %%n in (%lowern%,1,%uppern%) do (
    if %%m==%numm% (
      if %%n==%numn% (
        set /a sum=!sum!
      ) else (
        if !cellstatus[%%m][%%n]!==alive set /a sum+=1
      )
    ) else (
      if !cellstatus[%%m][%%n]!==alive set /a sum+=1
    )
  )
)
goto:!cell[%numm%][%numn%]!

exit /b

:0
set alive=3
set death=0 1 2 4 5 6 7 8 
for %%i in (%alive%) do if %sum%==%%i set cell[%numm%][%numn%]=1
for %%i in (%death%) do if %sum%==%%i set cell[%numm%][%numn%]=0
exit /b

:1
set alive=2 3
set death=0 1 4 5 6 7 8
for %%i in (%alive%) do if %sum%==%%i set cell[%1][%2]=1
for %%i in (%death%) do if %sum%==%%i set cell[%1][%2]=0
exit /b

:_display
echo.
for /l %%m in (1,1,%m%) do (
  set m%%m= 
  for /l %%n in (1,1,%m%) do set m%%m=!m%%m! !cell[%%m][%%n]!
  echo !m%%m!
)

exit /b
Output:

Blinking example:

0 0 0
1 1 1
0 0 0

0 1 0
0 1 0
0 1 0

0 0 0
1 1 1
0 0 0

0 1 0
0 1 0
0 1 0

0 0 0
1 1 1
0 0 0
Input:
10 35 5
Output:
1 1 0 0 0 0 1 1 0 0
1 1 0 0 1 1 0 1 1 0
1 0 1 1 0 0 0 1 0 0
0 1 0 1 0 1 0 1 0 1
1 0 0 0 1 0 0 1 0 1
0 0 0 1 0 0 0 0 0 0
0 0 0 0 0 0 1 1 0 0
0 0 1 0 0 0 0 0 0 0
1 0 1 0 0 0 0 0 1 1
1 1 0 0 1 0 0 1 1 0

1 1 0 0 0 1 1 1 1 0
0 0 0 1 1 1 0 0 1 0
1 0 0 1 0 1 0 1 0 0
1 1 0 1 0 0 0 1 0 0
0 0 1 1 1 0 1 0 0 0
0 0 0 0 0 0 1 1 1 0
0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 1 1 0
1 0 1 1 0 0 0 1 1 1
1 1 0 0 0 0 0 1 1 1

0 0 0 0 0 1 1 1 1 0
1 1 1 1 0 0 0 0 1 0
1 1 0 1 0 1 0 1 1 0
1 1 0 0 0 1 0 1 0 0
0 1 1 1 1 1 1 0 1 0
0 0 0 1 0 1 1 1 0 0
0 0 0 0 0 0 1 0 0 0
0 1 1 0 0 0 0 1 0 1
1 0 1 0 0 0 1 0 0 0
1 1 1 0 0 0 0 1 0 1

0 1 1 0 0 0 1 1 1 0
1 0 0 1 0 1 0 0 0 1
0 0 0 1 0 0 0 1 1 0
0 0 0 0 0 0 0 0 0 0
1 1 0 1 0 0 0 0 1 0
0 0 0 1 0 0 0 0 0 0
0 0 1 0 0 1 0 0 1 0
0 1 1 0 0 0 1 1 0 0
1 0 0 1 0 0 1 1 0 0
1 0 1 0 0 0 0 0 0 0

0 1 1 0 0 0 1 1 1 0
0 1 0 1 1 0 0 0 0 1
0 0 0 0 1 0 0 0 1 0
0 0 1 0 0 0 0 1 1 0
0 0 1 0 0 0 0 0 0 0
0 1 0 1 1 0 0 0 0 0
0 1 1 1 0 0 1 1 0 0
0 1 1 1 0 1 0 0 1 0
1 0 0 1 0 0 1 1 0 0
0 1 0 0 0 0 0 0 0 0

Befunge

Takes as input the width and height of the universe, followed by the pattern (which is terminated by the end of file). If your interpreter can't easily redirect the input from a file, or doesn't handle end-of-file detection, you can also type in the pattern manually and mark the end of input with a ~ character.

The pattern format itself is fairly lenient in what it accepts. You can use either space or . for dead cells, and o, O, * or # for live cells. This should make it fairly easy to cut and paste a number of existing formats, including the Life 1.05 format and the Plaintext .cells format used on the LifeWiki website (comments aren't supported though, so make sure to copy just the pattern itself).

In Befunge-93, the maximum value for the width and height of the universe is 127, but there is an additional constraint of 4080 cells in total, so the largest universe would really be something like 120x34 or 68x60. Befunge-98 has no real limit on the size, although in practice a much larger universe will probably be unbearably slow.

00p10p20p30p&>40p&>50p60p>$#v~>:55+-vv+`1:%3:+*g04p03< >3/"P"%\56v>p\56*8*/8+:v
v5\`\"~"::-*3p06!:!-+67:_^#!<*<!g06!<>1+70g*\:3/"P"%v^ ^::+*g04%<*0v`1:%3\gp08<
>6*`*#v_55+-#v_p10g1+10p>^pg08g07+gp08:+8/*8*65\p07:<^ >/10g-50g^87>+1+:01p/8/v
>%#74#<-!!70p 00g::1+00p:20g\-:0`*+20p10g::30g\-:0`*+^ ^2+2+g03*<*:v+g06p09:%2<
.v,:*93"[2J"0<>"H["39*,,,50g0v!:-1,+55$_:40g3*20g+2+2/\-40g%50g3^/%\ >:3-\3-90v
O>"l52?[">:#,_^v/3+2:*g05g04$_>:10p40g0^!:-1,g+4\0%2/+1+`1:%3\g+8<^: $v10!*-g<<
g+70g80gp:#v_$^>1-:::"P"%\"P"/8+:10v  >/10g+1-50g+50g%40g*+::3/"P"^>!|>g*70g80g
:p00%g04:-1<<$_^#!:pg01%"P"\*8%8gp<<  ^3\%g04+g04-1+g00%3:%9+4:-1p06\<90p01/g04
Input:

Here's an example of what the input could look like for the Blinker pattern in a 5x5 universe:

5
5
OOO

And for a more complicated example, this is the Queen bee pattern in a 50x30 universe:

50
30
...*
..*.*
.*...*
..***
**...**
Output:

In order to produce an animated view of the universe evolving, we use a few basic ANSI escape sequences to reset the cursor position between frames. Without ANSI support, you'll just see the individual frames scrolling past with a bit of junk inbetween. The output shown below is just an extract of the first three generations of the Blinker in a 5x5 universe.

.....   .....   .....
.....   ..O..   .....
.OOO.   ..O..   .OOO.
.....   ..O..   .....
.....   .....   .....

Brainf***

A life-program written in Brainf***

With Example-Output.

Brat

width = 3
height = 3
rounds = 3

universe = [[0 1 0]
            [0 1 0]
            [0 1 0]]

next = height.of({width.of(0)})

cell = { x, y |
  true? x < width && { x >= 0 && { y >= 0 && { y < height }}}
  {
    universe[y][x]
  }
  { 0 }
}

neighbors = { x, y |
  cell(x - 1, y - 1) +
  cell(x, y - 1) +
  cell(x + 1, y - 1) +
  cell(x + 1, y) +
  cell(x + 1, y + 1) +
  cell(x, y + 1) +
  cell(x - 1, y + 1) +
  cell(x - 1, y)
}

set_next = { x, y, v |
  next[y][x] = v
}

step = {
  universe.each_with_index { row, y |
    row.each_with_index { c, x |
      n = neighbors(x, y)

      when { n < 2 } { set_next x,y, 0 }
           { n > 3 } { set_next x, y, 0 }
           { n == 3 } { set_next x, y, 1 }
           { true } { set_next x, y, c }
    }
  }

  u2 = universe
  universe = next
  next = u2
}

display = {
  p universe.map({ r |
    r.map({ n | true? n == 0, '-', "O" }).join
  }).join("\n")
}

rounds.times {
  display
  p
  step
}
Output:
-O-
-O-
-O-

---
OOO
---

-O-
-O-
-O-

BQN

Life{
   r¯1(1)¯1(2+≢𝕩)𝕩
   s´ (1∾<r)  34 = <+´ ¯101 (1) ¯101  <r
   1(1) ¯1(1) 1 ¯1s
}

blinker>000,111,000
(<".#") ¨˜  Life(3) blinker
Output:
┌─                         
· ┌─      ┌─      ┌─       
  ╵"...   ╵".#.   ╵"...    
    ###     .#.     ###    
    ..."    .#."    ..."   
        ┘       ┘       ┘  
                          ┘

C

Play game of life on your console: gcc -std=c99 -Wall game.c; ./a.out [width] [height]

#include <stdio.h>
#include <stdlib.h>
#include <unistd.h>

#define for_x for (int x = 0; x < w; x++)
#define for_y for (int y = 0; y < h; y++)
#define for_xy for_x for_y
void show(void *u, int w, int h)
{
	int (*univ)[w] = u;
	printf("\033[H");
	for_y {
		for_x printf(univ[y][x] ? "\033[07m  \033[m" : "  ");
		printf("\033[E");
	}
	fflush(stdout);
}

void evolve(void *u, int w, int h)
{
	unsigned (*univ)[w] = u;
	unsigned new[h][w];

	for_y for_x {
		int n = 0;
		for (int y1 = y - 1; y1 <= y + 1; y1++)
			for (int x1 = x - 1; x1 <= x + 1; x1++)
				if (univ[(y1 + h) % h][(x1 + w) % w])
					n++;

		if (univ[y][x]) n--;
		new[y][x] = (n == 3 || (n == 2 && univ[y][x]));
	}
	for_y for_x univ[y][x] = new[y][x];
}

void game(int w, int h)
{
	unsigned univ[h][w];
	for_xy univ[y][x] = rand() < RAND_MAX / 10 ? 1 : 0;
	while (1) {
		show(univ, w, h);
		evolve(univ, w, h);
		usleep(200000);
	}
}

int main(int c, char **v)
{
	int w = 0, h = 0;
	if (c > 1) w = atoi(v[1]);
	if (c > 2) h = atoi(v[2]);
	if (w <= 0) w = 30;
	if (h <= 0) h = 30;
	game(w, h);
}

Also see Conway's Game of Life/C

C for Arduino

Play game of life on your arduino (using FastLED) - based on the C example.

#include <FastLED.h>

#define LED_PIN     3
#define LED_TYPE    WS2812B
#define WIDTH       20
#define HEIGHT      15
#define NUM_LEDS    (WIDTH*HEIGHT)
#define BRIGHTNESS  100
#define COLOR_ORDER GRB
#define SERPENTINE  1
#define FRAMERATE   1
#define SCALE       1

CRGB leds[NUM_LEDS];

#include <stdio.h>
#include <stdlib.h>
#include <unistd.h>

#define for_x for (int x = 0; x < w; x++)
#define for_y for (int y = 0; y < h; y++)
#define for_xy for_x for_y

const int w = WIDTH, h = HEIGHT;
unsigned univ[h][w];

int getLEDpos(int x, int y){ // for a serpentine raster
    return (y%2 || !SERPENTINE) ? y*WIDTH + x : y*WIDTH + (WIDTH - 1 - x);
}

void show(void *u, int w, int h)
{
    int (*univ)[w] = u;
    for_xy {
        leds[getLEDpos(x, y)] = univ[y][x] ? CRGB::White: CRGB::Black;
    }
    FastLED.show();
}

void evolve(void *u, int w, int h)
{
    unsigned (*univ)[w] = u;
    unsigned newU[h][w];

    for_y for_x {
        int n = 0;
        for (int y1 = y - 1; y1 <= y + 1; y1++)
            for (int x1 = x - 1; x1 <= x + 1; x1++)
                if (univ[(y1 + h) % h][(x1 + w) % w])
                    n++;

        if (univ[y][x]) n--;
        newU[y][x] = (n == 3 || (n == 2 && univ[y][x]));
    }
    for_y for_x univ[y][x] = newU[y][x];
}

void setup(){
    //Initialize leds after safety period
    FastLED.delay(500);
    FastLED.addLeds<LED_TYPE, LED_PIN, COLOR_ORDER>(leds, NUM_LEDS).setCorrection( TypicalLEDStrip );
    FastLED.setBrightness(  BRIGHTNESS );
    
    //Seed random with analog noise
    randomSeed(analogRead(0));

    for_xy univ[y][x] = random() %10 <= 1 ? 1 : 0;
}

void loop(){
    show(univ, w, h);
    evolve(univ, w, h);
    FastLED.delay(1000/FRAMERATE);
}

C for Arduino

Play game of life on your arduino (using two MAX7219 led 'screens') - based on the C example.

#include <MaxMatrix.h>

int DIN = 11;   // DIN pin of MAX7219 module
int CS = 12;    // CS pin of MAX7219 module
int CLK = 13;   // CLK pin of MAX7219 module
int DIN2 = 8;   // DIN pin of MAX7219 module
int CS2 = 9;    // CS pin of MAX7219 module
int CLK2 = 10;   // CLK pin of MAX7219 module
int maxInUse = 1;

//setup two screens
MaxMatrix m(DIN, CS, CLK, maxInUse); 
MaxMatrix m2(DIN2, CS2, CLK2, maxInUse); 

void setup() {
  randomSeed(analogRead(0));
  m.init(); // MAX7219 initialization
  m.setIntensity(0); // initial led matrix intensity, 0-15
  m.clear(); // Clears the display
  m2.init(); // MAX7219 initialization
  m2.setIntensity(0); // initial led matrix intensity, 0-15
  m2.clear(); // Clears the display
}

void loop() {
  game(16,8);//w,h
}

void setDot(int x,int y,bool isOn){
  if(x<8){
    m.setDot(x,y,isOn); 
  }else{
    m2.setDot(x-8,y,isOn); 
  }
}

void show(void *u, int w, int h){
  int (*univ)[w] = u;
  for (int y = 0; y < h; y++){
    for (int x = 0; x < w; x++){
      bool sh=(univ[y][x]==1);
      setDot(x,y,sh); 
    }
  }    
}
 
void evolve(void *u, int w, int h){
  unsigned (*univ)[w] = u;
  unsigned newar[h][w];
 
  for (int y = 0; y < h; y++){
    for (int x = 0; x < w; x++){
      int n = 0;
      for (int y1 = y - 1; y1 <= y + 1; y1++)
        for (int x1 = x - 1; x1 <= x + 1; x1++)
          if (univ[(y1 + h) % h][(x1 + w) % w])
            n++;
   
      if (univ[y][x]) n--;
      newar[y][x] = (n == 3 || (n == 2 && univ[y][x]));
     
    }
  } 
 
  for (int y = 0; y < h; y++){
    for (int x = 0; x < w; x++){
      univ[y][x] = newar[y][x];
    }
  }
}
 
void game(int w, int h) {
  unsigned univ[h][w];
  for (int x = 0; x < w; x++){
    for (int y = 0; y < h; y++){
      univ[y][x] = random(0, 100)>65 ? 1 : 0;
    }
  }
  int sc=0;
  while (1) {
    show(univ, w, h);
    evolve(univ, w, h);
    delay(150);
    sc++;if(sc>150)break;
  }
}

C#

using System;
using System.Text;
using System.Threading;
 
namespace ConwaysGameOfLife
{
    // Plays Conway's Game of Life on the console with a random initial state.
    class Program
    {
        // The delay in milliseconds between board updates.
        private const int DELAY = 50;
 
        // The cell colors.
        private const ConsoleColor DEAD_COLOR = ConsoleColor.White;
        private const ConsoleColor LIVE_COLOR = ConsoleColor.Black;
 
        // The color of the cells that are off of the board.
        private const ConsoleColor EXTRA_COLOR = ConsoleColor.Gray;
 
        private const char EMPTY_BLOCK_CHAR = ' ';
        private const char FULL_BLOCK_CHAR = '\u2588';
 
        // Holds the current state of the board.
        private static bool[,] board;
 
        // The dimensions of the board in cells.
        private static int width = 32;
        private static int height = 32;
 
        // True if cell rules can loop around edges.
        private static bool loopEdges = true;
 
 
        static void Main(string[] args)
        {
            // Use initializeRandomBoard for a larger, random board.
            initializeDemoBoard();
 
            initializeConsole();
 
            // Run the game until the Escape key is pressed.
            while (!Console.KeyAvailable || Console.ReadKey(true).Key != ConsoleKey.Escape) {
                Program.drawBoard();
                Program.updateBoard();
 
                // Wait for a bit between updates.
                Thread.Sleep(DELAY);
            }
        }
 
        // Sets up the Console.
        private static void initializeConsole()
        {
            Console.BackgroundColor = EXTRA_COLOR;
            Console.Clear();
 
            Console.CursorVisible = false;
 
            // Each cell is two characters wide.
            // Using an extra row on the bottom to prevent scrolling when drawing the board.
            int width = Math.Max(Program.width, 8) * 2 + 1;
            int height = Math.Max(Program.height, 8) + 1;
            Console.SetWindowSize(width, height);
            Console.SetBufferSize(width, height);
 
            Console.BackgroundColor = DEAD_COLOR;
            Console.ForegroundColor = LIVE_COLOR;
        }
 
        // Creates the initial board with a random state.
        private static void initializeRandomBoard()
        {
            var random = new Random();
 
            Program.board = new bool[Program.width, Program.height];
            for (var y = 0; y < Program.height; y++) {
                for (var x = 0; x < Program.width; x++) {
                    // Equal probability of being true or false.
                    Program.board[x, y] = random.Next(2) == 0;
                }
            }
        }
 
        // Creates a 3x3 board with a blinker.
        private static void initializeDemoBoard()
        {
            Program.width = 3;
            Program.height = 3;
 
            Program.loopEdges = false;
 
            Program.board = new bool[3, 3];
            Program.board[1, 0] = true;
            Program.board[1, 1] = true;
            Program.board[1, 2] = true;
        }
 
        // Draws the board to the console.
        private static void drawBoard()
        {
            // One Console.Write call is much faster than writing each cell individually.
            var builder = new StringBuilder();
 
            for (var y = 0; y < Program.height; y++) {
                for (var x = 0; x < Program.width; x++) {
                    char c = Program.board[x, y] ? FULL_BLOCK_CHAR : EMPTY_BLOCK_CHAR;
 
                    // Each cell is two characters wide.
                    builder.Append(c);
                    builder.Append(c);
                }
                builder.Append('\n');
            }
 
            // Write the string to the console.
            Console.SetCursorPosition(0, 0);
            Console.Write (builder.ToString());
        }
 
        // Moves the board to the next state based on Conway's rules.
        private static void updateBoard()
        {
            // A temp variable to hold the next state while it's being calculated.
            bool[,] newBoard = new bool[Program.width, Program.height];
 
            for (var y = 0; y < Program.height; y++) {
                for (var x = 0; x < Program.width; x++) {
                    var n = countLiveNeighbors(x, y);
                    var c = Program.board[x, y];
 
                    // A live cell dies unless it has exactly 2 or 3 live neighbors.
                    // A dead cell remains dead unless it has exactly 3 live neighbors.
                    newBoard[x, y] = c && (n == 2 || n == 3) || !c && n == 3;
                }
            }
 
            // Set the board to its new state.
            Program.board = newBoard;
        }
 
        // Returns the number of live neighbors around the cell at position (x,y).
        private static int countLiveNeighbors(int x, int y)
        {
            // The number of live neighbors.
            int value = 0;
 
            // This nested loop enumerates the 9 cells in the specified cells neighborhood.
            for (var j = -1; j <= 1; j++) {
                // If loopEdges is set to false and y+j is off the board, continue.
                if (!Program.loopEdges && y + j < 0 || y + j >= Program.height) {
                    continue;
                }
 
                // Loop around the edges if y+j is off the board.
                int k = (y + j + Program.height) % Program.height;
 
                for (var i = -1; i <= 1; i++) {
                    // If loopEdges is set to false and x+i is off the board, continue.
                    if (!Program.loopEdges && x + i < 0 || x + i >= Program.width) {
                        continue;
                    }
 
                    // Loop around the edges if x+i is off the board.
                    int h = (x + i + Program.width) % Program.width;
 
                    // Count the neighbor cell at (h,k) if it is alive.
                    value += Program.board[h, k] ? 1 : 0;
                }
            }
 
            // Subtract 1 if (x,y) is alive since we counted it as a neighbor.
            return value - (Program.board[x, y] ? 1 : 0);
        }
    }
}

Output:

Frame 1:    Frame 2:    Frame 3:
              ██              
██████        ██        ██████
              ██

C++

Considering that the simplest implementation in C++ would lack any use of the object-oriented paradigm, this code was specifically written to demonstrate the various object-oriented features of C++. Thus, while it is somewhat verbose, it fully simulates Conway's Game of Life and is relatively simple to expand to feature different starting shapes.

#include <iostream>
#define HEIGHT 4
#define WIDTH 4

struct Shape {
public:
    char xCoord;
    char yCoord;
    char height;
    char width;
    char **figure;
};

struct Glider : public Shape {
    static const char GLIDER_SIZE = 3;
    Glider( char x , char y );
    ~Glider();
};

struct Blinker : public Shape {
    static const char BLINKER_HEIGHT = 3;
    static const char BLINKER_WIDTH = 1;
    Blinker( char x , char y );
    ~Blinker();
};

class GameOfLife {
public:
    GameOfLife( Shape sh );
    void print();
    void update();
    char getState( char state , char xCoord , char yCoord , bool toggle);
    void iterate(unsigned int iterations);
private:
    char world[HEIGHT][WIDTH];
    char otherWorld[HEIGHT][WIDTH];
    bool toggle;
    Shape shape;
};

GameOfLife::GameOfLife( Shape sh ) :
    shape(sh) ,
    toggle(true) 
{
    for ( char i = 0; i < HEIGHT; i++ ) {
        for ( char j = 0; j < WIDTH; j++ ) {
            world[i][j] = '.';
        }
    }
    for ( char i = shape.yCoord; i - shape.yCoord < shape.height; i++ ) {
        for ( char j = shape.xCoord; j - shape.xCoord < shape.width; j++ ) {
            if ( i < HEIGHT && j < WIDTH ) {
                world[i][j] = 
                    shape.figure[ i - shape.yCoord ][j - shape.xCoord ];
            }
        }
    }
}

void GameOfLife::print() {
    if ( toggle ) {
        for ( char i = 0; i < HEIGHT; i++ ) {
            for ( char j = 0; j < WIDTH; j++ ) {
                std::cout << world[i][j];
            }
            std::cout << std::endl;
        }
    } else {
        for ( char i = 0; i < HEIGHT; i++ ) {
            for ( char j = 0; j < WIDTH; j++ ) {
                std::cout << otherWorld[i][j];
            }
            std::cout << std::endl;
        }
    }
    for ( char i = 0; i < WIDTH; i++ ) {
        std::cout << '=';
    }
    std::cout << std::endl;
}

void GameOfLife::update() {
    if (toggle) {
        for ( char i = 0; i < HEIGHT; i++ ) {
            for ( char j = 0; j < WIDTH; j++ ) {
                otherWorld[i][j] = 
                    GameOfLife::getState(world[i][j] , i , j , toggle);
            }
        }
        toggle = !toggle;
    } else {
        for ( char i = 0; i < HEIGHT; i++ ) {
            for ( char j = 0; j < WIDTH; j++ ) {
                world[i][j] = 
                    GameOfLife::getState(otherWorld[i][j] , i , j , toggle);
            }
        }
        toggle = !toggle;
    }
}

char GameOfLife::getState( char state, char yCoord, char xCoord, bool toggle ) {
    char neighbors = 0;
    if ( toggle ) {
        for ( char i = yCoord - 1; i <= yCoord + 1; i++ ) {
            for ( char j = xCoord - 1; j <= xCoord + 1; j++ ) {
                if ( i == yCoord && j == xCoord ) {
                    continue;
                }
                if ( i > -1 && i < HEIGHT && j > -1 && j < WIDTH ) {
                    if ( world[i][j] == 'X' ) {
                        neighbors++;
                    }
                }
            }
        }
    } else {
        for ( char i = yCoord - 1; i <= yCoord + 1; i++ ) {
            for ( char j = xCoord - 1; j <= xCoord + 1; j++ ) {
                if ( i == yCoord && j == xCoord ) {
                    continue;
                }
                if ( i > -1 && i < HEIGHT && j > -1 && j < WIDTH ) {
                    if ( otherWorld[i][j] == 'X' ) {
                        neighbors++;
                    }
                }
            }
        }
    }
    if (state == 'X') {
        return ( neighbors > 1 && neighbors < 4 ) ? 'X' : '.';
    }
    else {
        return ( neighbors == 3 ) ? 'X' : '.';
    }
}

void GameOfLife::iterate( unsigned int iterations ) {
    for ( int i = 0; i < iterations; i++ ) {
        print();
        update();
    }
}

Glider::Glider( char x , char y ) {
    xCoord = x;
    yCoord = y;
    height = GLIDER_SIZE;
    width = GLIDER_SIZE;
    figure = new char*[GLIDER_SIZE];
    for ( char i = 0; i < GLIDER_SIZE; i++ ) {
        figure[i] = new char[GLIDER_SIZE];
    }
    for ( char i = 0; i < GLIDER_SIZE; i++ ) {
        for ( char j = 0; j < GLIDER_SIZE; j++ ) {
            figure[i][j] = '.';
        }
    }
    figure[0][1] = 'X';
    figure[1][2] = 'X';
    figure[2][0] = 'X';
    figure[2][1] = 'X';
    figure[2][2] = 'X';
}

Glider::~Glider() {
    for ( char i = 0; i < GLIDER_SIZE; i++ ) {
        delete[] figure[i];
    }
    delete[] figure;
}

Blinker::Blinker( char x , char y ) {
    xCoord = x;
    yCoord = y;
    height = BLINKER_HEIGHT;
    width = BLINKER_WIDTH;
    figure = new char*[BLINKER_HEIGHT];
    for ( char i = 0; i < BLINKER_HEIGHT; i++ ) {
        figure[i] = new char[BLINKER_WIDTH];
    }
    for ( char i = 0; i < BLINKER_HEIGHT; i++ ) {
        for ( char j = 0; j < BLINKER_WIDTH; j++ ) {
            figure[i][j] = 'X';
        }
    }
}

Blinker::~Blinker() {
    for ( char i = 0; i < BLINKER_HEIGHT; i++ ) {
        delete[] figure[i];
    }
    delete[] figure;
}

int main() {
    Glider glider(0,0);
    GameOfLife gol(glider);
    gol.iterate(5);
    Blinker blinker(1,0);
    GameOfLife gol2(blinker);
    gol2.iterate(4);
}
Output:
first a glider, then a blinker, over a few iterations

(reformatted for convenience).

.X.. .... .... .... ....
..X. X.X. ..X. .X.. ..X.
XXX. .XX. X.X. ..XX ...X
.... .X.. .XX. .XX. .XXX
==== ==== ==== ==== ====

.X.. .... .X.. 
.X.. XXX. .X..
.X.. .... .X..
.... .... ....
==== ==== ====

Alternate version

Another aproach - a pretty simple one.
This version allows you to start the automata with different set of rules. Just for the fun of it.

#include <algorithm>
#include <vector>
#include <iostream>
#include <string>

typedef unsigned char byte; 

class world {
public:
    world( int x, int y ) : _wid( x ), _hei( y ) {
        int s = _wid * _hei * sizeof( byte );
        _cells = new byte[s];
        memset( _cells, 0, s );
    }
    ~world() {
        delete [] _cells;
    }
    int wid() const {
        return _wid;
    }
    int hei() const {
        return _hei;
    }
    byte at( int x, int y ) const {
        return _cells[x + y * _wid];
    }
    void set( int x, int y, byte c ) {
        _cells[x + y * _wid] = c;
    }
    void swap( world* w ) {
        memcpy( _cells, w->_cells, _wid * _hei * sizeof( byte ) );
    }
private:
    int _wid, _hei;
    byte* _cells;
};
class rule {
public:
    rule( world* w ) : wrd( w ) {
        wid = wrd->wid();
        hei = wrd->hei();
        wrdT = new world( wid, hei );
    }
    ~rule() {
        if( wrdT ) delete wrdT;
    }
    bool hasLivingCells() {
        for( int y = 0; y < hei; y++ )
            for( int x = 0; x < wid; x++ )
                if( wrd->at( x, y ) ) return true;
        std::cout << "*** All cells are dead!!! ***\n\n";
        return false;
    }
    void swapWrds() {
        wrd->swap( wrdT );
    }
    void setRuleB( std::vector<int>& birth ) {
        _birth = birth;
    }
    void setRuleS( std::vector<int>& stay ) {
        _stay = stay;
    }
    void applyRules() {
        int n;
        for( int y = 0; y < hei; y++ ) {
            for( int x = 0; x < wid; x++ ) {
                n = neighbours( x, y );
                if( wrd->at( x, y ) ) {
                    wrdT->set( x, y, inStay( n ) ? 1 : 0 );
                } else {
                    wrdT->set( x, y, inBirth( n ) ? 1 : 0 );
                }
            }
        }
    }
private:
    int neighbours( int xx, int yy ) {
        int n = 0, nx, ny;
        for( int y = -1; y < 2; y++ ) {
            for( int x = -1; x < 2; x++ ) {
                if( !x && !y ) continue;
                nx = ( wid + xx + x ) % wid;
                ny = ( hei + yy + y ) % hei;
                n += wrd->at( nx, ny ) > 0 ? 1 : 0;
            }
        }
        return n;
    }
    bool inStay( int n ) {
        return( _stay.end() != find( _stay.begin(), _stay.end(), n ) );
    }
    bool inBirth( int n ) {
        return( _birth.end() != find( _birth.begin(), _birth.end(), n ) );
    }
    int wid, hei;
    world *wrd, *wrdT;
    std::vector<int> _stay, _birth;
};
class cellular {
public:
    cellular( int w, int h ) : rl( 0 ) {
        wrd = new world( w, h );
    }
    ~cellular() {
        if( rl ) delete rl;
        delete wrd;
    }
    void start( int r ) {
        rl = new rule( wrd );
        gen = 1;
        std::vector<int> t;
        switch( r ) {
            case 1: // conway
                t.push_back( 2 ); t.push_back( 3 ); rl->setRuleS( t );
                t.clear(); t.push_back( 3 ); rl->setRuleB( t );
                break;
            case 2: // amoeba
                t.push_back( 1 ); t.push_back( 3 ); t.push_back( 5 ); t.push_back( 8 ); rl->setRuleS( t );
                t.clear(); t.push_back( 3 ); t.push_back( 5 ); t.push_back( 7 ); rl->setRuleB( t );
                break;
            case 3: // life34
                t.push_back( 3 ); t.push_back( 4 ); rl->setRuleS( t );
                rl->setRuleB( t );
                break;
            case 4: // maze
                t.push_back( 1 ); t.push_back( 2 ); t.push_back( 3 ); t.push_back( 4 ); t.push_back( 5 ); rl->setRuleS( t );
                t.clear(); t.push_back( 3 ); rl->setRuleB( t );
                break;
        }

        /* just for test - shoud read from a file */
        /* GLIDER */
        wrd->set( 6, 1, 1 ); wrd->set( 7, 2, 1 );
        wrd->set( 5, 3, 1 ); wrd->set( 6, 3, 1 );
        wrd->set( 7, 3, 1 );
        /* BLINKER */
        wrd->set( 1, 3, 1 ); wrd->set( 2, 3, 1 );
        wrd->set( 3, 3, 1 );
        /******************************************/
        generation();
    }
private:
    void display() {
        system( "cls" );
        int wid = wrd->wid(),
            hei = wrd->hei();
        std::cout << "+" << std::string( wid, '-' ) << "+\n";
        for( int y = 0; y < hei; y++ ) {
            std::cout << "|";
            for( int x = 0; x < wid; x++ ) {
                if( wrd->at( x, y ) ) std::cout << "#";
                else std::cout << ".";
            }
            std::cout << "|\n";
        }
        std::cout << "+" << std::string( wid, '-' ) << "+\n";
        std::cout << "Generation: " << gen << "\n\nPress [RETURN] for the next generation...";
        std::cin.get();
    }
    void generation() {
        do {
            display();
            rl->applyRules();
            rl->swapWrds();
            gen++;
        }
        while ( rl->hasLivingCells() );
    }
    rule* rl;
    world* wrd;
    int gen; 
};

int main( int argc, char* argv[] ) {
    cellular c( 20, 12 );
    std::cout << "\n\t*** CELLULAR AUTOMATA ***" << "\n\n Which one you want to run?\n\n\n";
    std::cout << " [1]\tConway's Life\n [2]\tAmoeba\n [3]\tLife 34\n [4]\tMaze\n\n > ";
    int o; 
    do {
        std::cin >> o;
    } 
    while( o < 1 || o > 4 );
    std::cin.ignore();
    c.start( o );
    return system( "pause" );
}
Output:

+--------------------+ +--------------------+ +--------------------+ +--------------------+ |....................| |....................| |....................| |....................| |......#.............| |....................| |....................| |....................| |.......#............| |..#..#.#............| |.......#............| |..#...#.............| |.###.###............| |..#...##............| |.###.#.#............| |..#....##...........| |....................| |..#...#.............| |......##............| |..#...##............| |....................| |....................| |....................| |....................| |....................| |....................| |....................| |....................| |....................| |....................| |....................| |....................| +--------------------+ +--------------------+ +--------------------+ +--------------------+ Generation: 1 Generation: 2 Generation: 3 Generation: 4

Simple Without Classes

Shows a glider over 20 generations Board edges wrap around to simulate infinite board

#include <iostream>
#include <vector>
#include <numeric>

// ----------------------------------------------------------------------------

using Row   = std::vector<int>;
using Cells = std::vector<Row>;

// ----------------------------------------------------------------------------

Cells board = {
    {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},
    {0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},
    {0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},
    {0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},
    {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},
    {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},
    {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},
    {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},
    {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},
    {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, 
};

int numRows = 10;
int numCols = 20;

// ----------------------------------------------------------------------------

int getNeighbor(int row, int col, Cells& board) {
    // use modulus to get wrapping effect at board edges
    return board.at((row + numRows) % numRows).at((col + numCols) % numCols);
}

int getCount(int row, int col, Cells& board) {
    int count = 0;
    std::vector<int> deltas {-1, 0, 1};
    for (int dc : deltas) {
        for (int dr : deltas) {
            if (dr || dc) {
                count += getNeighbor(row + dr, col + dc, board);
            }
        }
    }
    return count;
}

void showCell(int cell) {
    std::cout << (cell ? "*" : " ");
}

void showRow(const Row& row) {
    std::cout << "|";
    for (int cell : row) {showCell(cell);}
    std::cout << "|\n";
}

void showCells(Cells board) {
    for (const Row& row : board) { showRow(row); }
}

int tick(Cells& board, int row, int col) {
    int count = getCount(row, col, board);
    bool birth = !board.at(row).at(col) && count == 3;
    bool survive = board.at(row).at(col) && (count == 2 || count == 3);
    return birth || survive;
}

void updateCells(Cells& board) {
    Cells original = board;
    for (int row = 0; row < numRows; row++) {
        for (int col = 0; col < numCols; col++) {
            board.at(row).at(col) = tick(original, row, col);
        }
    }
}

int main () {
    for (int gen = 0; gen < 20; gen++) {
        std::cout << "\ngeneration " << gen << ":\n";
        showCells(board);
        updateCells(board);
    }
}
Output:

generation 0: | | | * | | * | | *** | | | | | | | | | | | | |

generation 1: | | | | | * * | | ** | | * | | | | | | | | | | |

generation 2: | | | | | * | | * * | | ** | | | | | | | | | | |

generation 3: | | | | | * | | ** | | ** | | | | | | | | | | | ...

Chapel

config const gridHeight: int = 3;
config const gridWidth: int = 3;

enum State { dead = 0, alive = 1 };

class ConwaysGameofLife {
  
  var gridDomain: domain(2);
  var computeDomain: subdomain( gridDomain );
  var grid: [gridDomain] int;
  
  proc ConwaysGameofLife( height: int, width: int ) {
    this.gridDomain = {0..#height+2, 0..#width+2};
    this.computeDomain = this.gridDomain.expand( -1 );
  }
  
  proc step(){
    
    var tempGrid: [this.computeDomain] State;
    forall (i,j) in this.computeDomain {
      var isAlive = this.grid[i,j] == State.alive;
      var numAlive = (+ reduce this.grid[ i-1..i+1, j-1..j+1 ]) - if isAlive then 1 else 0;      
      tempGrid[i,j] = if ( (2 == numAlive && isAlive) || numAlive == 3 ) then State.alive else State.dead ;
    }
    
    this.grid[this.computeDomain] = tempGrid;
    
  }
  
  proc this( i: int, j: int ) ref : State {
    return this.grid[i,j];
  }
  
  proc prettyPrint(): string {
    var str: string;
    for i in this.gridDomain.dim(1) {
      if i == 0 || i == gridDomain.dim(1).last {
        for j in this.gridDomain.dim(2) {
          str += "-";
        }
      } else {
        for j in this.gridDomain.dim(2) {
          if j == 0 || j == this.gridDomain.dim(2).last {
            str += "|";
          } else {
            str += if this.grid[i,j] == State.alive then "#" else " ";
          }
        }
      }
      str += "\n";
    }
    return str;
  }

}

proc main{
  var game = new ConwaysGameofLife( gridHeight, gridWidth );
  game[gridHeight/2 + 1, gridWidth/2     ] = State.alive;
  game[gridHeight/2 + 1, gridWidth/2 + 1 ] = State.alive;
  game[gridHeight/2 + 1, gridWidth/2 + 2 ] = State.alive;
  for i in 1..3 {
    writeln( game.prettyPrint() );
    game.step();
  }
}

Output:

-----
|   |
|###|
|   |
-----

-----
| # |
| # |
| # |
-----

-----
|   |
|###|
|   |
-----

Clojure

Based on the implementation by Christophe Grand here: http://clj-me.cgrand.net/2011/08/19/conways-game-of-life/ This implementation models the live cells as a set of coordinates.

(defn moore-neighborhood [[x y]]
  (for [dx [-1 0 1]
        dy [-1 0 1]
        :when (not (= [dx dy] [0 0]))]
    [(+ x dx) (+ y dy)]))

(defn step [set-of-cells]
  (set (for [[cell count] (frequencies (mapcat moore-neighborhood set-of-cells))
             :when (or (= 3 count)
                       (and (= 2 count) (contains? set-of-cells cell)))]
         cell)))

(defn print-world 
  ([set-of-cells] (print-world set-of-cells 10))
  ([set-of-cells world-size]
     (let [r (range 0 (+ 1 world-size))]
       (pprint (for [y r] (apply str (for [x r] (if (set-of-cells [x y]) \# \.))))))))

(defn run-life [world-size num-steps set-of-cells]
  (loop [s num-steps 
         cells set-of-cells]
    (print-world cells world-size)
    (when (< 0 s) 
      (recur (- s 1) (step cells)))))

(def *blinker* #{[1 2] [2 2] [3 2]})
(def *glider* #{[1 0] [2 1] [0 2] [1 2] [2 2]})

COBOL

identification division.
program-id. game-of-life-program.

data division.
working-storage section.
01  grid.
    05 cell-table.
        10 row occurs 5 times.
            15 cell pic x value space occurs 5 times.
    05 next-gen-cell-table.
        10 next-gen-row occurs 5 times.
            15 next-gen-cell pic x occurs 5 times.
01  counters.
    05 generation pic 9.
    05 current-row pic 9.
    05 current-cell pic 9.
    05 living-neighbours pic 9.
    05 neighbour-row pic 9.
    05 neighbour-cell pic 9.
    05 check-row pic s9.
    05 check-cell pic s9.

procedure division.
control-paragraph.
    perform blinker-paragraph varying current-cell from 2 by 1
    until current-cell is greater than 4.
    perform show-grid-paragraph through life-paragraph
    varying generation from 0 by 1
    until generation is greater than 2.
    stop run.
blinker-paragraph.
    move '#' to cell(3,current-cell).
show-grid-paragraph.
    display 'GENERATION ' generation ':'.
    display '   +---+'.
    perform show-row-paragraph varying current-row from 2 by 1
    until current-row is greater than 4.
    display '   +---+'.
    display ''.
life-paragraph.
    perform update-row-paragraph varying current-row from 2 by 1
    until current-row is greater than 4.
    move next-gen-cell-table to cell-table.
show-row-paragraph.
    display '   |' with no advancing.
    perform show-cell-paragraph varying current-cell from 2 by 1
    until current-cell is greater than 4.
    display '|'.
show-cell-paragraph.
    display cell(current-row,current-cell) with no advancing.
update-row-paragraph.
    perform update-cell-paragraph varying current-cell from 2 by 1
    until current-cell is greater than 4.
update-cell-paragraph.
    move 0 to living-neighbours.
    perform check-row-paragraph varying check-row from -1 by 1
    until check-row is greater than 1.
    evaluate living-neighbours,
        when 2 move cell(current-row,current-cell) to next-gen-cell(current-row,current-cell),
        when 3 move '#' to next-gen-cell(current-row,current-cell),
        when other move space to next-gen-cell(current-row,current-cell),
    end-evaluate.
check-row-paragraph.
    add check-row to current-row giving neighbour-row.
    perform check-cell-paragraph varying check-cell from -1 by 1
    until check-cell is greater than 1.
check-cell-paragraph.
    add check-cell to current-cell giving neighbour-cell.
    if cell(neighbour-row,neighbour-cell) is equal to '#',
    and check-cell is not equal to zero or check-row is not equal to zero,
    then add 1 to living-neighbours.

end program game-of-life-program.
Output:
GENERATION 0:
   +---+
   |   |
   |###|
   |   |
   +---+

GENERATION 1:
   +---+
   | # |
   | # |
   | # |
   +---+

GENERATION 2:
   +---+
   |   |
   |###|
   |   |
   +---+

Common Lisp

(defun next-life (array &optional results)
  (let* ((dimensions (array-dimensions array))
         (results (or results (make-array dimensions :element-type 'bit))))
    (destructuring-bind (rows columns) dimensions
      (labels ((entry (row col)
                 "Return array(row,col) for valid (row,col) else 0."
                 (if (or (not (< -1 row rows))
                         (not (< -1 col columns)))
                   0
                   (aref array row col)))
               (neighbor-count (row col &aux (count 0))
                 "Return the sum of the neighbors of (row,col)."
                 (dolist (r (list (1- row) row (1+ row)) count)
                   (dolist (c (list (1- col) col (1+ col)))
                     (unless (and (eql r row) (eql c col))
                       (incf count (entry r c))))))
               (live-or-die? (current-state neighbor-count)
                 (if (or (and (eql current-state 1)
                              (<=  2 neighbor-count 3))
                         (and (eql current-state 0)
                              (eql neighbor-count 3)))
                   1
                   0)))
        (dotimes (row rows results)
          (dotimes (column columns)
            (setf (aref results row column)
                  (live-or-die? (aref array row column)
                                (neighbor-count row column)))))))))

(defun print-grid (grid &optional (out *standard-output*))
  (destructuring-bind (rows columns) (array-dimensions grid)
    (dotimes (r rows grid)
      (dotimes (c columns (terpri out))
        (write-char (if (zerop (aref grid r c)) #\+ #\#) out)))))

(defun run-life (&optional world (iterations 10) (out *standard-output*))
  (let* ((world (or world (make-array '(10 10) :element-type 'bit)))
         (result (make-array (array-dimensions world) :element-type 'bit)))
    (do ((i 0 (1+ i))) ((eql i iterations) world)
      (terpri out) (print-grid world out)
      (psetq world (next-life world result)
             result world))))
(run-life (make-array '(3 3) 
                      :element-type 'bit
                      :initial-contents '((0 0 0) 
                                          (1 1 1)
                                          (0 0 0)))
          3)

produces

+++
###
+++

+#+
+#+
+#+

+++
###
+++

A version using a sparse list of living cells rather than an explicit board.

(defun moore-neighborhood (cell)
  (let ((r '(-1 0 1)))
    (mapcan
	 (lambda (delta-x)
	   (loop for delta-y in r
	      unless (and (= delta-x 0) (= delta-y 0))
	      collect (cons (+ (car cell) delta-x) (+ (cdr cell) delta-y))))
	 r)))

(defun frequencies (cells)
  (let ((h (make-hash-table :test #'equal)))
    (loop for c in cells
       if (gethash c h)
         do (incf (gethash c h))
       else
       do (setf (gethash c h) 1))
    h))

(defun life-step (cells)
  (let ((f (frequencies (mapcan #'moore-neighborhood cells))))
    (loop for k being the hash-keys in f
       when (or 
	     (= (gethash k f) 3) 
	     (and (= (gethash k f) 2) (member k cells :test #'equal)))
	 collect k)))

(defun print-world (live-cells &optional (world-size 10))
  (dotimes (y world-size)
    (dotimes (x world-size)
      (if (member (cons x y) live-cells :test #'equal)
	  (format t "X")
	  (format t ".")))
    (format t "~%")))

(defun run-life (world-size steps cells)
  (print-world cells world-size)
  (format t "~%")
  (when (< 0 steps)
    (run-life world-size (- steps 1) (life-step cells))))

(defparameter *blinker* '((1 . 2) (2 . 2) (3 . 2)))
(defparameter *glider* '((1 . 0) (2 . 1) (0 . 2) (1 . 2) (2 . 2)))

D

import std.stdio, std.string, std.algorithm, std.array, std.conv;

struct GameOfLife {
  enum Cell : char { dead = ' ', alive = '#' }
  Cell[][] grid, newGrid;

  this(in int x, in int y) pure nothrow @safe {
    grid = new typeof(grid)(y + 2, x + 2);
    newGrid = new typeof(grid)(y + 2, x + 2);
  }

  void opIndexAssign(in string[] v, in size_t y, in size_t x)
  pure /*nothrow*/ @safe /*@nogc*/ {
    foreach (immutable nr, row; v)
      foreach (immutable nc, state; row)
        grid[y + nr][x + nc] = state.to!Cell;
  }

  void iteration() pure nothrow @safe @nogc {
    newGrid[0][] = Cell.dead;
    newGrid[$ - 1][] = Cell.dead;
    foreach (row; newGrid)
      row[0] = row[$ - 1] = Cell.dead;

    foreach (immutable r; 1 .. grid.length - 1)
      foreach (immutable c; 1 .. grid[0].length - 1) {
        uint count = 0;
        foreach (immutable i; -1 .. 2)
          foreach (immutable j; -1 .. 2)
            if (i != 0 || j != 0)
              count += grid[r + i][c + j] == Cell.alive;
        immutable a = count == 3 ||
                      (count == 2 && grid[r][c] == Cell.alive);
        newGrid[r][c] = a ? Cell.alive : Cell.dead;
      }

    grid.swap(newGrid);
  }

  string toString() const pure /*nothrow @safe*/ {
    auto ret = "-".replicate(grid[0].length - 1) ~ "\n";
    foreach (const row; grid[1 .. $ - 1])
      ret ~= "|%(%c%)|\n".format(row[1 .. $ - 1]);
    return ret ~ "-".replicate(grid[0].length - 1);
  }
}

void main() /*@safe*/ {
  immutable glider1 = ["  #", "# #", " ##"];
  immutable glider2 = ["#  ", "# #", "## "];

  auto uni = GameOfLife(60, 20);
  uni[3,  2] = glider1;
  uni[3, 15] = glider2;
  uni[3, 19] = glider1;
  uni[3, 32] = glider2;
  uni[5, 50] = [" #  #", "#  ", "#   #", "#### "];
  uni.writeln;

  foreach (immutable _; 0 .. 20) {
    uni.iteration;
    uni.writeln;
  }
}
Output, first iteration:
-------------------------------------------------------------
|                                                            |
|                                                            |
|   #          #     #          #                            |
| # #          # # # #          # #                          |
|  ##          ##   ##          ##                 #  #      |
|                                                 #          |
|                                                 #   #      |
|                                                 ####       |
|                                                            |
|                                                            |
|                                                            |
|                                                            |
|                                                            |
|                                                            |
|                                                            |
|                                                            |
|                                                            |
|                                                            |
|                                                            |
|                                                            |
-------------------------------------------------------------

Faster Version

Same output.

import std.stdio, std.string, std.algorithm, std.typetuple,
       std.array, std.conv;

struct GameOfLife {
  enum Cell : char { dead = ' ', alive = '#' }
  Cell[] grid, newGrid;
  immutable size_t nCols;

  this(in int nx, in int ny) pure nothrow @safe {
    nCols = nx + 2;
    grid = new typeof(grid)(nCols * (ny + 2));
    newGrid = new typeof(grid)(grid.length);
  }

  void opIndexAssign(in string[] v, in size_t y, in size_t x)
  pure /*nothrow*/ @safe /*@nogc*/ {
    foreach (immutable nr, const row; v)
      foreach (immutable nc, immutable state; row)
        grid[(y + nr) * nCols + x + nc] = state.to!Cell;
  }

  void iteration() pure nothrow @safe @nogc {
    newGrid[0 .. nCols] = Cell.dead;
    newGrid[$ - nCols .. $] = Cell.dead;
    foreach (immutable nr; 1 .. (newGrid.length / nCols) - 1) {
      newGrid[nr * nCols + 0] = Cell.dead;
      newGrid[nr * nCols + nCols - 1] = Cell.dead;
    }

    foreach (immutable nr; 1 .. (grid.length / nCols) - 1) {
      size_t nr_nCols = nr * nCols;
      foreach (immutable nc; 1 .. nCols - 1) {
        uint count = 0;
        /*static*/ foreach (immutable i; TypeTuple!(-1, 0, 1))
          /*static*/ foreach (immutable j; TypeTuple!(-1, 0, 1))
            static if (i != 0 || j != 0)
              count += (grid[nr_nCols + i * nCols + nc + j] == Cell.alive);
        immutable a = count == 3 ||
                      (count == 2 && grid[nr_nCols + nc] == Cell.alive);
        newGrid[nr_nCols + nc] = a ? Cell.alive : Cell.dead;
      }
    }

    swap(grid, newGrid);
  }

  string toString() const pure /*nothrow @safe*/ {
    string ret = "-".replicate(nCols - 1) ~ "\n";
    foreach (immutable nr; 1 .. (grid.length / nCols) - 1)
      ret ~= "|%(%c%)|\n".format(grid[nr * nCols + 1 .. nr * nCols + nCols - 1]);
    return ret ~ "-".replicate(nCols - 1);
  }
}

void main() {
  immutable glider1 = ["  #", "# #", " ##"];
  immutable glider2 = ["#  ", "# #", "## "];

  auto uni = GameOfLife(60, 20);
  uni[3,  2] = glider1;
  uni[3, 15] = glider2;
  uni[3, 19] = glider1;
  uni[3, 32] = glider2;
  uni[5, 50] = [" #  #", "#  ", "#   #", "#### "];
  uni.writeln;

  foreach (immutable _; 0 .. 20) {
    uni.iteration;
    uni.writeln;
  }
}

Dart

/**
* States of a cell. A cell is either [ALIVE] or [DEAD].
* The state contains its [symbol] for printing.
*/
class State {
  const State(this.symbol);

  static final ALIVE = const State('#');
  static final DEAD = const State(' ');

  final String symbol;
}

/**
* The "business rule" of the game. Depending on the count of neighbours,
* the [cellState] changes.
*/
class Rule {
  Rule(this.cellState);

  reactToNeighbours(int neighbours) {
    if (neighbours == 3) {
      cellState = State.ALIVE;
    } else if (neighbours != 2) {
      cellState = State.DEAD;
    }
  }

  var cellState;
}

/**
* A coordinate on the [Grid].
*/
class Point {
  const Point(this.x, this.y);

  operator +(other) => new Point(x + other.x, y + other.y);

  final int x;
  final int y;
}

/**
* List of the relative indices of the 8 cells around a cell.
*/
class Neighbourhood {
  List<Point> points() {
    return [
      new Point(LEFT, UP), new Point(MIDDLE, UP), new Point(RIGHT, UP),
      new Point(LEFT, SAME), new Point(RIGHT, SAME),
      new Point(LEFT, DOWN), new Point(MIDDLE, DOWN), new Point(RIGHT, DOWN)
    ];
  }

  static final LEFT = -1;
  static final MIDDLE = 0;
  static final RIGHT = 1;
  static final UP = -1;
  static final SAME = 0;
  static final DOWN = 1;
}

/**
* The grid is an endless, two-dimensional [field] of cell [State]s.
*/
class Grid {
  Grid(this.xCount, this.yCount) {
    _field = new Map();
    _neighbours = new Neighbourhood().points();
  }

  set(point, state) {
    _field[_pos(point)] = state;
  }

  State get(point) {
    var state = _field[_pos(point)];
    return state != null ? state : State.DEAD;
  }

  int countLiveNeighbours(point) =>
    _neighbours.filter((offset) => get(point + offset) == State.ALIVE).length;

  _pos(point) => '${(point.x + xCount) % xCount}:${(point.y + yCount) % yCount}';

  print() {
    var sb = new StringBuffer();
    iterate((point) { sb.add(get(point).symbol); }, (x) { sb.add("\n"); });
    return sb.toString();
  }

  iterate(eachCell, [finishedRow]) {
    for (var x = 0; x < xCount; x++) {
      for (var y = 0; y < yCount; y++) {
         eachCell(new Point(x, y));
      }
      if(finishedRow != null) {
        finishedRow(x);
      }
    }
  }

  final xCount, yCount;
  List<Point> _neighbours;
  Map<String, State> _field;
}

/**
* The game updates the [grid] in each step using the [Rule].
*/
class Game {
  Game(this.grid);

  tick() {
    var newGrid = createNewGrid();

    grid.iterate((point) {
      var rule = new Rule(grid.get(point));
      rule.reactToNeighbours(grid.countLiveNeighbours(point));
      newGrid.set(point, rule.cellState);
    });

    grid = newGrid;
  }

  createNewGrid() => new Grid(grid.xCount, grid.yCount);

  printGrid() => print(grid.print());

  Grid grid;
}

main() {
  // Run the GoL with a blinker.
  runBlinker();
}

runBlinker() {
  var game = new Game(createBlinkerGrid());

  for(int i = 0; i < 3; i++) {
    game.printGrid();
    game.tick();
  }
  game.printGrid();
}

createBlinkerGrid() {
  var grid = new Grid(4, 4);
  loadBlinker(grid);
  return grid;
}

loadBlinker(grid) => blinkerPoints().forEach((point) => grid.set(point, State.ALIVE));

blinkerPoints() => [new Point(0, 1), new Point(1, 1), new Point(2, 1)];

Test cases driving the design of this code:

#import('<path to sdk>/lib/unittest/unittest.dart');

main() {
  group('rules', () {
    test('should let living but lonely cell die', () {
      var rule = new Rule(State.ALIVE);
      rule.reactToNeighbours(1);
      expect(rule.cellState, State.DEAD);
    });
    test('should let proper cell live on', () {
      var rule = new Rule(State.ALIVE);
      rule.reactToNeighbours(2);
      expect(rule.cellState, State.ALIVE);
    });
    test('should let dead cell with three neighbours be reborn', () {
      var rule = new Rule(State.DEAD);
      rule.reactToNeighbours(3);
      expect(rule.cellState, State.ALIVE);
    });
    test('should let living cell with too many neighbours die', () {
      var rule = new Rule(State.ALIVE);
      rule.reactToNeighbours(4);
      expect(rule.cellState, State.DEAD);
    });
  });

  group('grid', () {
    var origin = new Point(0, 0);
    test('should have state', () {
      var grid = new Grid(1, 1);
      expect(grid.get(origin), State.DEAD);
      grid.set(origin, State.ALIVE);
      expect(grid.get(origin), State.ALIVE);
    });
    test('should have dimension', () {
      var grid = new Grid(2, 3);
      expect(grid.get(origin), State.DEAD);
      grid.set(origin, State.ALIVE);
      expect(grid.get(origin), State.ALIVE);
      expect(grid.get(new Point(1, 2)), State.DEAD);
      grid.set(new Point(1, 2), State.ALIVE);
      expect(grid.get(new Point(1, 2)), State.ALIVE);
    });
    test('should be endless', () {
      var grid = new Grid(2, 4);
      grid.set(new Point(2, 4), State.ALIVE);
      expect(grid.get(origin), State.ALIVE);
      grid.set(new Point(-1, -1), State.ALIVE);
      expect(grid.get(new Point(1, 3)), State.ALIVE);
    });
    test('should print itself', () {
      var grid = new Grid(1, 2);
      grid.set(new Point(0, 1), State.ALIVE);
      expect(grid.print(), " #\n");
    });
  });

  group('game', () {
    test('should exists', () {
     var game = new Game(null);
     expect(game, isNotNull);
    });
    test('should create a new grid when ticked', () {
      var grid = new Grid(1, 1);
      var game = new Game(grid);
      game.tick();
      expect(game.grid !== grid);
    });
    test('should have a grid with the same dimension after tick', (){
      var game = new Game(new Grid(2, 3));
      game.tick();
      expect(game.grid.xCount, 2);
      expect(game.grid.yCount, 3);
    });
    test('should apply rules to middle cell', (){
      var grid = new Grid(3, 3);
      grid.set(new Point(1, 1), State.ALIVE);
      var game = new Game(grid);
      game.tick();
      expect(game.grid.get(new Point(1, 1)), State.DEAD);

      grid.set(new Point(0, 0), State.ALIVE);
      grid.set(new Point(1, 0), State.ALIVE);
      game = new Game(grid);
      game.tick();
      expect(game.grid.get(new Point(1, 1)), State.ALIVE);
    });
    test('should apply rules to all cells', (){
      var grid = new Grid(3, 3);
      grid.set(new Point(0, 1), State.ALIVE);
      grid.set(new Point(1, 0), State.ALIVE);
      grid.set(new Point(1, 1), State.ALIVE);
      var game = new Game(grid);
      game.tick();
      expect(game.grid.get(new Point(0, 0)), State.ALIVE);
    });
  });
}
Output:
 #
 #
 #



###



 #
 #
 #



###


Delphi

Translation of: Go

Thanks Rudy Velthuis for the Velthuis.Console library.

program game_of_life;

{$APPTYPE CONSOLE}



uses
  System.SysUtils,
  Velthuis.Console; // CrlScr

type
  TBoolMatrix = TArray<TArray<Boolean>>;

  TField = record
    s: TBoolMatrix;
    w, h: Integer;
    procedure SetValue(x, y: Integer; b: boolean);
    function Next(x, y: Integer): boolean;
    function State(x, y: Integer): boolean;
    class function NewField(w1, h1: Integer): TField; static;
  end;

  TLife = record
    a, b: TField;
    w, h: Integer;
    class function NewLife(w1, h1: Integer): TLife; static;
    procedure Step;
    function ToString: string;
  end;

{ TField }

class function TField.NewField(w1, h1: Integer): TField;
var
  s1: TBoolMatrix;
begin
  SetLength(s1, h1);
  for var i := 0 to High(s1) do
    SetLength(s1[i], w1);
  with Result do
  begin
    s := s1;
    w := w1;
    h := h1;
  end;
end;

function TField.Next(x, y: Integer): boolean;
var
  _on: Integer;
begin
  _on := 0;
  for var i := -1 to 1 do
    for var j := -1 to 1 do
      if self.State(x + i, y + j) and not ((j = 0) and (i = 0)) then
        inc(_on);
  Result := (_on = 3) or (_on = 2) and self.State(x, y);
end;

procedure TField.SetValue(x, y: Integer; b: boolean);
begin
  self.s[y, x] := b;
end;

function TField.State(x, y: Integer): boolean;
begin
  while y < 0 do
    inc(y, self.h);
  while x < 0 do
    inc(x, self.w);
  result := self.s[y mod self.h, x mod self.w]
end;

{ TLife }

class function TLife.NewLife(w1, h1: Integer): TLife;
var
  a1: TField;
begin
  a1 := TField.NewField(w1, h1);
  for var i := 0 to (w1 * h1 div 2) do
    a1.SetValue(Random(w1), Random(h1), True);
  with Result do
  begin
    a := a1;
    b := TField.NewField(w1, h1);
    w := w1;
    h := h1;
  end;
end;

procedure TLife.Step;
var
  tmp: TField;
begin
  for var y := 0 to self.h - 1 do
    for var x := 0 to self.w - 1 do
      self.b.SetValue(x, y, self.a.Next(x, y));
  tmp := self.a;
  self.a := self.b;
  self.b := tmp;
end;

function TLife.ToString: string;
begin
  result := '';
  for var y := 0 to self.h - 1 do
  begin
    for var x := 0 to self.w - 1 do
    begin
      var b: char := ' ';
      if self.a.State(x, y) then
        b := '*';
      result := result + b;
    end;
    result := result + #10;
  end;
end;

begin
  Randomize;

  var life := TLife.NewLife(80, 15);

  for var i := 1 to 300 do
  begin
    life.Step;
    ClrScr;
    writeln(life.ToString);
    sleep(30);
  end;
  readln;
end.
Output:
                *  ***   *        *                   *
                 *  **                                           **      *
                  ****     *                                   *  *      *
                       *** *                               *  ** *       *
                      *** **                              * *  *
                *        *                                   *
              ** **   ****                                ** *
              ******    **                                  * *
               *  *                                     * *** **     ***
                **                                          * *
                      *                                 *    **
                      *                                   * *
                  *  *            *                         *
                    * ***        * *                  *     **
                    * ***        * *                  *                    ***

E

Just does three generations of a blinker in a dead-boundary grid, as specified. (User:Kevin Reid has graphical and wrapping versions.)

def gridWidth := 3
def gridHeight := 3
def X := 0..!gridWidth
def Y := 0..!gridHeight

def makeFlexList := <elib:tables.makeFlexList>
def makeGrid() {
  def storage := makeFlexList.fromType(<type:java.lang.Boolean>, gridWidth * gridHeight)
  storage.setSize(gridWidth * gridHeight)

  def grid {
    to __printOn(out) {
      for y in Y {
        out.print("[")
        for x in X {
          out.print(grid[x, y].pick("#", " "))
        }
        out.println("]")
      }
    }
    to get(xb :int, yb :int) {
      return if (xb =~ x :X && yb =~ y :Y) {
        storage[y * gridWidth + x]
      } else {
        false
      }
    }
    to put(x :X, y :Y, c :boolean) { 
      storage[y * gridWidth + x] := c
    }
  }
  return grid
}

def mooreNeighborhood := [[-1,-1],[0,-1],[1,-1],[-1,0],[1,0],[-1,1],[0,1],[1,1]]
def computeNextLife(prevGrid, nextGrid) {
  for y in Y {
    for x in X {
      var neighbors := 0
      for [nx, ny] ? (prevGrid[x+nx, y+ny]) in mooreNeighborhood {
        neighbors += 1
      }
      def self := prevGrid[x, y]
      nextGrid[x, y] := (self && neighbors == 2 || neighbors == 3)
    }
  }
}

var currentFrame := makeGrid()
var nextFrame := makeGrid()
currentFrame[1, 0] := true
currentFrame[1, 1] := true
currentFrame[1, 2] := true

for _ in 1..3 {
  def frame := nextFrame
  computeNextLife(currentFrame, frame)
  nextFrame := currentFrame
  currentFrame := frame
  println(currentFrame)
}

EasyLang

Run it

n = 70
time = 0.1
# 
nx = n + 1
subr init
   for r = 1 to n
      for c = 1 to n
         i = r * nx + c
         if randomf < 0.3
            f[i] = 1
         .
      .
   .
.
f = 100 / n
subr show
   clear
   for r = 1 to n
      for c = 1 to n
         if f[r * nx + c] = 1
            move c * f - f r * f - f
            rect f * 0.9 f * 0.9
         .
      .
   .
.
subr update
   swap f[] p[]
   for r = 1 to n
      sm = 0
      i = r * nx + 1
      sr = p[i - nx] + p[i] + p[i + nx]
      for c = 1 to n
         sl = sm
         sm = sr
         in = i + 1
         sr = p[in - nx] + p[in] + p[in + nx]
         s = sl + sm + sr
         if s = 3 or s = 4 and p[i] = 1
            f[i] = 1
         else
            f[i] = 0
         .
         i = in
      .
   .
.
on timer
   update
   show
   timer time
.
on mouse_down
   c = mouse_x div f + 1
   r = mouse_y div f + 1
   i = r * nx + c
   f[i] = 1 - f[i]
   show
   timer 3
.
len f[] nx * nx + nx
len p[] nx * nx + nx
init
timer 0

eC

Library: Ecere
import "ecere"

define seed = 12345;
define popInit = 1000;
define width = 100;
define height = 100;
define cellWidth = 4;
define cellHeight = 4;

Array<byte> grid { size = width * height };
Array<byte> newState { size = width * height };

class GameOfLife : Window
{
   caption = $"Conway's Game of Life";
   background = lightBlue;
   borderStyle = sizable;
   hasMaximize = true;
   hasMinimize = true;
   hasClose = true;
   clientSize = { width * cellWidth, height * cellHeight };

   Timer tickTimer
   {
      delay = 0.05, started = true, userData = this;

      bool DelayExpired()
      {
         int y, x, ix = 0;
         for(y = 0; y < height; y++)
         {
            for(x = 0; x < width; x++, ix++)
            {
               int nCount = 0;
               byte alive;
               if(x > 0       && y > 0        && grid[ix - width - 1]) nCount++;
               if(               y > 0        && grid[ix - width    ]) nCount++;
               if(x < width-1 && y > 0        && grid[ix - width + 1]) nCount++;
               if(x > 0                       && grid[ix         - 1]) nCount++;
               if(x < width - 1               && grid[ix         + 1]) nCount++;
               if(x > 0       && y < height-1 && grid[ix + width - 1]) nCount++;
               if(               y < height-1 && grid[ix + width    ]) nCount++;
               if(x < width-1 && y < height-1 && grid[ix + width + 1]) nCount++;

               if(grid[ix])
                  alive = nCount >= 2 && nCount <= 3; // Death
               else
                  alive = nCount == 3; // Birth
               newState[ix] = alive;
            }
         }
         memcpy(grid.array, newState.array, width * height);
         Update(null);
         return true;
      }
   };

   void OnRedraw(Surface surface)
   {
      int x, y;
      int ix = 0;

      surface.background = navy;
      for(y = 0; y < height; y++)
      {
         for(x = 0; x < width; x++, ix++)
         {
            if(grid[ix])
            {
               int sy = y * cellHeight;
               int sx = x * cellWidth;
               surface.Area(sx, sy, sx + cellWidth-1, sy + cellHeight-1);
            }
         }
      }
   }

   bool OnCreate()
   {
      int i;

      RandomSeed(seed);

      for(i = 0; i < popInit; i++)
      {
         int x = GetRandom(0, width-1);
         int y = GetRandom(0, height-1);

         grid[y * width + x] = 1;
      }
      return true;
   }
}

GameOfLife life {};

Egel

import "prelude.eg"
import "io.ego"

using System
using List
using IO

def boardsize = 5

def empty = [ X Y -> 0 ]

def insert =
    [ X Y BOARD -> 
        [ X0 Y0 -> if and (X0 == X) (Y0 == Y) then 1
                    else BOARD X0 Y0 ] ]

def coords =
    let R = fromto 0 (boardsize - 1) in
        [ XX YY -> map (\X -> map (\Y -> X Y) YY) XX ] R R

def printcell =
    [ 0 -> print ". "
    | _ -> print "* " ]

def printboard =
    [ BOARD ->
        let M  = map [XX -> let _ = map [(X Y) -> printcell (BOARD X Y)] XX in print "\n" ] coords in
            nop ]

def count =
    [ BOARD, X, Y ->
        (BOARD (X - 1) (Y - 1)) + (BOARD (X) (Y - 1)) + (BOARD (X+1) (Y - 1)) +
        (BOARD (X - 1) Y) + (BOARD (X+1) Y) +
        (BOARD (X - 1) (Y+1)) + (BOARD (X) (Y+1)) + (BOARD (X+1) (Y+1)) ]

def next =
    [ 0 N -> if N == 3 then 1 else 0
    | _ N -> if or (N == 2) (N == 3) then 1 else 0 ]

def updateboard =
    [ BOARD ->
        let XX = map (\(X Y) -> X Y (BOARD X Y) (count BOARD X Y)) (flatten coords) in
        let YY = map (\(X Y C N) -> X Y (next C N)) XX in
            foldr [(X Y 0) BOARD -> BOARD | (X Y _) BOARD -> insert X Y BOARD ] empty YY ]

def blinker =
    (insert 1 2) @ (insert 2 2) @ (insert 3 2)

def main = 
    let GEN0 = blinker empty in
    let GEN1 = updateboard GEN0 in
    let GEN2 = updateboard GEN1 in
    let _ = map [ G -> let _ = print "generation:\n" in printboard G ] {GEN0, GEN1, GEN2} in
        nop

Elena

ELENA 6.x, using cellular library

import extensions;
import system'threading;
import system'text;
import cellular;

const int maxX = 48;
const int maxY = 28;

const int DELAY = 50;

sealed class Model
{
   Space   _space;
   RuleSet _ruleSet;
   bool    _started;

   Func<Space, object> OnUpdate : event;
    
   constructor newRandomset(RuleSet transformSet)
   {
      _space := IntMatrixSpace.allocate(maxY, maxX, randomSet);

      _ruleSet := transformSet;
        
      _started := false
   }
    
   private onUpdate()
   {
      OnUpdate.?(_space)
   }
    
   run()
   {
      if (_started)
      { 
         _space.update(_ruleSet) 
      }
      else
      {
         _started := true
      };
        
      self.onUpdate()
   }
}

singleton gameOfLifeRuleSet : RuleSet
{
   int proceed(Space s, int x, int y)
   {
      int cell := s.at(x, y);
      int number := s.LiveCell(x, y, 1); // NOTE : number of living cells around the self includes the cell itself
      
      if (cell == 0 && number == 3)
      {
         ^ 1 
      }
      else if (cell == 1 && (number == 4 || number == 3))
      {
         ^ 1 
      }
      else
      {
         ^ 0
      }
   }
}

public extension presenterOp : Space
{
   print()
   {
      console.setCursorPosition(0, 0);
     
      int columns := self.Columns;
      int rows := self.Rows;
     
      auto line := new TextBuilder();
      for(int i := 0; i < rows; i += 1)
      {
         line.clear();
         for(int j := 0; j < columns; j += 1)
         {
            int cell := self.at(i, j);
             
            line.write((cell == 0).iif(" ","o"));
         };
         
         console.writeLine(line.Value)
      }
   }
}

public program()
{
    auto model := Model.newRandomset(gameOfLifeRuleSet);
    console.clear();
    
    model.OnUpdate := (Space sp){ sp.print() };

    until (console.KeyAvailable)
    {
        model.run();
        
        threadControl.sleep(DELAY)
    };

    console.readChar()
}

Elixir

Works with: Elixir version 1.2
Translation of: Ruby
defmodule Conway do
  def game_of_life(name, size, generations, initial_life\\nil) do
    board = seed(size, initial_life)
    print_board(board, name, size, 0)
    reason = generate(name, size, generations, board, 1)
    case reason do
      :all_dead -> "no more life."
      :static   -> "no movement"
      _         -> "specified lifetime ended"
    end
    |> IO.puts
    IO.puts ""
  end
  
  defp new_board(n) do
    for x <- 1..n, y <- 1..n, into: %{}, do: {{x,y}, 0}
  end

  defp seed(n, points) do
    if points do
      points
    else # randomly seed board
      (for x <- 1..n, y <- 1..n, do: {x,y}) |> Enum.take_random(10)
    end
    |> Enum.reduce(new_board(n), fn pos,acc -> %{acc | pos => 1} end)
  end
  
  defp generate(_, _, generations, _, gen) when generations < gen, do: :ok
  defp generate(name, size, generations, board, gen) do
    new = evolve(board, size)
    print_board(new, name, size, gen)
    cond do
      barren?(new) -> :all_dead
      board == new -> :static
      true         -> generate(name, size, generations, new, gen+1)
    end
  end
  
  defp evolve(board, n) do
    for x <- 1..n, y <- 1..n, into: %{}, do: {{x,y}, fate(board, x, y, n)}
  end
  
  defp fate(board, x, y, n) do
    irange = max(1, x-1) .. min(x+1, n)
    jrange = max(1, y-1) .. min(y+1, n)
    sum = ((for i <- irange, j <- jrange, do: board[{i,j}]) |> Enum.sum) - board[{x,y}]
    cond do
      sum == 3                       -> 1
      sum == 2 and board[{x,y}] == 1 -> 1
      true                           -> 0
    end
  end
  
  defp barren?(board) do
    Enum.all?(board, fn {_,v} -> v == 0 end)
  end

  defp print_board(board, name, n, generation) do
    IO.puts "#{name}: generation #{generation}"
    Enum.each(1..n, fn y ->
      Enum.map(1..n, fn x -> if board[{x,y}]==1, do: "#", else: "." end)
      |> IO.puts
    end)
  end
end

Conway.game_of_life("blinker", 3, 2, [{2,1},{2,2},{2,3}])
Conway.game_of_life("glider", 4, 4, [{2,1},{3,2},{1,3},{2,3},{3,3}])
Conway.game_of_life("random", 5, 10)
Output:
blinker: generation 0
.#.
.#.
.#.
blinker: generation 1
...
###
...
blinker: generation 2
.#.
.#.
.#.
specified lifetime ended

glider: generation 0
.#..
..#.
###.
....
glider: generation 1
....
#.#.
.##.
.#..
glider: generation 2
....
..#.
#.#.
.##.
glider: generation 3
....
.#..
..##
.##.
glider: generation 4
....
..#.
...#
.###
specified lifetime ended

random: generation 0
.#...
#.#..
#...#
###.#
..#..
random: generation 1
.#...
#....
#.#..
#.#..
..##.
random: generation 2
.....
#....
#....
..#..
.###.
random: generation 3
.....
.....
.#...
..##.
.###.
random: generation 4
.....
.....
..#..
...#.
.#.#.
random: generation 5
.....
.....
.....
...#.
..#..
random: generation 6
.....
.....
.....
.....
.....
no more life.

Emacs Lisp

#!/usr/bin/env emacs -script
;; -*- lexical-binding: t -*-
;; run: ./conways-life conways-life.config
(require 'cl-lib)

(defconst blinker '("***"))
(defconst toad '(".***" "***."))
(defconst pentomino-p '(".**" ".**" ".*."))
(defconst pi-heptomino '("***" "*.*" "*.*"))
(defconst glider '(".*." "..*" "***"))
(defconst pre-pulsar '("***...***" "*.*...*.*" "***...***"))
(defconst ship '("**." "*.*" ".**"))
(defconst pentadecathalon '("**********"))
(defconst clock '("..*." "*.*." ".*.*" ".*.."))

(defmacro swap (a b)
  `(setq ,b (prog1 ,a (setq ,a ,b))))

(cl-defstruct world rows cols data)

(defun new-world (rows cols)
  (make-world :rows rows :cols cols :data (make-vector (* rows cols) nil)))

(defmacro world-pt (w r c)
  `(+ (* (mod ,r (world-rows ,w)) (world-cols ,w))
      (mod ,c (world-cols ,w))))

(defmacro world-ref (w r c)
  `(aref (world-data ,w) (world-pt ,w ,r ,c)))

(defun print-world (world)
  (dotimes (r (world-rows world))
    (dotimes (c (world-cols world))
      (princ (format "%c" (if (world-ref world r c) ?* ?.))))
    (terpri)))

(defun insert-pattern (world row col shape)
  (let ((r row)
        (c col))
    (unless (listp shape)
      (setq shape (symbol-value shape)))
    (dolist (row-data shape)
      (dolist (col-data (mapcar 'identity row-data))
        (setf (world-ref world r c) (not (or (eq col-data ?.))))
        (setq c (1+ c)))
      (setq r (1+ r))
      (setq c col))))

(defun neighbors (world row col)
  (let ((n 0))
    (dolist (offset '((1 . 1) (1 . 0) (1 . -1) (0 . 1) (0 . -1) (-1 . 1) (-1 . 0) (-1 . -1)))
      (when (world-ref world (+ row (car offset)) (+ col (cdr offset)))
        (setq n (1+ n))))
    n))

(defun advance-generation (old new)
  (dotimes (r (world-rows old))
    (dotimes (c (world-cols old))
      (let ((n (neighbors old r c)))
        (setf (world-ref new r c)
              (if (world-ref old r c)
                  (or (= n 2) (= n 3))
                (= n 3)))))))

(defun read-config (file-name)
  (with-temp-buffer
    (insert-file-contents-literally file-name)
    (read (current-buffer))))

(defun get-config (key config)
  (let ((val (assoc key config)))
    (if (null val)
        (error (format "missing value for %s" key))
      (cdr val))))

(defun insert-patterns (world patterns)
  (dolist (p patterns)
    (apply 'insert-pattern (cons world p))))

(defun simulate-life (file-name)
  (let* ((config (read-config file-name))
         (rows (get-config 'rows config))
         (cols (get-config 'cols config))
         (generations (get-config 'generations config))
         (a (new-world rows cols))
         (b (new-world rows cols)))
    (insert-patterns a (get-config 'patterns config))
    (dotimes (g generations)
      (princ (format "generation %d\n" g))
      (print-world a)
      (advance-generation a b)
      (swap a b))))

(simulate-life (elt command-line-args-left 0))

Configuration file, which defines the size starting patterns and how long the simulation will run.

((rows . 8)
 (cols . 10)
 (generations . 3)
 (patterns
  ;; Blinker is defined in the script.
  (1 1 blinker)
  ;; This is a custom pattern.
  (4 4 (".***"
        "***."))))
Output:
generation 0
..........
.***......
..........
..........
.....***..
....***...
..........
..........
generation 1
..*.......
..*.......
..*.......
......*...
....*..*..
....*..*..
.....*....
..........
generation 2
..........
.***......
..........
..........
.....***..
....***...
..........
..........

Erlang

-module(life).

-export([bang/1]).


-define(CHAR_DEAD,   32).  % " "
-define(CHAR_ALIVE, 111).  % "o"
-define(CHAR_BAR,    45).  % "-"

-define(GEN_INTERVAL, 100).


-record(state, {x            :: non_neg_integer()
               ,y            :: non_neg_integer()
               ,n            :: pos_integer()
               ,bar          :: nonempty_string()
               ,board        :: array()
               ,gen_count    :: pos_integer()
               ,gen_duration :: non_neg_integer()
               ,print_time   :: non_neg_integer()
               }).


%% ============================================================================
%% API
%% ============================================================================

bang(Args) ->
    [X, Y] = [atom_to_integer(A) || A <- Args],
    {Time, Board} = timer:tc(fun() -> init_board(X, Y) end),
    State = #state{x            = X
                  ,y            = Y
                  ,n            = X * Y
                  ,bar          = [?CHAR_BAR || _ <- lists:seq(1, X)]
                  ,board        = Board
                  ,gen_count    = 1  % Consider inital state to be generation 1
                  ,gen_duration = Time
                  ,print_time   = 0  % There was no print time yet
    },
    life_loop(State).


%% ============================================================================
%% Internal
%% ============================================================================

life_loop(
    #state{x            = X
          ,y            = Y
          ,n            = N
          ,bar          = Bar
          ,board        = Board
          ,gen_count    = GenCount
          ,gen_duration = Time
          ,print_time   = LastPrintTime
    }=State) ->

    {PrintTime, ok} = timer:tc(
        fun() ->
            do_print_screen(Board, Bar, X, Y, N, GenCount, Time, LastPrintTime)
        end
    ),

    {NewTime, NewBoard} = timer:tc(
        fun() ->
            next_generation(X, Y, Board)
        end
    ),

    NewState = State#state{board        = NewBoard
                          ,gen_count    = GenCount + 1
                          ,gen_duration = NewTime
                          ,print_time   = PrintTime
    },

    NewTimeMil = NewTime / 1000,
    NextGenDelay = at_least_zero(round(?GEN_INTERVAL - NewTimeMil)),
    timer:sleep(NextGenDelay),

    life_loop(NewState).


at_least_zero(Integer) when Integer >= 0 -> Integer;
at_least_zero(_) -> 0.


do_print_screen(Board, Bar, X, Y, N, GenCount, Time, PrintTime) ->
    ok = do_print_status(Bar, X, Y, N, GenCount, Time, PrintTime),
    ok = do_print_board(Board).


do_print_status(Bar, X, Y, N, GenCount, TimeMic, PrintTimeMic) ->
    TimeSec = TimeMic / 1000000,
    PrintTimeSec = PrintTimeMic / 1000000,
    ok = io:format("~s~n", [Bar]),
    ok = io:format(
        "X: ~b Y: ~b CELLS: ~b GENERATION: ~b DURATION: ~f PRINT TIME: ~f~n",
        [X, Y, N, GenCount, TimeSec, PrintTimeSec]
    ),
    ok = io:format("~s~n", [Bar]).


do_print_board(Board) ->
    % It seems that just doing a fold should be faster than map + to_list
    % combo, but, after measuring several times, map + to_list has been
    % consistently (nearly twice) faster than either foldl or foldr.
    RowStrings = array:to_list(
        array:map(
            fun(_, Row) ->
                array:to_list(
                    array:map(
                        fun(_, State) ->
                            state_to_char(State)
                        end,
                        Row
                    )
                )
            end,
            Board
        )
    ),

    ok = lists:foreach(
        fun(RowString) ->
            ok = io:format("~s~n", [RowString])
        end,
        RowStrings
    ).


state_to_char(0) -> ?CHAR_DEAD;
state_to_char(1) -> ?CHAR_ALIVE.


next_generation(W, H, Board) ->
    array:map(
        fun(Y, Row) ->
            array:map(
                fun(X, State) ->
                    Neighbors = filter_offsides(H, W, neighbors(X, Y)),
                    States = neighbor_states(Board, Neighbors),
                    LiveNeighbors = lists:sum(States),
                    new_state(State, LiveNeighbors)
                end,
                Row
            )
        end,
        Board
    ).


new_state(1, LiveNeighbors) when LiveNeighbors  <  2 -> 0;
new_state(1, LiveNeighbors) when LiveNeighbors  <  4 -> 1;
new_state(1, LiveNeighbors) when LiveNeighbors  >  3 -> 0;
new_state(0, LiveNeighbors) when LiveNeighbors =:= 3 -> 1;
new_state(State, _LiveNeighbors) -> State.


neighbor_states(Board, Neighbors) ->
    [array:get(X, array:get(Y, Board)) || {X, Y} <- Neighbors].


filter_offsides(H, W, Coordinates) ->
    [{X, Y} || {X, Y} <- Coordinates, is_onside(X, Y, H, W)].


is_onside(X, Y, H, W) when (X >= 0) and (Y >= 0) and (X < W) and (Y < H) -> true;
is_onside(_, _, _, _) -> false.


neighbors(X, Y) ->
    [{X + OffX, Y + OffY} || {OffX, OffY} <- offsets()].


offsets() ->
    [offset(D) || D <- directions()].


offset('N')  -> { 0, -1};
offset('NE') -> { 1, -1};
offset('E')  -> { 1,  0};
offset('SE') -> { 1,  1};
offset('S')  -> { 0,  1};
offset('SW') -> {-1,  1};
offset('W')  -> {-1,  0};
offset('NW') -> {-1, -1}.


directions() ->
    ['N', 'NE', 'E', 'SE', 'S', 'SW', 'W', 'NW'].


init_board(X, Y) ->
    array:map(fun(_, _) -> init_row(X) end, array:new(Y)).


init_row(X) ->
    array:map(fun(_, _) -> init_cell_state() end, array:new(X)).


init_cell_state() ->
    crypto:rand_uniform(0, 2).


atom_to_integer(Atom) ->
    list_to_integer(atom_to_list(Atom)).

ERRE

This is a simple implementation of Conway's game of Life with an endless world. Test pattern configuration is 'glider'.

PROGRAM LIFE

!$INTEGER

!$KEY
!for C-64 compatibility

CONST Xmax=38,Ymax=20

DIM x,y,N
DIM WORLD[39,21],NextWORLD[39,21]

BEGIN

! Glider test
!------------------------------------------
WORLD[1,1]=1 WORLD[1,2]=0 WORLD[1,3]=0
WORLD[2,1]=0 WORLD[2,2]=1 WORLD[2,3]=1
WORLD[3,1]=1 WORLD[3,2]=1 WORLD[3,3]=0
!------------------------------------------

PRINT(CHR$(12);"Press any key to interrupt")
LOOP
  PRINT(CHR$(11);) PRINT
  PRINT(STRING$(Xmax+2,"-"))
  !---------- endless world ---------
  FOR y=1 TO Ymax DO
    WORLD[0,y]=WORLD[Xmax,y]
    WORLD[Xmax+1,y]=WORLD[1,y]
  END FOR
  FOR x=1 TO Xmax DO
    WORLD[x,0]=WORLD[x,Ymax]
    WORLD[x,Ymax+1]=WORLD[x,1]
  END FOR
  WORLD[0,0]=WORLD[Xmax,Ymax]
  WORLD[Xmax+1,Ymax+1]=WORLD[1,1]
  WORLD[Xmax+1,0]=WORLD[1,Ymax]
  WORLD[0,Ymax+1]=WORLD[Xmax,1]
  !---------- endless world ---------
  FOR y=1 TO Ymax DO
    PRINT("|";)
    FOR x=1 TO Xmax DO
      PRINT(CHR$(32+WORLD[x,y]*3);)
      N=WORLD[x-1,y-1]+WORLD[x-1,y]+WORLD[x-1,y+1]+WORLD[x,y-1]
      N=N+WORLD[x,y+1]+WORLD[x+1,y-1]+WORLD[x+1,y]+WORLD[x+1,y+1]
      IF (WORLD[x,y]<>0 AND (N=2 OR N=3)) OR (WORLD[x,y]=0 AND N=3) THEN
        NextWORLD[x,y]=1
      ELSE
        NextWORLD[x,y]=0
      END IF
    END FOR
    PRINT("|")
  END FOR
  PRINT(STRING$(Xmax+2,"-"))
  PAUSE(0.1)

  FOR x=0 TO Xmax+1 DO
    FOR y=0 TO Ymax+1 DO
      WORLD[x,y]=NextWORLD[x,y]
      NextWORLD[x,y]=0
    END FOR
  END FOR
  REPEAT
      GET(A$)
  UNTIL A$<>""
  EXIT IF A$=CHR$(27)
END LOOP

PRINT("Press any key to exit")
REPEAT
UNTIL GETKEY$<>""
END PROGRAM

F#

The following F# implementation uses for visualization and is easily compiled into a standalone executable:
let count (a: _ [,]) x y =
  let m, n = a.GetLength 0, a.GetLength 1
  let mutable c = 0
  for x in x-1..x+1 do
    for y in y-1..y+1 do
      if x>=0 && x<m && y>=0 && y<n && a.[x, y] then
        c <- c + 1
  if a.[x, y] then c-1 else c

let rule (a: _ [,]) x y =
  match a.[x, y], count a x y with
  | true, (2 | 3) | false, 3 -> true
  | _ -> false

open System.Windows
open System.Windows.Media.Imaging

[<System.STAThread>]
do
  let rand = System.Random()
  let n = 256
  let game = Array2D.init n n (fun _ _ -> rand.Next 2 = 0) |> ref
  let image = Controls.Image(Stretch=Media.Stretch.Uniform)
  let format = Media.PixelFormats.Gray8
  let pixel = Array.create (n*n) 0uy
  let update _ =
    game := rule !game |> Array2D.init n n
    for x in 0..n-1 do
      for y in 0..n-1 do
        pixel.[x+y*n] <- if (!game).[x, y] then 255uy else 0uy
    image.Source <-
      BitmapSource.Create(n, n, 1.0, 1.0, format, null, pixel, n)
  Media.CompositionTarget.Rendering.Add update
  Window(Content=image, Title="Game of Life")
  |> (Application()).Run |> ignore

Fermat

;{Conway's Game of Life in Fermat}
;{square grid with wrap-around boundaries}

size:=50;                         {how big a grid do you want? This fits my screen OK, change this for your own screen}

Array w1[size,size], w2[size,size];      {set up an active world and a 'scratchpad' world}
act:=1;
buf:=2;
%[1]:=[w1];                      {Fermat doesn't have 3D arrays in the normal sense--}
%[2]:=[w2];                      {we need to use the somewhat odd "array of arrays" functionality}

Func Cls = for i = 1 to size do !!; od.;     {"clear screen" by printing a bunch of newlines}

Func Draw =                     {draw the active screen}
    for i = 1 to size do
        for j = 1 to size do
            if %[act][i, j] = 1 then !('# ') else !('. ') fi;
        od;
        !;
    od;
.;

Func Rnd =                                   {randomize the grid with a density of 40% live cells}
    for i = 1 to size do
        for j = 1 to size do
            if Rand|5<2 then %[act][i, j] := 1 else %[act][i, j] := 0 fi;
        od;
    od;
    Cls;
    Draw;
.;

Func Blinker =                               {clears the screen except for a blinker in the top left corner}
    for i = 1 to size do
        for j = 1 to size do
            %[act][i, j] := 0;
        od;
    od;
    %[act][1,2] := 1;
    %[act][2,2] := 1;
    %[act][3,2] := 1;
    Cls;
    Draw;
.;

Func Iter =                                 {do one iteration}
    for i = 1 to size do
        if i = 1 then im := size else im := i - 1 fi;        {handle wrap around}
        if i = size then ip := 1 else ip := i + 1 fi;
        for j = 1 to size do
            if j = 1 then jm := size else jm := j - 1 fi;
            if j = size then jp := 1 else jp := j + 1 fi;
            neigh :=  %[act][im, jm];                        {count neigbours}
            neigh :+ (%[act][im, j ]);
            neigh :+ (%[act][im, jp]);
            neigh :+ (%[act][i , jm]);
            neigh :+ (%[act][i , jp]);
            neigh :+ (%[act][ip, jm]);
            neigh :+ (%[act][ip, j ]);
            neigh :+ (%[act][ip, jp]);
            if neigh < 2 or neigh > 3 then %[buf][i, j] := 0 fi;      {alive and dead rules}
            if neigh = 2 then %[buf][i, j] := %[act][i, j] fi;
            if neigh = 3 then %[buf][i, j] := 1 fi;                              
        od;
    od;
    Swap(act, buf);     {rather than copying the scratch over into the active, just exchange their identities}
    Cls;
    Draw;
.;

choice := 9;
while choice <> 0 do              {really rough menu, not the point of this exercise}
    ?choice;
    if choice=4 then Cls fi;
    if choice=3 then Blinker fi;
    if choice=2 then Rnd fi;
    if choice=1 then Iter fi;
od;

!!'John Horton Conway (26 December 1937 – 11 April 2020)';
Output:
One iteration starting from random soup, showing a few well-known objects (blinker, block, glider, beehive, loaf)
# . . . . . . . . . # . . # . . . . . . . . # . . . . . . . . . . . . . . . . . . . . . . # # . . . 
. . . . . . . # . . # . . . # . . . . # # . # # . . # # # . . . . . . . . . . . . . . . # # . # . # 
. . . . . . # . # # . . . # . . . . . # # . # . . . # . . # . . . . . . . . . . . . . . # # . . # . 
. . . . . . # . # . # . . # . . . . . # . # # . . # . . . # . . . . # # . . . . . . . . . . . . . . 
. . . . . . . # . # # . . # . . . # # # # . . . . # . . # . . . . # . . # . . . . . . . . . . . . . 
. . . . . . . . . . . . # . . . . # . . . . . . . . . . . . . . . . # . . # . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . # # # . . . . . . # # . . . . . . # . . # . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . # . . . . . . . . . . . . . . . # . # . . . . . . . . . . . . . 
. . . . # # # . . . . . . . . . . . # . . . . # # . . . . . . . . . . # . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . # # # # . . # . # . . . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . # # . . # . . # . . . . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . # # # . . . . . . . # # . . . . . # . . . . . . . . . . # . . . . . . . . . . . . . . . 
. . . . . . # # # . . . . . . . . . . . # # . . . . . . . . . . . # . # . . . . . . . . . . . . . . 
. . . . . # . . # . # # . . . . . . # # . # . . . . . . . . . . . # . . # . . . . . . . . . . . . . 
. . . . . . # # . # # . . . . . . . . # # . . . . . . . . . . . . . # # . . . . . . . . . . . . . . 
. . . . . . # # # # # . . . . . . . . # . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . . # . . # . . . . . . . . . . . . . . . . . . . . . . . . . . . . . # # . . . . . . . . 
. . . . . . . . # # . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . # # . . . . . . . 
. . . . . . . . # # . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . # # . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . # # # . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . # # . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . # . # # . . . . . . # # # 
# . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . # # . . . . . . # . . . 
# . . . . . . # # . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . # # . # 
. . . . . . # . . # . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . . # # . . . . . . . . . . . . . . . . . . . . . . . . . . . . # # . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . # . # . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . # . . . . . . . . . . . 
# . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . # # # 
# # . . . . . . . # # . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . # . # # 
. # # . . . . . . # # . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . # # . . # 
. # . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . # . # . # # . . . . . . . # # . . . 
# . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . # . # . # . . . . . . . . . # # . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . # . . . . # . # # . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . # . . . # # # # . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . # # # . . # # . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . # # # . . . . . . . . . . . . . . . . . . . . . . . . # . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . # # # . . . . . . . . . . # . . . . . . . . 
. . . . . . . . . . . . # . . . . . . . . . . . . . . # . # . # # . # . . . . . . # . . . . . . . . 
. . . . . . . . . . . . # . . . . . . . . . . . . . # . . . . . . . . # . . . . . . . . . . . . . . 
. . . . . . . . . . . . # . . . . . . . . . . . . # . . # # # # . . . # . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . # # # . . . . . . # . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . # # . 
. . . . . . . . . . . . . . . . . # # . . . . . . . . . . . . . . . . . . . . . . . . . . . # . # . 
. . . . . . . . . . . . # # . . # . . . . . . . . . . . . . . . . . . . . . . . . . . . . # . . # . 
. . . . . . . . . . . . # . # . . # . . . . . . . . . . . . . . # . . . . . . . . . . . . # . . . . 
. . . . . . . . . . . . # . . . . . . # . . . . . . . . . . . # . . # . . . . . . . . . # # . # . . 
. . . . . . . . . . . . . . . . . . # . . . . . . . . . . . . . # # . . . . . . . . . . . . . . # # 
. . . . . . . . . . . # . # . . . . # . . # . . . . . . . . . . . . . . . . . . . . . . . # # # . # 

Forth

gencell uses an optimization for the core Game of Life rules: new state = (old state | neighbors == 3).

 \ The fast wrapping requires dimensions that are powers of 2.
 1 6 lshift constant w \ 64
 1 4 lshift constant h \ 16
 
 : rows    w * 2* ;
 1 rows constant row
 h rows constant size
 
 create world size allot
 world   value old
 old w + value new
 
 variable gens
 : clear  world size erase     0 gens ! ;
 : age  new old to new to old  1 gens +! ;
 
 : col+  1+ ;
 : col-  1- dup w and + ; \ avoid borrow into row
 : row+  row + ;
 : row-  row - ;
 : wrap ( i -- i ) [ size w - 1- ] literal and ;
 : w@ ( i -- 0/1 ) wrap old + c@ ;
 : w! ( 0/1 i -- ) wrap old + c! ;
 
 : foreachrow ( xt -- )
   size 0 do  I over execute  row +loop drop ;
 
 : showrow ( i -- ) cr
   old + w over + swap do I c@ if [char] * else bl then emit loop ;
 : show  ['] showrow foreachrow  cr ." Generation " gens @ . ;
 
 : sum-neighbors ( i -- i n )
   dup  col- row- w@
   over      row- w@ +
   over col+ row- w@ +
   over col-      w@ +
   over col+      w@ +
   over col- row+ w@ +
   over      row+ w@ +
   over col+ row+ w@ + ;
 : gencell ( i -- )
   sum-neighbors  over old + c@
   or 3 = 1 and   swap new + c! ;
 : genrow ( i -- )
   w over + swap do I gencell loop ;
 : gen  ['] genrow foreachrow  age ;
 
 : life  begin gen 0 0 at-xy show key? until ;

 \ patterns
 char | constant '|'
 : pat ( i addr len -- )
   rot dup 2swap  over + swap do
     I c@ '|' = if drop row+ dup else
     I c@ bl  = 1+ over w!  col+ then
   loop 2drop ;
 
 : blinker s" ***" pat ;
 : toad s" ***| ***" pat ;
 : pentomino s" **| **| *" pat ;
 : pi s" **| **|**" pat ;
 : glider s"  *|  *|***" pat ;
 : pulsar s" *****|*   *" pat ;
 : ship s"  ****|*   *|    *|   *" pat ;
 : pentadecathalon s" **********" pat ;
 : clock s"  *|  **|**|  *" pat ;

 clear  0 glider show
  *
   *
 ***
 
 Generation 0  ok
 gen show
 
 * *
  **
  *
 Generation 1  ok

Fortran

Works with: Fortran version 90 and later
 PROGRAM LIFE_2D
   IMPLICIT NONE
 
   INTEGER, PARAMETER :: gridsize = 10
   LOGICAL :: cells(0:gridsize+1,0:gridsize+1) = .FALSE.
   INTEGER :: i, j, generation=0
   REAL :: rnums(gridsize,gridsize)
 
 !  Start patterns
 !  **************
 !  cells(2,1:3) = .TRUE.                                                  ! Blinker
 !  cells(3,4:6) = .TRUE. ; cells(4,3:5) = .TRUE.                          ! Toad
 !  cells(1,2) = .TRUE. ; cells(2,3) = .TRUE. ; cells(3,1:3) = .TRUE.      ! Glider
    cells(3:5,3:5) = .TRUE. ; cells(6:8,6:8) = .TRUE.                      ! Figure of Eight
 !  CALL RANDOM_SEED
 !  CALL RANDOM_NUMBER(rnums)
 !  WHERE (rnums>0.6) cells(1:gridsize,1:gridsize) = .TRUE.                ! Random universe
   
   CALL Drawgen(cells(1:gridsize, 1:gridsize), generation)
   DO generation = 1, 8
      CALL NextgenV2(cells)
      CALL Drawgen(cells(1:gridsize, 1:gridsize), generation)
   END DO
 
 CONTAINS
 
   SUBROUTINE Drawgen(cells, gen)
     LOGICAL, INTENT(IN OUT) :: cells(:,:)
     INTEGER, INTENT(IN) :: gen
 
     WRITE(*, "(A,I0)") "Generation ", gen 
     DO i = 1, SIZE(cells,1)
        DO j = 1, SIZE(cells,2)
           IF (cells(i,j)) THEN
              WRITE(*, "(A)", ADVANCE = "NO") "#"
           ELSE
              WRITE(*, "(A)", ADVANCE = "NO") " "
           END IF
        END DO
        WRITE(*,*)
     END DO
     WRITE(*,*)
   END SUBROUTINE Drawgen
 
  SUBROUTINE Nextgen(cells)
     LOGICAL, INTENT(IN OUT) :: cells(0:,0:)
     LOGICAL :: buffer(0:SIZE(cells, 1)-1, 0:SIZE(cells, 2)-1)
     INTEGER :: neighbours, i, j
   
     buffer = cells   ! Store current status
     DO j = 1, SIZE(cells, 2)-2
        DO i = 1, SIZE(cells, 1)-2
          if(buffer(i, j)) then
            neighbours = sum(count(buffer(i-1:i+1, j-1:j+1), 1)) - 1
          else
            neighbours = sum(count(buffer(i-1:i+1, j-1:j+1), 1))
          end if
  
          SELECT CASE(neighbours)
            CASE (0:1, 4:8)
               cells(i,j) = .FALSE.
  
            CASE (2)
               ! No change
  
            CASE (3)
               cells(i,j) = .TRUE.
          END SELECT
          
        END DO
     END DO
  END SUBROUTINE Nextgen

!###########################################################################
!   In this version instead of cycling through all points an integer array
! is used the sum the live neighbors of all points. The sum is done with
! the entire array cycling through the eight positions of the neighbors.
!   Executing a grid size of 10000 in 500 generations this version gave a 
! speedup of almost 4 times.
!###########################################################################
  PURE SUBROUTINE NextgenV2(cells)
     LOGICAL, INTENT(IN OUT) :: cells(:,:)
     INTEGER(KIND=1) :: buffer(1:SIZE(cells, 1)-2,1:SIZE(cells, 2)-2)
     INTEGER :: gridsize, i, j
     
     gridsize=SIZE(cells, 1)
     buffer=0
     
     DO j=-1, 1
        DO i=-1,1
           IF(i==0 .AND. j==0) CYCLE
           WHERE(cells(i+2:gridsize-i-1,j+2:gridsize-j-1)) buffer=buffer+1
        END DO
     END DO

     WHERE(buffer<2 .or. buffer>3) cells(2:gridsize-1,2:gridsize-1) = .FALSE.
     WHERE(buffer==3) cells(2:gridsize-1,2:gridsize-1) = .TRUE.
  END SUBROUTINE NextgenV2
!###########################################################################
 END PROGRAM LIFE_2D
Output:
Blinker
 Generation 0
    
  ### 
    
 
 Generation 1
  #  
  #  
  #  
 
 Generation 2
    
 ###
Figure of Eight (a period eight oscillator)
 Generation 0
           
           
   ###      
   ###      
   ###      
      ###   
      ###   
      ###   
           
           
 
 Generation 1
           
    #       
   # #      
  #   #     
   #   #    
    #   #   
     #   #  
      # #   
       #    
           
 
 Generation 2
           
    #       
   ###      
  ### #     
   #   #    
    #   #   
     # ###  
      ###   
       #    
           
 
 Generation 3
           
   ###      
  #         
  #   #     
  #  # #    
    # #  #  
     #   #  
         #  
      ###   
           
 
 Generation 4
    #       
   ##       
  # ##      
 ###  #     
   # # #    
    # # #   
     #  ### 
      ## #  
       ##   
       #    
 
 Generation 5
   ##       
           
 #   #      
 #    #     
   # # #    
    # # #   
     #    # 
      #   # 
           
       ##   
 
 Generation 6
           
    #       
           
  # ###     
    ## #    
    # ##    
     ### #  
           
       #    
           
 
 Generation 7
           
           
   ##       
   ## #     
       #    
    #       
     # ##   
       ##   
           
         
 
 Generation 8
           
           
   ###      
   ###      
   ###      
      ###   
      ###   
      ###

Frink

Simple solution using two dictionaries (a display and a toggle) to store grid and track changes. The program outputs an animation of the game.

start = now[]
// Generate a random 10x10 grid with "1" being on and "0" being off
instructions = ["1000100110","0001100010","1000111101","1001111110","0000110011","1111000001","0100001110","1011101001","1001011000","1101110111"]

// Create dictionary of starting positions.
rowCounter = 0
display = new dict
for instructionStr = instructions
{
   rowCounter = rowCounter + 1
   columnCounter = 0
   instructionArr = charList[instructionStr]
   for instruction = instructionArr
   {
      columnCounter = columnCounter + 1
      arr = [rowCounter,columnCounter]
      if instruction == "1"
         display@arr = 1
      else
         display@arr = 0
   }
}

// Create toggle dictionary to track changes. It starts off with everything off.
toggle = new dict
multifor[x,y] = [new range[1,10],new range[1,10]]
{
   arr = [x,y]
   toggle@arr = 0
}

// Animate the game of life
a = new Animation[3/s]
win = undef

// Loop through 10 changes to the grid. The starting points will tick down to two stable unchanging shapes in 10 steps.
for i = 1 to 12 // 12 steps so animation will pause on final state.
{
   // Graphics item for this frame of the animation.
   g = new graphics
   g.backgroundColor[1,1,1]
   // Add in a transparent shape to prevent the image from jiggle to automatic scaling.
   g.color[0,0,0,0] // Transparent black
   g.fillRectSides[-1, -1, 12, 12] // Set minimum size
   g.clipRectSides[-1, -1, 12, 12] // Set maximum size
   g.color[0,0,0] // Color back to default black
   multifor[x1,y1] = [new range[1,10],new range[1,10]]
   {
      tval = [x1,y1]
      // This is programmed with a hard edge. Points beyond the border aren't considered.
      xmax = min[x1+1,10]
      xmin = max[x1-1,1]
      ymax = min[y1+1,10]
      ymin = max[y1-1,1]
      // Range will be 8 surrounding cells or cells up to border.
      pointx = new range[xmin,xmax]
      pointy = new range[ymin,ymax]
      pointsum = 0
      status = 0
      // Process each surrounded point
      multifor[x2,y2] = [pointx,pointy]
      {
         // Assign the array to a variable so it can be used as a dictionary reference.
         point = [x2,y2]
         if x2 == x1 && y2 == y1
         {
            status = display@point
         } else // Calculate the total of surrounding points
         {
            pointsum = pointsum + display@point
         }
      }
      // Animate if the point is on.
      if status == 1
      {
         g.color[0,0,0]
         g.fillEllipseCenter[x1,y1,1,1]
      }
      toggle@tval = status // This will be overwritten if needed by neighbor check conditions below.
	  // Check if off point has 3 on point neighbors
      if status == 0 && pointsum == 3
      {
         toggle@tval = 1
      }
	  // Check if on point has between 2 and 3 on point neighbors
      if status == 1 && (pointsum < 2 || pointsum > 3)
      {
         toggle@tval = 0
      }
   }
   // Add the current frame to the animation
   a.add[g]
   // Replace the current display with the toggle values.
   for toggleKeys = keys[toggle]
   {
      val = toggle@toggleKeys
      display@toggleKeys = val
   }
}

// Write the animation file
a.write["FrinkAnimationGoL.gif",400,400]

end = now[]
println["Program run time: " + ((end - start)*1.0 -> "seconds")]

FunL

import lists.zipWithIndex
import util.Regex

data Rule( birth, survival )

val Mirek = Regex( '([0-8]+)/([0-8]+)' )
val Golly = Regex( 'B([0-8]+)/S([0-8]+)' )

def decode( rule ) =
  def makerule( b, s ) = Rule( [int(d) | d <- b], [int(d) | d <- s] )

  case rule
    Mirek( s, b ) -> makerule( b, s )
    Golly( b, s ) -> makerule( b, s )
    _ -> error( "unrecognized rule: $rule" )

def fate( state, crowding, rule ) = crowding in rule( int(state) )

def crowd( buffer, x, y ) =
  res = 0

  def neighbour( x, y ) =
    if x >= 0 and x < N and y >= 0 and y < N
      res += int( buffer(x, y) )

  for i <- x-1..x+1
    neighbour( i, y - 1 )
    neighbour( i, y + 1 )

  neighbour( x - 1, y )
  neighbour( x + 1, y )
  res

def display( buffer ) =
  for j <- 0:N
    for i <- 0:N
      print( if buffer(i, j) then '*' else '\u00b7' )

    println()

def generation( b1, b2, rule ) =
  for i <- 0:N, j <- 0:N
    b2(i, j) = fate( b1(i, j), crowd(b1, i, j), rule )

def pattern( p, b, x, y ) =
  for (r, j) <- zipWithIndex( list(WrappedString(p).stripMargin().split('\n')).drop(1).dropRight(1) )
    for i <- 0:r.length()
      b(x + i, y + j) = r(i) == '*'

var current = 0
val LIFE = decode( '23/3' )
val N = 4
val buffers = (array( N, N, (_, _) -> false ), array( N, N ))

def reset =
  for i <- 0:N, j <- 0:N
    buffers(0)(i, j) = false

  current = 0

def iteration =
  display( buffers(current) )
  generation( buffers(current), buffers(current = (current + 1)%2), LIFE )
  println( 5'-' )

// two patterns to be tested
blinker = '''
  |
  |***
  '''

glider = '''
  | *
  |  *
  |***
  '''

// load "blinker" pattern and run for three generations
pattern( blinker, buffers(0), 0, 0 )

repeat 3
  iteration()

// clear grid, load "glider" pattern and run for five generations
reset()
pattern( glider, buffers(0), 0, 0 )

repeat 5
  iteration()
Output:
····
***·
····
····
-----
·*··
·*··
·*··
····
-----
····
***·
····
····
-----
·*··
··*·
***·
····
-----
····
*·*·
·**·
·*··
-----
····
··*·
*·*·
·**·
-----
····
·*··
··**
·**·
-----
····
··*·
···*
·***
-----

Furor

// Life simulator (game). Console (CLI) version.
// It is a 'cellular automaton', and was invented by Cambridge mathematician John Conway.

// The Rules

// For a space that is 'populated':
//     Each cell with one or no neighbors dies, as if by solitude.
//     Each cell with four or more neighbors dies, as if by overpopulation.
//     Each cell with two or three neighbors survives.
// For a space that is 'empty' or 'unpopulated'
//     Each cell with three neighbors becomes populated.
// -----------------------------------------------------
#g
// Get the terminal-resolution:
terminallines   -- sto tlin
terminalcolumns    sto tcol
// .............................
// Verify the commandline parameters:
argc 3 < { #s ."Usage: " 0 argv print SPACE 1 argv print ." lifeshape-file.txt\n" end }
2 argv 'f !istrue { #s ."The given file ( " 2 argv print ." ) doesn't exist!\n" end }
startingshape 2 argv filetolist // read the file into the list
startingshape maxlinelength sto maxlinlen
neighbour    @tlin @tcol createlist   // Generate the stringarray for the neighbour-calculations
livingspace  @tlin @tcol createlist   // Generate the stringarray for the actual generations
cellscreen   @tlin @tcol createscreen // Generate the stringarray for the visible livingspace
// Calculate offset for the shape ( it must be put to the centre):
@tlin startingshape~ - 2 / sto originlin
@tcol @maxlinlen     - 2 / sto origincol

startingshape {{|
{{}} {{|}} {{-}} [[]] 32 > { 1 }{ 0 } sto emblem
livingspace @originlin {{|}} + @origincol {{-}} + @emblem [[^]]
|}}

cursoroff
// ==================================================================
{... // infinite loop starts
sbr §renderingsbr
topleft cellscreen !printlist
."Generation: " {...} print fflush // print the number of the generations.
neighbour 0 filluplist // fill up the neighbour list with zero value
// Calculate neighbourhoods
neighbour {{|
{{|}} {{-}} sbr §neighbors
{{}} {{|}} {{-}} @n [[^]] // store the neighbournumber
|}}

// Now, kill everybody if the neighbors are less than 2 or more than 3:
neighbour {{|
{{|}} {{-}} sbr §killsbr
|}}

// Generate the newborn cells:
neighbour {{|
{{}} {{|}} {{-}} [[]] 3 == { livingspace {{|}} {{-}} 1 [[^]] }
|}}

50000 usleep
//2 sleep
...} // infinite loop ends
// ==================================================================
end
killsbr:
sto innerindex sto outerindex
neighbour @outerindex @innerindex [[]] 2 < then §kill
neighbour @outerindex @innerindex [[]] 3 > then §kill
rts
kill: livingspace @outerindex @innerindex 0 [[^]] rts
// ==========================================================
neighbors: // This subroutine calculates the quantity of neighborhood
sto y sto x zero n
livingspace @x ? @tlin --                 @y ? @tcol --                  [[]] sum n // upleft    corner
livingspace @x ? @tlin --                 @y                             [[]] sum n // upmid     corner
livingspace @x ? @tlin --                 @y ++ dup  @tcol == { drop 0 } [[]] sum n // upright   corner
livingspace @x                            @y ? @tcol --                  [[]] sum n // midleft   corner
livingspace @x                            @y ++ dup  @tcol == { drop 0 } [[]] sum n // midright  corner
livingspace @x ++ dup @tlin == { drop 0 } @y ? @tcol --                  [[]] sum n // downleft  corner
livingspace @x ++ dup @tlin == { drop 0 } @y                             [[]] sum n // downmid   corner
livingspace @x ++ dup @tlin == { drop 0 } @y ++ dup  @tcol == { drop 0 } [[]] sum n // downright corner
rts
// ==========================================================
renderingsbr:
livingspace {{|
cellscreen   {{|}} {{-}}
{{}} {{|}} {{-}} [[]] { '* }{ 32 } [[^]]
|}}
rts

{ „startingshape” }
{ „livingspace” }
{ „cellscreen” }
{ „innerindex” }
{ „outerindex” }
{ „maxlinlen” }
{ „neighbour” }
{ „originlin” }
{ „origincol” }
{ „emblem” }
{ „tlin” }
{ „tcol” }
{ „x” } { „y” } { „n” }

Peri

###sysinclude standard.uh
###sysinclude args.uh
###sysinclude str.uh
###sysinclude system.uh
// Life simulator (game).
// It is a 'cellular automaton', and was invented by Cambridge mathematician John Conway.

// The Rules

// For a space that is 'populated':
//     Each cell with one or no neighbors dies, as if by solitude.
//     Each cell with four or more neighbors dies, as if by overpopulation.
//     Each cell with two or three neighbors survives.
// For a space that is 'empty' or 'unpopulated'
//     Each cell with three neighbors becomes populated.
// --------------------------------------------------------------------------------------------
#g
// Get the terminal-resolution:
terminallines   -- sto tlin
terminalcolumns    sto tcol
// .............................
// Verify the commandline parameters:
argc 3 < { #s ."Usage: " 0 argv print SPACE    1 argv print ." lifeshape-file.txt\n" end }
2 argv 'f inv istrue { #s ."The given file ( " 2 argv print ." ) doesn't exist!\n"   end }
2 argv filetolist sto startingshape // read the file into the list
[[startingshape]]~~~  sto maxlinlen
@tlin @tcol [[mem]]   sto neighbour   // Generate the stringarray for the neighbour-calculations
@tlin @tcol [[mem]]   sto livingspace // Generate the stringarray for the actual generations
@tlin @tcol [[mem]]!  sto cellscreen  // Generate the stringarray for the visible livingspace
// Calculate offset for the shape ( it must be put to the centre):
@tlin startingshape~ - 2 / sto originlin
@tcol @maxlinlen     - 2 / sto origincol

startingshape~ shaperead: {{ {{}} [[startingshape]]~ {{ {{}}§shaperead {{}} [[startingshape]][]
32 > { 1 }{ 0 } sto emblem
@originlin {{}}§shaperead + @origincol {{}} + @emblem inv [[livingspace]][]
}}
}}
cursoroff
// ==================================================================
{.. // infinite loop starts
sbr §renderingsbr
topleft @cellscreen ![[print]]
."Generation: " {..} print fflush // print the number of the generations.
0 [[neighbour]][^] // fill up the neighbour list with zero value
// Calculate neighbourhoods
@tlin linloop: {{ // loop for every lines
@tcol          {{ // loop for every columns
{{}}§linloop {{}} sbr §neighbors
{{}}§linloop {{}} @nn inv [[neighbour]][] // store the neighbournumber
}} }}
// Now, kill everybody if the neighbors are less than 2 or more than 3:
@tlin linloop2: {{ // loop for every lines
@tcol           {{ // loop for every columns
{{}}§linloop2 {{}} [[neighbour]][] 2 < then §kill
{{}}§linloop2 {{}} [[neighbour]][] 3 > then §kill
{{<}} // Continue the inner loop
kill: {{}}§linloop2 {{}} 0 inv [[livingspace]][]
}} }}
@tlin linloop3: {{ // loop for every lines
@tcol           {{ // loop for every columns
// Generate the newborn cells:
{{}}§linloop3 {{}} [[neighbour]][] 3 == { {{}}§linloop3 {{}} 1 inv [[livingspace]][] }
}} }}
50000 inv sleep
..} // infinite loop ends
// ==================================================================
end
// ==========================================================
neighbors: // This subroutine calculates the quantity of neighborhood
sto xx sto yy zero nn
@yy ?   @tlin -- @xx ?   @tcol --  [[livingspace]][] sum nn // upleft    corner
@yy              @xx ?   @tcol --  [[livingspace]][] sum nn // upmid     corner
@yy ++?  tlin    @xx ?   @tcol --  [[livingspace]][] sum nn // upright   corner
@yy ?   @tlin -- @xx               [[livingspace]][] sum nn // midleft   corner
@yy ++?  tlin    @xx               [[livingspace]][] sum nn // midright  corner
@yy ?   @tlin -- @xx ++?  tcol     [[livingspace]][] sum nn // downleft  corner
@yy              @xx ++?  tcol     [[livingspace]][] sum nn // downmid   corner
@yy ++?  tlin    @xx ++?  tcol     [[livingspace]][] sum nn // downright corner
rts
// ==========================================================
renderingsbr:
@tlin livingspaceloop: {{ @tcol {{
{{}}§livingspaceloop {{}}
{{}}§livingspaceloop {{}} [[livingspace]][] { '* }{ 32 } inv [[cellscreen]][]
}}
}}
rts

{ „tlin” }
{ „tcol” }
{ „startingshape” }
{ „maxlinlen” }
{ „livingspace” }
{ „neighbour” }
{ „originlin” }
{ „origincol” }
{ „emblem” }
{ „cellscreen” }
{ „xx” } { „yy” } { „nn” }

Futhark

This example is incorrect. Please fix the code and remove this message.
Details: Futhark's syntax has changed, so this example will not compile
fun bint(b: bool): int = if b then 1 else 0
fun intb(x: int): bool = if x == 0 then False else True

fun to_bool_board(board: [][]int): [][]bool =
  map (fn (r: []int): []bool  => map intb r) board

fun to_int_board(board: [][]bool): [][]int =
  map (fn (r: []bool): []int  => map bint r) board

fun cell_neighbors(i: int, j: int, board: [n][m]bool): int =
  unsafe
  let above = (i - 1) % n
  let below = (i + 1) % n
  let right = (j + 1) % m
  let left = (j - 1) % m in
  bint board[above,left] + bint board[above,j]  + bint board[above,right] +
  bint board[i,left] + bint board[i,right] +
  bint board[below,left] + bint board[below,j] + bint board[below,right]

fun all_neighbours(board: [n][m]bool): [n][m]int =
  map (fn (i: int): []int  =>
        map (fn (j: int): int  => cell_neighbors(i,j,board)) (iota m))
      (iota n)

fun iteration(board: [n][m]bool): [n][m]bool =
  let lives = all_neighbours(board) in
  zipWith (fn (lives_r: []int) (board_r: []bool): []bool  =>
            zipWith (fn (neighbors: int) (alive: bool): bool  =>
                      if neighbors < 2
                      then False
                      else if neighbors == 3 then True
                      else if alive && neighbors < 4 then True
                      else False)
                    lives_r board_r)
           lives board

fun main(int_board: [][]int, iterations: int): [][]int =
  -- We accept the board as integers for convenience, and then we
  -- convert to booleans here.
  let board = to_bool_board int_board in
  loop (board) = for i < iterations do
    iteration board in
  to_int_board board


FutureBasic

This is just the basic central routine.

Short a(4, 4), c(4, 4) // Initialize arrays of cells and a working copy

void local fn seed
  Short x, y
  // Blinker
  a(1, 2) = 1 : a(2, 2) = 1 : a(3, 2) =  1
  for y = 1 to 3 : for x = 1 to 3
    print a(x, y); // Draw array
  next : print : next : print
end fn

void local fn nextGen
  Short x, y, dx, dy, n
  // Calculate next generation on temporary board
  for y = 1 to 3 : for x = 1 to 3
    c(x, y) = 0 // Initialize
    n = -a(x, y) // Don't count center cell
    for dy = -1 to 1 : for dx = -1 to 1
      n += a(x + dx, y + dy) // Count the neighbours
    next : next
    c(x, y) = ( n == 3 ) or ( n == 2 and a(x, y) ) // Conway’s rule
  next : next
  // Copy temp array to actual array and draw
  for y = 1 to 3 : for x = 1 to 3
    a(x, y) = c(x, y) // Copy
    print a(x, y); // Draw
  next : print : next : print
end fn

fn seed
fn nextGen 
fn nextGen

handleevents // Go into Mac event loop

Just three generations, as requested:

000
111
000

010
010
010

000
111
000


Go

package main

import (
	"bytes"
	"fmt"
	"math/rand"
	"time"
)

type Field struct {
	s    [][]bool
	w, h int
}

func NewField(w, h int) Field {
	s := make([][]bool, h)
	for i := range s {
		s[i] = make([]bool, w)
	}
	return Field{s: s, w: w, h: h}
}

func (f Field) Set(x, y int, b bool) {
	f.s[y][x] = b
}

func (f Field) Next(x, y int) bool {
	on := 0
	for i := -1; i <= 1; i++ {
		for j := -1; j <= 1; j++ {
			if f.State(x+i, y+j) && !(j == 0 && i == 0) {
				on++
			}
		}
	}
	return on == 3 || on == 2 && f.State(x, y)
}

func (f Field) State(x, y int) bool {
	for y < 0 {
		y += f.h
	}
	for x < 0 {
		x += f.w
	}
	return f.s[y%f.h][x%f.w]
}

type Life struct {
	w, h int
	a, b Field
}

func NewLife(w, h int) *Life {
	a := NewField(w, h)
	for i := 0; i < (w * h / 2); i++ {
		a.Set(rand.Intn(w), rand.Intn(h), true)
	}
	return &Life{
		a: a,
		b: NewField(w, h),
		w: w, h: h,
	}
}

func (l *Life) Step() {
	for y := 0; y < l.h; y++ {
		for x := 0; x < l.w; x++ {
			l.b.Set(x, y, l.a.Next(x, y))
		}
	}
	l.a, l.b = l.b, l.a
}

func (l *Life) String() string {
	var buf bytes.Buffer
	for y := 0; y < l.h; y++ {
		for x := 0; x < l.w; x++ {
			b := byte(' ')
			if l.a.State(x, y) {
				b = '*'
			}
			buf.WriteByte(b)
		}
		buf.WriteByte('\n')
	}
	return buf.String()
}

func main() {
	l := NewLife(80, 15)
	for i := 0; i < 300; i++ {
		l.Step()
		fmt.Print("\x0c")
		fmt.Println(l)
		time.Sleep(time.Second / 30)
	}
}

Running this program will compute and draw the first 300 "frames". The final frame looks like this:

        ** ****        *                                                        
         * **                                                                   
          *                                         **                          
*                                                  *  *                         
 *                   **        ****                 **                         *
  *                  **       *  **                                             
  *                      **        *                                            
                         **      *                                              
  ****              *        *                                     **         * 
 ***   **           *         ** ****                             *  *        **
* **     *  **      *              **                              **           
  *    *** ***                                                                  
            * **                                                                
         **   **       **                                                       
         ** *  *      * *                                                       

Groovy

class GameOfLife {

	int generations
	int dimensions
	def board
	
	GameOfLife(generations = 5, dimensions = 5) {
		this.generations = generations
		this.dimensions = dimensions
		this.board = createBlinkerBoard()
	}

	static def createBlinkerBoard() {
		[
			[].withDefault{0},
			[0,0,1].withDefault{0},
			[0,0,1].withDefault{0},
			[0,0,1].withDefault{0}
		].withDefault{[]}
	}

	static def createGliderBoard() {
		[
			[].withDefault{0},
			[0,0,1].withDefault{0},
			[0,0,0,1].withDefault{0},
			[0,1,1,1].withDefault{0}
		].withDefault{[]}
	}

	static def getValue(board, point) {
		def x,y
		(x,y) = point
		if(x < 0 || y < 0) {
			return 0
		}
		board[x][y] ? 1 : 0
	}
	
	static def countNeighbors(board, point) {
		def x,y
		(x,y) = point
		def neighbors = 0
		neighbors += getValue(board, [x-1,y-1])
		neighbors += getValue(board, [x-1,y])
		neighbors += getValue(board, [x-1,y+1])
		neighbors += getValue(board, [x,y-1])
		neighbors += getValue(board, [x,y+1])
		neighbors += getValue(board, [x+1,y-1])
		neighbors += getValue(board, [x+1,y])
		neighbors += getValue(board, [x+1,y+1])
		neighbors
	}

	static def conwaysRule(currentValue, neighbors) {
		def newValue = 0
		if(neighbors == 3 || (currentValue && neighbors == 2)) {
			newValue = 1
		}
		newValue
	}
	
	static def createNextGeneration(currentBoard, dimensions) {
		def newBoard = [].withDefault{[].withDefault{0}}
		(0..(dimensions-1)).each { row ->
			(0..(dimensions-1)).each { column ->
				def point = [row, column]
				def currentValue = getValue(currentBoard, point)
				def neighbors = countNeighbors(currentBoard, point)
				newBoard[row][column] = conwaysRule(currentValue, neighbors)
			}
		}
		newBoard
	}

	static def printBoard(generationCount, board, dimensions) {
		println "Generation ${generationCount}"
		println '*' * 80
		(0..(dimensions-1)).each { row ->
			(0..(dimensions-1)).each { column ->
				print board[row][column] ? 'X' : '.'
			}
			print System.getProperty('line.separator')
		}
		println ''
	}
	
	def start() {
		(1..generations).each { generation ->
			printBoard(generation, this.board, this.dimensions)
			this.board = createNextGeneration(this.board, this.dimensions)
		}
	}
	
}

// Blinker
def game = new GameOfLife()
game.start()

// Glider
game = new GameOfLife(10, 10)
game.board = game.createGliderBoard()
game.start()

The output of this program:

Generation 1
********************************************************************************
.....
..X..
..X..
..X..
.....

Generation 2
********************************************************************************
.....
.....
.XXX.
.....
.....

Generation 3
********************************************************************************
.....
..X..
..X..
..X..
.....

Generation 4
********************************************************************************
.....
.....
.XXX.
.....
.....

Generation 5
********************************************************************************
.....
..X..
..X..
..X..
.....

Generation 1
********************************************************************************
..........
..X.......
...X......
.XXX......
..........
..........
..........
..........
..........
..........

Generation 2
********************************************************************************
..........
..........
.X.X......
..XX......
..X.......
..........
..........
..........
..........
..........

Generation 3
********************************************************************************
..........
..........
...X......
.X.X......
..XX......
..........
..........
..........
..........
..........

Generation 4
********************************************************************************
..........
..........
..X.......
...XX.....
..XX......
..........
..........
..........
..........
..........

Generation 5
********************************************************************************
..........
..........
...X......
....X.....
..XXX.....
..........
..........
..........
..........
..........

Generation 6
********************************************************************************
..........
..........
..........
..X.X.....
...XX.....
...X......
..........
..........
..........
..........

Generation 7
********************************************************************************
..........
..........
..........
....X.....
..X.X.....
...XX.....
..........
..........
..........
..........

Generation 8
********************************************************************************
..........
..........
..........
...X......
....XX....
...XX.....
..........
..........
..........
..........

Generation 9
********************************************************************************
..........
..........
..........
....X.....
.....X....
...XXX....
..........
..........
..........
..........

Generation 10
********************************************************************************
..........
..........
..........
..........
...X.X....
....XX....
....X.....
..........
..........
..........

Haskell

import Data.Array.Unboxed

type Grid = UArray (Int,Int) Bool
 -- The grid is indexed by (y, x).

life :: Int -> Int -> Grid -> Grid
{- Returns the given Grid advanced by one generation. -}
life w h old =
    listArray b (map f (range b))
  where b@((y1,x1),(y2,x2)) = bounds old
        f (y, x) = ( c && (n == 2 || n == 3) ) || ( not c && n == 3 )
          where c = get x y
                n = count [get (x + x') (y + y') |
                    x' <- [-1, 0, 1], y' <- [-1, 0, 1],
                    not (x' == 0 && y' == 0)]

        get x y | x < x1 || x > x2 = False
                | y < y1 || y > y2 = False
                | otherwise       = old ! (y, x)

count :: [Bool] -> Int
count = length . filter id

Example of use:

import Data.List (unfoldr)

grid :: [String] -> (Int, Int, Grid)
grid l = (width, height, a)
  where (width, height) = (length $ head l, length l)
        a = listArray ((1, 1), (height, width)) $ concatMap f l
        f = map g
        g '.' = False
        g _   = True

printGrid :: Int -> Grid -> IO ()
printGrid width = mapM_ f . split width . elems
  where f = putStrLn . map g
        g False = '.'
        g _     = '#'

split :: Int -> [a] -> [[a]]
split n = takeWhile (not . null) . unfoldr (Just . splitAt n)

blinker = grid
   [".#.",
    ".#.",
    ".#."]

glider = grid
   ["............",
    "............",
    "............",
    ".......###..",
    ".......#....",
    "........#...",
    "............"]

printLife :: Int -> (Int, Int, Grid) -> IO ()
printLife n (w, h, g) = mapM_ f $ take n $ iterate (life w h) g
  where f g = do
            putStrLn "------------------------------"
            printGrid w g

main = printLife 10 glider

Here's the gridless version. It could probably be improved with some light use of Data.Set, but I leave that as an exercise for the reader. Note that the function lifeStep is the solution in its entirety. The rest of this code deals with printing and test data for the particular model of the world we're using.

module Main where
import Data.List

lifeStep :: [(Int, Int)] -> [(Int, Int)]
lifeStep cells = [head g | g <- grouped cells, viable g]
  where grouped = group . sort . concatMap neighbors
        neighbors (x, y) = [(x+dx, y+dy) | dx <- [-1..1], dy <- [-1..1], (dx,dy) /= (0,0)]
        viable [_,_,_] = True
        viable [c,_] = c `elem` cells
        viable _ = False


showWorld :: [(Int, Int)] -> IO ()
showWorld cells = mapM_ putStrLn $ worldToGrid cells
  where worldToGrid cells = [[cellChar (x, y) | x <- [least..greatest]] | y <- [least..greatest]]
        cellChar cell = if cell `elem` cells then '#' else '.'
        (least, greatest) = worldBounds cells

worldBounds cells = (least, greatest)
  where least = min x y
        greatest = max x' y'
        (x, y) = head cells
        (x', y') = last cells

runLife :: Int -> [(Int, Int)] -> IO ()
runLife steps cells = rec (steps - 1) cells
  where rec 0 cells = showWorld cells
        rec s cells = do showWorld cells
                         putStrLn ""
                         rec (s - 1) $ lifeStep cells

glider = [(1, 0), (2, 1), (0, 2), (1, 2), (2, 2)]
blinker = [(1, 0), (1, 1), (1, 2)]

main :: IO ()
main = do
  putStrLn "Glider >> 10"
  putStrLn "------------"
  runLife 10 glider
  putStrLn ""
  putStrLn "Blinker >> 3"
  putStrLn "------------"
  runLife 3 blinker

HolyC

Conway's Game of Life in HolyC for TempleOS ported from Conway's_Game_of_Life#C.

Also see the TempleOS implementation of Conway's Game of Life which makes use of the graphics engine.

Icon and Unicon

global limit

procedure main(args)
    n := args[1] | 50        # default is a 50x50 grid
    limit := args[2] | &null #  optional limit to number of generations
    write("Enter the starting pattern, end with EOF")
    grid := getInitialGrid(n)
    play(grid)
end

# This procedure reads in the initial pattern, inserting it
#   into an nXn grid of cells.  The nXn grid also gets a
#   new border of empty cells, which just makes the test simpler
#   for determining what do with a cell on each generation.
# It would be better to let the user move the cursor and click
#   on cells to create/delete living cells, but this version
#   assumes a simple ASCII terminal.
procedure getInitialGrid(n)
    static notBlank, allStars
    initial {
        notBlank := ~' '            
        allStars := repl("*",*notBlank)
        }

    g := []                # store as an array of strings

    put(g,repl(" ",n))
    while r := read() do {                        # read in rows of grid
        r := left(r,n)                            #   force each to length n
        put(g," "||map(r,notBlank,allStars)||" ") #   and making any life a '*'
        }
    while *g ~= (n+2) do
        put(g,repl(" ",n))
   
    return g
end

# Simple-minded procedure to 'play' Life from a starting grid.
procedure play(grid)
    while not allDone(grid) do {
        display(grid)
        grid := onePlay(grid)
        }
end

# Display the grid
procedure display(g)
    write(repl("-",*g[1]))
    every write(!g)
    write(repl("-",*g[1]))
end

# Compute one generation of Life from the current one.
procedure onePlay(g)
    ng := []
    every put(ng, !g)        # new generation starts as copy of old
    every ng[r := 2 to *g-1][c := 2 to *g-1] := case sum(g,r,c) of {
                            3:       "*"     # cell lives (or is born)
                            2:       g[r][c] # cell unchanged
                            default: " "     # cell dead
                            }
    return ng
end

# Return the number of living cells surrounding the current cell.
procedure sum(g,r,c)
    cnt := 0
    every (i := -1 to 1, j := -1 to 1) do
        if ((i ~= 0) | (j ~= 0)) & (g[r+i][c+j] == "*") then cnt +:= 1
    return cnt
end
            
# Check to see if all the cells have died or we've exceeded the 
#   number of allowed generations.
procedure allDone(g)
   static count
   initial count := 0
   return ((count +:= 1) > \limit) | (trim(!g) == " ")
end

A sample run:

->life 3 3
Enter the starting pattern, end with EOF

***
---
   
     
 *** 
   
   
---
---
   
  *  
  *  
  *
   
---
---
   
     
 *** 
   
   
---
->

INTERCAL

Works with: [the Pit] version 1

J

Solution:

pad=: 0,0,~0,.0,.~]
life=: (3 3 (+/ e. 3+0,4&{)@,;._3 ])@pad
NB. the above could also be a one-line solution:
life=: (3 3 (+/ e. 3+0,4&{)@,;._3 ])@(0,0,~0,.0,.~])

In other words, given a life instance, the next generation can be found by:

  1. . adding extra empty cells, surrounding the life instance,
  2. . tessellating the result, finding every overlapping 3 by 3 subinstance,
  3. . totaling the number of live cells in each subinstance,
  4. . treating a subinstance as a live cell iff that total is a member of the sequence 3,x where x is 3 if the center cell was previously dead, and 4 if the center cell was previously alive (that said, note that 4 is also the index of the center cell, with the sub instance arranged as a flat list).

Example (showing generations 0, 1 and 2 of a blinker):

   life^:0 1 2 #:0 7 0
0 0 0
1 1 1
0 0 0

0 1 0
0 1 0
0 1 0

0 0 0
1 1 1
0 0 0

Example (showing start and six following generations of a glider)

   blocks=: (2 2$2) ((7 u:' ▗▖▄▝▐▞▟▘▚▌▙▀▜▛█') {~ #.@,);._3 >.&.-:@$ {. ]
   blocks"2 life^:(i.7) 4 5{.#:1 5 3
▖▌ 
▝▘ 

▝▄ 
▝▘ 

 ▚   
▝▀ 

▗▗ 
 ▛   

 ▗   
▝▟ 

 ▖   
 ▟▘

 ▗   
 ▄▌

JAMES II/Rule-based Cellular Automata

Library: JAMES II
@caversion 1;

dimensions 2;

//using Moore neighborhood
neighborhood moore;

//available states
state DEAD, ALIVE;

/*
 if current state is ALIVE and the 
 neighborhood does not contain 2 or 
 3 ALIVE states the cell changes to 
 DEAD
*/
rule{ALIVE}:!ALIVE{2,3}->DEAD;

/*
 if current state is DEAD and there 
 are exactly 3 ALIVE cells in the 
 neighborhood the cell changes to 
 ALIVE
*/
rule{DEAD}:ALIVE{3}->ALIVE;

Animated output for the blinker example:

Java

public class GameOfLife{
	public static void main(String[] args){
		String[] dish= {
				"_#_",
				"_#_",
				"_#_",};
		int gens= 3;
		for(int i= 0;i < gens;i++){
			System.out.println("Generation " + i + ":");
			print(dish);
			dish= life(dish);
		}
	}

	public static String[] life(String[] dish){
		String[] newGen= new String[dish.length];
		for(int row= 0;row < dish.length;row++){//each row
			newGen[row]= "";
			for(int i= 0;i < dish[row].length();i++){//each char in the row
				String above= "";//neighbors above
				String same= "";//neighbors in the same row
				String below= "";//neighbors below
				if(i == 0){//all the way on the left
					//no one above if on the top row
					//otherwise grab the neighbors from above
					above= (row == 0) ? null : dish[row - 1].substring(i,
									i + 2);
					same= dish[row].substring(i + 1, i + 2);
					//no one below if on the bottom row
					//otherwise grab the neighbors from below
					below= (row == dish.length - 1) ? null : dish[row + 1]
									.substring(i, i + 2);
				}else if(i == dish[row].length() - 1){//right
					//no one above if on the top row
					//otherwise grab the neighbors from above
					above= (row == 0) ? null : dish[row - 1].substring(i - 1,
									i + 1);
					same= dish[row].substring(i - 1, i);
					//no one below if on the bottom row
					//otherwise grab the neighbors from below
					below= (row == dish.length - 1) ? null : dish[row + 1]
									.substring(i - 1, i + 1);
				}else{//anywhere else
					//no one above if on the top row
					//otherwise grab the neighbors from above
					above= (row == 0) ? null : dish[row - 1].substring(i - 1,
									i + 2);
					same= dish[row].substring(i - 1, i)
									+ dish[row].substring(i + 1, i + 2);
					//no one below if on the bottom row
					//otherwise grab the neighbors from below
					below= (row == dish.length - 1) ? null : dish[row + 1]
									.substring(i - 1, i + 2);
				}
				int neighbors= getNeighbors(above, same, below);
				if(neighbors < 2 || neighbors > 3){
					newGen[row]+= "_";//<2 or >3 neighbors -> die
				}else if(neighbors == 3){
					newGen[row]+= "#";//3 neighbors -> spawn/live
				}else{
					newGen[row]+= dish[row].charAt(i);//2 neighbors -> stay
				}
			}
		}
		return newGen;
	}

	public static int getNeighbors(String above, String same, String below){
		int ans= 0;
		if(above != null){//no one above
			for(char x: above.toCharArray()){//each neighbor from above
				if(x == '#') ans++;//count it if someone is here
			}
		}
		for(char x: same.toCharArray()){//two on either side
			if(x == '#') ans++;//count it if someone is here
		}
		if(below != null){//no one below
			for(char x: below.toCharArray()){//each neighbor below
				if(x == '#') ans++;//count it if someone is here
			}
		}
		return ans;
	}

	public static void print(String[] dish){
		for(String s: dish){
			System.out.println(s);
		}
	}
}
Output:
Generation 0:
_#_
_#_
_#_
Generation 1:
___
###
___
Generation 2:
_#_
_#_
_#_

Stretch

This fills in a random 10% of the grid, then activates the Game on it. Uncomment the call to the setCustomConfig function to use your own input. Just mind the grid limits. Use the input file given below to create a cool screensaver on your terminal.

//package conway;

import java.util.*;
import java.io.*;

public class GameOfLife 
{
	//Set grid size
	int l=20,b=60;
	public static void main(String[] args)
	{
		
		GameOfLife now=new GameOfLife();
		now.setGame();
	}
	void setGame()
	{
		char[][] config=new char[l][b];
		startGame(config,l,b);
	}
	void startGame(char[][] mat,int l, int b)
	{
		Scanner s=new Scanner(System.in);
		String ch="";
		float per=0;
		while(!ch.equals("y"))
		{
			per=setConfig(mat);
			//setCustomConfig(mat,"GOLglidergun.txt");
			display2D(mat);
			System.out.println((per*100)+"% of grid filled.");
			System.out.println("Begin? y/n");
			ch=s.nextLine();
		}
		while(!ch.equals("x"))
		{
			mat=transform(mat,l,b);
			display2D(mat);
			
			System.out.println("Ctrl+Z to stop.");
			
			try
			{
				Thread.sleep(100);
			}
			catch(Exception e)
			{
				System.out.println("Something went horribly wrong.");
			}
			
			//ch=s.nextLine();
		}
		s.close();
		System.out.println("Game Over");
	}
	
	char[][] transform(char[][] mat,int l, int b)
	{
		
		char[][] newmat=new char[l][b];
		for(int i=0;i<l;i++)
			for(int j=0;j<b;j++)
				newmat[i][j]=flip(mat,i,j);
		return newmat;
	}
	char flip(char[][] mat,int i, int j)
	{
		int count=around(mat,i,j);
		if(mat[i][j]=='*')
		{
			if(count<2||count>3)
				return '_';
			return '*';
		}
		else
		{
			if(count==3)
				return '*';
			return '_';
		}
	}
	int around(char[][] mat, int i, int j)
	{
		int count=0;
		for(int x=i-1;x<=i+1;x++)
			for(int y=j-1;y<=j+1;y++)
			{
				if(x==i&&y==j)
					continue;
				count+=eval(mat,x,y);
			}
		return count;
	}
	int eval(char[][] mat, int i, int j)
	{
		if(i<0||j<0||i==l||j==b)
			return 0;
		if(mat[i][j]=='*')
			return 1;
		return 0;
	}
	
	float setCustomConfig(char[][] arr,String infile)
	{
		try
		{
			BufferedReader br=new BufferedReader(new FileReader(infile));
			String line;
			for(int i=0;i<arr.length;i++)
			{
				line=br.readLine();
				for(int j=0;j<arr[0].length;j++)
					arr[i][j]=line.charAt(j);
			}
			br.close();
		}
		catch(Exception e)
		{
			System.out.println(e.getMessage());
		}
		return 0;
	}
	
	float setConfig(char[][] arr)
	{
		//Enter percentage of grid to be filled.
		float per=0.10f;//(float)Math.random();
		for(int i=0;i<arr.length;i++)
			setConfig1D(arr[i],per);
		return per;
	}
	void setConfig1D(char[] arr,float per)
	{
		for(int i=0;i<arr.length;i++)
		{
			if(Math.random()<per)
				arr[i]='*';
			else
				arr[i]='_';
		}
	}
	void display2D(char[][] arr)
	{
		for(int i=0;i<arr.length;i++)
			display1D(arr[i]);
		System.out.println();
	}
	void display1D(char[] arr)
	{
		for(int i=0;i<arr.length;i++)
			System.out.print(arr[i]);
		System.out.println();
	}
}

Glider Gun design. Save it in GOLglidergun.txt and uncomment the setCustomConfig function.

____________________________________________________________
_________________________*__________________________________
_______________________*_*__________________________________
_____________**______**____________**_______________________
____________*___*____**____________**_______________________
_**________*_____*___**_____________________________________
_**________*___*_**____*_*__________________________________
___________*_____*_______*__________________________________
____________*___*___________________________________________
_____________**_____________________________________________
____________________________________________________________
____________________________________________________________
____________________________________________________________
____________________________________________________________
____________________________________________________________
____________________________________________________________
____________________________________________________________
____________________________________________________________
____________________________________________________________
____________________________________________________________

Swing

See Conway's Game of Life/Java/Swing

Java 10

import static java.util.List.of;

class GameOfLife {

   boolean[][] board = new boolean[3][3];

   GameOfLife() {}

   GameOfLife(String[] board) {
      set((i, j, s) -> board[i].charAt(j * 2) == '■');
   }

   void set(Setter setter) {
      for (int i = 0; i < board.length; i++) {
         for (int j = 0; j < board[i].length; j++) {
            board[i][j] = setter.set(i, j, board[i][j]);
         }
      }
   }

   void get(Getter getter) {
      set((i, j, s) -> {
         getter.get(i, j, s);
         return s;
      });
   }

   int countNeighbors(int i, int j) {
      var counter = new Getter() {
         int count;

         @Override
         public void get(int li, int lj, boolean state) {
            if (distance(i, j, li, lj) == 1 && board[li][lj])
               count++;
         }
      };
      get(counter);
      return counter.count;
   }

   int distance(int i, int j, int li, int lj) {
      return Math.max(
           Math.abs(i - li),
           Math.abs(j - lj));
   }

   GameOfLife makeNextGeneration() {
      var n = new GameOfLife();
      n.set((i, j, s) -> {
         var alive = board[i][j];
         int c = countNeighbors(i, j);
         if (alive) {
            return c == 2 || c == 3;
         } else {
            return c == 3;
         }
      });
      return n;
   }

   void print() {
      get((i, j, s) -> {
         if (j == 0)
            System.out.println();
         System.out.print(s ? "■ " : "□ ");
      });
   }

   interface Setter {
      boolean set(int i, int j, boolean state);
   }

   interface Getter {
      void get(int i, int j, boolean state);
   }

   public static void main(String[] args) {
      String[] board = {
           "□ ■ □ ",
           "□ ■ □ ",
           "□ ■ □ ",
      };
      var gol = new GameOfLife(board);
      for (var generation : of(0, 1, 2)) {
         gol.print();
         System.out.println("\n");
         gol = gol.makeNextGeneration();
      }
   }

}

Outputs:

□ ■ □ 
□ ■ □ 
□ ■ □ 


□ □ □ 
■ ■ ■ 
□ □ □ 


□ ■ □ 
□ ■ □ 
□ ■ □ 

JavaScript

Works with: SpiderMonkey
Works with: V8
function GameOfLife () {

	this.init = function (turns,width,height) {
		this.board = new Array(height);
		for (var x = 0; x < height; x++) {
			this.board[x] = new Array(width);
			for (var y = 0; y < width; y++) {
				this.board[x][y] = Math.round(Math.random());
			}
		}
		this.turns = turns;
	}

	this.nextGen = function() {
		this.boardNext = new Array(this.board.length);
		for (var i = 0; i < this.board.length; i++) {
			this.boardNext[i] = new Array(this.board[i].length);
		}
		for (var x = 0; x < this.board.length; x++) {
			for (var y = 0; y < this.board[x].length; y++) {
				var n = 0;
				for (var dx = -1; dx <= 1; dx++) {
					for (var dy = -1; dy <= 1; dy++) {
						if ( dx == 0 && dy == 0){}
						else if (typeof this.board[x+dx] !== 'undefined'
								&& typeof this.board[x+dx][y+dy] !== 'undefined'
								&& this.board[x+dx][y+dy]) {
							n++;
						}
					}	
				}
				var c = this.board[x][y];
				switch (n) {
					case 0:
					case 1:
						c = 0;
						break;
					case 2:
						break; 
					case 3:
						c = 1;
						break;
					default:
						c = 0;
				}
				this.boardNext[x][y] = c;
			}
		}
		this.board = this.boardNext.slice();
	}

	this.print = function() {
		for (var x = 0; x < this.board.length; x++) {
			var l = "";
			for (var y = 0; y < this.board[x].length; y++) {
				if (this.board[x][y])
					l += "X";
				else
					l += " ";
			}
			print(l);
		}
	}

	this.start = function() {
		for (var t = 0; t < this.turns; t++) {
			print("---\nTurn "+(t+1));
			this.print();
			this.nextGen()
		}
	}

}


var game = new GameOfLife();

print("---\n3x3 Blinker over three turns.");
game.init(3);
game.board = [
	[0,0,0],
	[1,1,1],
	[0,0,0]];
game.start();

print("---\n10x6 Glider over five turns.");
game.init(5);
game.board = [
	[0,0,0,0,0,0,0,0,0,0],
	[0,0,1,0,0,0,0,0,0,0],
	[0,0,0,1,0,0,0,0,0,0],
	[0,1,1,1,0,0,0,0,0,0],
	[0,0,0,0,0,0,0,0,0,0],
	[0,0,0,0,0,0,0,0,0,0]];
game.start();

print("---\nRandom 5x10");
game.init(5,5,10);
game.start();
Output:
---
3x3 Blinker over three turns.
---
Turn 1
   
XXX
   
---
Turn 2
 X 
 X 
 X 
---
Turn 3
   
XXX
   
---
10x6 Glider over five turns.
---
Turn 1
          
  X       
   X      
 XXX      
          
          
---
Turn 2
          
          
 X X      
  XX      
  X       
          
---
Turn 3
          
          
   X      
 X X      
  XX      
          
---
Turn 4
          
          
  X       
   XX     
  XX      
          
---
Turn 5
          
          
   X      
    X     
  XXX     
          
---
Random 5x10
---
Turn 1
XXXX 
   XX
X    
 XX X
  XX 
X   X
X    
X   X
 X   
X  XX
---
Turn 2
 XXXX
X  XX
 XX X
 XX  
  X X
 X X 
XX   
XX   
XX XX
     
---
Turn 3
 XX X
X    
X   X
     
     
XX X 
     
     
XXX  
     
---
Turn 4
 X   
X  X 
     
     
     
     
     
 X   
 X   
 X   
---
Turn 5
     
     
     
     
     
     
     
     
XXX  
     
Library: HTML5

Essentially the same as the above straight JavaScript but displayed in an HTML5 Canvas.

<html> 
	<head> 
		<title></title> 
		<script type="text/javascript"> 
 
function GameOfLife () {
 
	this.init = function (turns,width,height) {
		this.board = new Array(height);
		for (var x = 0; x < height; x++) {
			this.board[x] = new Array(width);
			for (var y = 0; y < width; y++) {
				this.board[x][y] = Math.round(Math.random());
			}
		}
		this.turns = turns;
	}
 
	this.nextGen = function() {
		this.boardNext = new Array(this.board.length);
		for (var i = 0; i < this.board.length; i++) {
			this.boardNext[i] = new Array(this.board[i].length);
		}
		for (var x = 0; x < this.board.length; x++) {
			for (var y = 0; y < this.board[x].length; y++) {
				var n = 0;
				for (var dx = -1; dx <= 1; dx++) {
					for (var dy = -1; dy <= 1; dy++) {
						if ( dx == 0 && dy == 0){}
						else if (typeof this.board[x+dx] !== 'undefined'
								&& typeof this.board[x+dx][y+dy] !== 'undefined'
								&& this.board[x+dx][y+dy]) {
							n++;
						}
					}	
				}
				var c = this.board[x][y];
				switch (n) {
					case 0:
					case 1:
						c = 0;
						break;
					case 2:
						break; 
					case 3:
						c = 1;
						break;
					default:
						c = 0;
				}
				this.boardNext[x][y] = c;
			}
		}
		this.board = this.boardNext.slice();
	}
 
	this.print = function(ctx,w,h) {
		if (!w)
			w = 8;
		if (!h)
			h = 8;
		for (var x = 0; x < this.board.length; x++) {
			var l = "";
			for (var y = 0; y < this.board[x].length; y++) {
				if (this.board[x][y])
				// x and y reversed to draw matrix like it looks in source
				// rather than the "actual" positions
					ctx.fillStyle = "orange";
				else
					ctx.fillStyle = "black";
				ctx.fillRect(y*h,x*w,h,w);
			}
		}
	}
 
	this.start = function(ctx,w,h) {
		for (var t = 0; t < this.turns; t++) {
			this.print(ctx,w,h);
			this.nextGen()
		}
	}
 
}
 
function init() {
	// Change document title and text under canvas
	document.title = "Conway's Game of Life";
 
	// Setup game boards for Conway's Game of Life
	var blinker = new GameOfLife();
	blinker.board = [
		[0,1,0],
		[0,1,0],
		[0,1,0]];
 
	var glider = new GameOfLife();
	glider.board = [
		[0,0,0,0,0,0],
		[0,0,1,0,0,0],
		[0,0,0,1,0,0],
		[0,1,1,1,0,0],
		[0,0,0,0,0,0],
		[0,0,0,0,0,0]];
 
	var random = new GameOfLife();
	random.init(null,8,8);
 
	// Get canvas contexts or return 1
	blinker.canvas = document.getElementById('blinker');
	glider.canvas = document.getElementById('glider');
	random.canvas = document.getElementById('random');
	if (blinker.canvas.getContext && glider.canvas.getContext && random.canvas.getContext) {
		blinker.ctx = blinker.canvas.getContext('2d');
		glider.ctx = glider.canvas.getContext('2d');
		random.ctx = random.canvas.getContext('2d');
	} else {
		return 1;
	}
 
 
	// Run main() at set interval
	setInterval(function(){run(glider,glider.ctx,25,25)},250);
	setInterval(function(){run(blinker,blinker.ctx,25,25)},250);
	setInterval(function(){run(random,random.ctx,25,25)},250);
	return 0;
}
 
function run(game,ctx,w,h) {
	game.print(ctx,w,h);
	game.nextGen()
 
	return 0;
}
 
		</script> 
	</head> 
	<body onLoad="init();"> 
		3x3 Blinker<br> 
		<canvas id="blinker" width="75" height="75"> 
			No canvas support found!
		</canvas><br><br> 
		6x6 Glider<br> 
		<canvas id="glider" width="150" height="150"> 
			No canvas support found!
		</canvas><br><br> 
		8x8 Random<br> 
		<canvas id="random" width="200" height="200"> 
			No canvas support found!
		</canvas><br> 
	</body> 
</html>
Output:
for 3x3 Blinker


More functional style:

const _ = require('lodash');

///////////////////
// LODASH IMPORT //
///////////////////

// import all lodash functions to the main namespace, but isNaN not to cause conflicts
_.each(_.keys(_), k => global[k === 'isNaN' ? '_isNaN' : k] = _[k]);

///////////////
// FUNCTIONS //
///////////////
const WORLD_WIDTH  = 3,
      WORLD_HEIGHT = 3,
      displayWorld = (world) => console.log(map(world, x => x.join(' ')).join('\n') + '\n'),

      aliveNeighbours = (world, x, y) => chain(range(-1, 2))
                                          .reduce((acc, i) => acc.concat(map(range(-1, 2), ii => [i, ii])), [])
                                          .reject(partial(isEqual, [0, 0]))
                                          .map(i => {
                                            try {
                                              return world[x + i[0]][y + i[1]];
                                            } catch (err) {
                                              return null;
                                            }
                                          })
                                          .compact()
                                          .value()
                                          .length,

      isAlive = (cell, numAliveNeighbours) => (cell === 1 && inRange(numAliveNeighbours, 2, 4)) || (cell === 0 && numAliveNeighbours === 3) ? 1 : 0,
      updateWorld = (world) => map(world, (row, rowidx) => map(row, (cell, colidx) => isAlive(cell, aliveNeighbours(world, rowidx, colidx))));


// let world = map(range(WORLD_WIDTH), partial(ary(map, 2), range(WORLD_HEIGHT), partial(random, 0, 1, false)));
let world = [[0, 0, 0], [1, 1, 1], [0, 0, 0]];

setInterval(() => {
  world = updateWorld(world)
  displayWorld(world);
}, 1000);

ES6 + :

const alive = 1;
const dead = 0;

const conwaysGameOfLife = (game) => {
  const newGame = []
  for (let y = 0; y < game.length; y += 1) {
    const newRow = []
    for (let x = 0; x < game[y].length; x += 1) {
      const cell = game[y][x];
      const prevX = x > 0 ? x - 1 : x;
      const nextX = x < game[y].length - 1 ? x + 2 : x + 1;
      const counter =
        (game[y - 1] ? game[y - 1].slice(prevX, nextX).reduce((acc, v) => acc + v) : 0) +
        (game[y][x - 1] || 0) + (game[y][x + 1] || 0) +
        (game[y + 1] ? game[y + 1].slice(prevX, nextX).reduce((acc, v) => acc + v) : 0)
      cell === alive
        ? counter > 1 && counter <= 3
          ? newRow.push(alive)
          : newRow.push(dead)
        : counter === 3
          ? newRow.push(alive)
          : newRow.push(dead)
    }
    newGame.push(newRow)
  }
  return newGame
}

const generateGame = (height, width) => {
  return Array.from({ length: height }, (v, k) => (
    Array.from({ length: width}, (v, k) => {
      return (Math.random() * 100 | 0) < 50 ? dead : alive
    })
  ))
}

const output = (game) =>{
  process.stdout.write('\033c');
  let screen = '';
  for (let i = 0; i < game.length; i += 1) {
    screen += game[i].join('')
    screen += '\n'
  }
  console.log(screen)
}

const setup = ((game) => {
  return () => {
    setInterval(() => {
    output(game)
    const newGame = conwaysGameOfLife(game)
    game = newGame
    }, 1000)
  }
})

// for random game
// const game = generateGame(10, 10)

// glider test
const game = [
  [0,0,0,0,0,0,0,0,0,0],
  [0,0,1,0,0,0,0,0,0,0],
  [0,0,0,1,0,0,0,0,0,0],
  [0,1,1,1,0,0,0,0,0,0],
  [0,0,0,0,0,0,0,0,0,0],
  [0,0,0,0,0,0,0,0,0,0]
];
const run = setup(game);
run()

jq

Works with: jq version 1.4

In this implementation, a "world" is simply a suitably constructed string as illustrated by world3 and world11 below. The "game" can be played either by creating separate frames (using frames(n)) or by calling animation(n; sleep) with sleep approximately equal to the number of milliseconds between refreshes.

# Notes on the implementation:

# 1. For efficiency, the implementation requires that the world
#    has boundaries, as illustrated in the examples.
# 2. For speed, the simulation uses the exploded string.
# 3. The ASCII values of the "alive" and "empty" symbols are 
#    hardcoded: "." => 46; " " => 32
# 4. To adjust the refresh rate, adjust the input to "spin".

def lines: split("\n")|length;
 
def cols: split("\n")[0]|length + 1;  # allow for the newline

# Is there a "." (46) at [x,y] relative to position i,
# assuming the width is w?
# Input is an array; result is 0 or 1 so we can easily count the total.
def isAlive(x; y; i; w): if .[i+ w*y + x] == 46 then 1 else 0 end;

def neighborhood(i;w):
  isAlive(-1; -1; i; w) + isAlive(0; -1; i; w) + isAlive(1; -1; i; w) +
  isAlive(-1;  0; i; w)                        + isAlive(1;  0; i; w) +
  isAlive(-1;  1; i; w) + isAlive(0;  1; i; w) + isAlive(1;  1; i; w) ;

# The basic rules:
def evolve(cell; sum) : 
  if   cell == 46 then if sum == 2 or sum == 3 then 46 else 32 end
  elif cell == 32 then if sum == 3 then 46 else 32 end
  else cell
  end ;

# [world, lines, cols] | next(w) => [world, lines, cols]
def next:
  .[0] as $world | .[1] as $lines | .[2] as $w
  | reduce range(0; $world|length) as $i
    ($world;
      .[$i] as $c
      | if $c == 32 or $c == 46 then
           # updates are "simultaneous" i.e. relative to $world, not "."
           ($world | neighborhood($i; $w)) as $sum
           | evolve($c; $sum) as $next
           | if $c == $next then . else .[$i] = $next end
        else .
        end )
  | [., $lines, $w] ;

Animation:

# "clear screen":
def cls: "\u001b[2J";

# Input: an integer; 1000 ~ 1 sec
def spin:
  reduce range(1; 500 * .) as $i
    (0; . + ($i|cos)*($i|cos) + ($i|sin)*($i|sin) )
  |  "" ;
 
# Animate n steps;
# if "sleep" is non-negative then cls and 
# sleep about "sleep" ms between frames.
def animate(n; sleep):
  if n == 0 then empty
  else (if sleep >= 0 then cls else "" end),
       (.[0]|implode), n, "\n",
       (sleep|spin),
       ( next|animate(n-1; sleep) )
  end ;
 
# Input: a string representing the initial state
def animation(n; sleep):
  [ explode, lines, cols] | animate(n; sleep) ;
 
# Input: a string representing the initial state
def frames(n):  animation(n; -1);

Examples:

def world3:
"+---+\n" +
"|   |\n" +
"|...|\n" +
"|   |\n" +
"+---+\n" ;

def world11:
"+-----------+\n" +
"|           |\n" +
"|   ..      |\n" +
"|    ...    |\n" +
"|      ..   |\n" +
"|           |\n" +
"+-----------+\n" ;

Task:

world3 | frames(3)
Output:
$ jq -n -r -f Game_of_life.jq

+---+
|   |
|...|
|   |
+---+

3




+---+
| . |
| . |
| . |
+---+

2




+---+
|   |
|...|
|   |
+---+

1

Animation example

# Animation of 100 frames with approximately 1 second between each update:
world11 | animation(100; 1000)

Jsish

From Javascript, SpiderMonkey entry.

/* Conway's game of life, in Jsish */
function GameOfLife () {
    this.title = "Conway's Game of Life";
    this.cls = "\u001B[H\u001B[2J";

    this.init = function (turns, width, height) {
        this.board = new Array(height);
        for (var x = 0; x < height; x++) {
            this.board[x] = new Array(width);
            for (var y = 0; y < width; y++) {
                this.board[x][y] = Math.round(Math.random());
            }
        }
        this.turns = turns;
    };

    this.nextGen = function() {
        this.boardNext = new Array(this.board.length);
        for (var i = 0; i < this.board.length; i++) {
            this.boardNext[i] = new Array(this.board[i].length);
        }
        for (var x = 0; x < this.board.length; x++) {
            for (var y = 0; y < this.board[x].length; y++) {
                var n = 0;
                for (var dx = -1; dx <= 1; dx++) {
                    for (var dy = -1; dy <= 1; dy++) {
                        if ( dx == 0 && dy == 0){}
                        else if (typeof this.board[x+dx] !== 'undefined'
                                && typeof this.board[x+dx][y+dy] !== 'undefined'
                                && this.board[x+dx][y+dy]) {
                            n++;
                        }
                    }
                }
                var c = this.board[x][y];
                switch (n) {
                    case 0:
                    case 1:
                        c = 0;
                        break;
                    case 2:
                        break;
                    case 3:
                        c = 1;
                        break;
                    default:
                        c = 0;
                }
                this.boardNext[x][y] = c;
            }
        }
        this.board = this.boardNext.slice(0);
    };

    this.print = function() {
        for (var x = 0; x < this.board.length; x++) {
            var l = "";
            for (var y = 0; y < this.board[x].length; y++) {
                if (this.board[x][y])
                    l += "X";
                else
                    l += " ";
            }
            puts(l);
        }
    };

    this.start = function() {
        for (var t = 0; t < this.turns; t++) {
            sleep(500);
            printf(this.cls);
            puts(this.title + "\n---\nTurn "+(t+1));
            this.print();
            this.nextGen();
        }
    };

}

var game = new GameOfLife();
if (Interp.conf('unitTest')) {
    game.init(3,3,3);
    game.title="---\n3x3 Blinker over three turns.";
    game.board = [
        [0,0,0],
        [1,1,1],
        [0,0,0]];
    game.cls="";
    game.start();
} else {
    game.init(3,3,3);
    game.title="---\n3x3 Blinker over three turns.";
    game.board = [
        [0,0,0],
        [1,1,1],
        [0,0,0]];
    game.start();

    game.init(5,10,6);
    game.title="---\n10x6 Glider over five turns.";
    game.board = [
        [0,0,0,0,0,0,0,0,0,0],
        [0,0,1,0,0,0,0,0,0,0],
        [0,0,0,1,0,0,0,0,0,0],
        [0,1,1,1,0,0,0,0,0,0],
        [0,0,0,0,0,0,0,0,0,0],
        [0,0,0,0,0,0,0,0,0,0]];
    game.start();

    var steps = (console.args[0]) ? parseInt(console.args[0]) || 1  : 50;
    game.init(steps, 32,16);
    game.title="---\nRandom 32x16, " + steps + " step" + ((steps === 1) ? "" : "s");
    game.start();
}

/*
=!EXPECTSTART!=
---
3x3 Blinker over three turns.
---
Turn 1

XXX

---
3x3 Blinker over three turns.
---
Turn 2
 X
 X
 X
---
3x3 Blinker over three turns.
---
Turn 3

XXX

=!EXPECTEND!=
*/
Output:
prompt$ jsish -u conwaysGame.jsi
[PASS] conwaysGame.jsi

Julia

Works with: julia version 0.3.5

Using the CellularAutomata package: https://github.com/natj/CellularAutomata.jl

julia> Pkg.add("CellularAutomata")
INFO: Installing CellularAutomata v0.1.2
INFO: Package database updated

julia> using CellularAutomata

julia> gameOfLife{T<:Int}(n::T, m::T, gen::T) = CA2d([3], [2,3], int(randbool(n, m)), gen)
gameOfLife (generic function with 1 method)

julia> gameOfLife(15, 30, 5)
30x15x5 Cellular Automaton
       # ##   #   ######  ###  ### ##
       #    ####    #  #  # ##  #####
         ## #   # ## ###   ## # # ## 
       #  # ##### # # # ## #     #  #
         ##  ## # #  ##     ###      
       #   #### ## ## ### # # # # # #
       # ## ##### #  ##### # ## ### #
        ### #   ##        ####  ## # 
        #### #   ## ##   ### ###  ###
         ## ####   #######  #    ## #
           # ## ##### ## #### # #####
        ##  ## ##### # # # #  #   # #
        #   # ## ##   ## ##   ##### #
        ##   # #   #  # #############
       #      ## #    # ###  ##  ##  


                # ###          #     
       #    # ## #      # #   #      
        ###     # #      #     ##    
        #   #   # # #   # ##  ## ####
        ###       #       # # ## # # 
       #           ##     #     # # #
                  ####        #      
                   ##  #             
               # ##    #      ##    #
        #      #                     
        #  #                #  ##   #
        ## #         #      # #     #
            #       ##              #
        ##   #   #   ##     #       #
          #  # ##                    


             #    ##                 
        ##     #         #    # #    
        ## # #  # ##    #  #    #####
           #      #       ## #   # ##
        ##       ## #     #  ##      
       ###           #     # ## #####
                  #  #               
                 #   ##       ##     
                # ##                 
                #             # #    
        # #                  # #     
        #####       ##       # #   ##
          # #       #        #     ##
       # #  ### #   ###              
         #    ### ####               


        ##      ###                  
       #### # #  #             ## ## 
        ##  #    ###     # ##  ##   #
            #            ### ## ##  #
         ##      ###      #    ##    
       # #       #####      #### ####
       ##           ##       #  #####
                 # ####              
                # #           #      
                 #            ##     
       ## #                  # ##    
        #   #       ##      ##     ##
                   #  #       #    # 
        ##### # ##    #             #
        #   #   # #   #


          ## # ## #
          ## #     #           ### ##
          # #    ##      # ###    # #
       ## ##             #   ##  #
       ####      #       ##
         ##      #   #      ##
        #        #          ## ##
       #         ###  #          ####
                # ####        ##
                 #           #  #
       ###                  ## ##   #
        ##          ##      ## #   ##
        # # ##      # #      #     #
       ####### ####  ###
            ##    #

GPU calculation based version

Requires a CUDA compatible graphics card and uses the ArrayFire library.

using ArrayFire
using Images
using LinearAlgebra

const blinker = [0 0 0; 1 1 1; 0 0 0]
const glider = [0 0 1; 1 0 1; 0 1 1]
const lwss = [0 1 1 1 1; 1 0 0 0 1; 0 0 0 0 1; 1 0 0 1 0]
const glidergun = [
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0;
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0;
  0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0;
  0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0;
  0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
  0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0;
  0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0;
  0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
  0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]

function lifegame(fname, initializer, mapsize=30, imgsteps=50, upscaleratio=20)
    kernel = convert(Array{Float32}, [1 1 1; 1 0 1; 1 1 1]) |> AFArray
    initialstate = zeros(Bool, mapsize, mapsize)
    mid = div(mapsize, 2)
    (xlen, ylen), (halfx, halfy) = size(initializer), div.(size(initializer), 2)
    x1, x2 = mid - halfx, isodd(xlen) ? mid + halfx : mid + halfx - 1
    y1, y2 = mid - halfy, isodd(ylen) ? mid + halfy : mid + halfy - 1
    initialstate[x1:x2, y1:y2] .= initializer
    state = initialstate .+ Float32(.0) |> AFArray
    img = zeros(Float32, mapsize * upscaleratio, mapsize * upscaleratio, imgsteps)
    for i in 1:imgsteps
        nb = convolve2(state, kernel, UInt32(0), UInt32(0))
        a = (nb == 2)
        b = (nb == 3)
        state = ((state .* a .+ b) > 0) + Float32(0)
        frame = imresize(state, ratio=upscaleratio)
        img[:, :, i] .= frame
    end
    save(fname, img)
end

lifegame("blinker.gif", blinker)
lifegame("glider.gif", glider)
lifegame("lwss.gif", lwss)
lifegame("glidergun.gif", glidergun, 90, 200)

Kotlin

This is based on the Go entry but has been altered in several respects.

In particular, it now allows for the blinker and glider patterns as well as an initially random pattern.

Also any cells beyond the boundary are now treated as dead as per the current task description.

The particular random pattern used now needs only 99 generations to reach stability.

// version 1.2.0

import java.util.Random

val rand = Random(0) // using a seed to produce same output on each run

enum class Pattern { BLINKER, GLIDER, RANDOM }

class Field(val w: Int, val h: Int) {
    val s = List(h) { BooleanArray(w) }

    operator fun set(x: Int, y: Int, b: Boolean) {
        s[y][x] = b
    }

    fun next(x: Int, y: Int): Boolean {
        var on = 0
        for (i in -1..1) {
            for (j in -1..1) {
                if (state(x + i, y + j) && !(j == 0 && i == 0)) on++
            }
        }
        return on == 3 || (on == 2 && state(x, y))
    }

    fun state(x: Int, y: Int): Boolean {
        if ((x !in 0 until w) || (y !in 0 until h)) return false
        return s[y][x]
    }
}

class Life(val pattern: Pattern) {
    val w: Int
    val h: Int
    var a: Field
    var b: Field

    init {
        when (pattern) {
            Pattern.BLINKER -> {
                w = 3
                h = 3
                a = Field(w, h)
                b = Field(w, h)
                a[0, 1] = true
                a[1, 1] = true
                a[2, 1] = true
            }

            Pattern.GLIDER -> {
                w = 4
                h = 4
                a = Field(w, h)
                b = Field(w, h)
                a[1, 0] = true
                a[2, 1] = true
                for (i in 0..2) a[i, 2] = true
            }

            Pattern.RANDOM -> {
                w = 80
                h = 15
                a = Field(w, h)
                b = Field(w, h)
                for (i in 0 until w * h / 2) {
                    a[rand.nextInt(w), rand.nextInt(h)] = true
                }
            }
        }
    }

    fun step() {
        for (y in 0 until h) {
            for (x in 0 until w) {
                b[x, y] = a.next(x, y)
            }
        }
        val t = a
        a = b
        b = t
    }

    override fun toString(): String {
        val sb = StringBuilder()
        for (y in 0 until h) {
            for (x in 0 until w) {
                val c = if (a.state(x, y)) '#' else '.'
                sb.append(c)
            }
            sb.append('\n')
        }
        return sb.toString()
    }
}

fun main(args: Array<String>) {
    val lives = listOf(
        Triple(Life(Pattern.BLINKER), 3, "BLINKER"),
        Triple(Life(Pattern.GLIDER), 4, "GLIDER"),
        Triple(Life(Pattern.RANDOM), 100, "RANDOM")
    )
    for ((game, gens, title) in lives) {
        println("$title:\n")
        repeat(gens + 1) {
            println("Generation: $it\n$game")
            Thread.sleep(30)
            game.step()
        }
        println()
    }
}
Output:

In the interests of brevity, only generations 0 and 100 are shown for the 'random' pattern:

BLINKER:

Generation: 0
...
###
...

Generation: 1
.#.
.#.
.#.

Generation: 2
...
###
...

Generation: 3
.#.
.#.
.#.


GLIDER:

Generation: 0
.#..
..#.
###.
....

Generation: 1
....
#.#.
.##.
.#..

Generation: 2
....
..#.
#.#.
.##.

Generation: 3
....
.#..
..##
.##.

Generation: 4
....
..#.
...#
.###


RANDOM:

Generation: 0
....###....#.#....###...#.#..#.###...#..#......#.#..#####......######...##.#.##.
####..###.#....#.#####.##.....####.##..####.####.........#.#.###...#.##.#.#.....
..##.##.#.##...#..#.#..#.#.#.#..####.#...#..##....#..##.........#.#..#....#...#.
..##..#..##.#.#.....#.##.##...#####...##.##.....##...#.....##......###..##.#..##
......##..........#.#.#.......#..#.##.#.##....#.#...#.#.#.#.....#..#.......#.#.#
.#.#.....#####..#..##............#.#.#...###..#...##.....#..##...#.#.##.#..##...
.##.#.#.##.#..#####.....##..#.####..#.#..#...#.#..#...#.#.#.#....#.#..#.#.#..##.
.#..#..#.....#...###..###.....####..........##.##.####.....#..##..####..#...##..
..##.#...#.#..#.#....#..#...##.#..##.......#.#..##..##..##.#.....##.#......#.#.#
#.######..#.#.#.###.#....###.....#.....#..#......####.#.#..#....#...#.......#.#.
#...#..###.##....#.#..##..#..#.#.#...#..#....#....##...#..#..#.#....#...##....#.
#....##.......#.####.##..#....#.#....#....#######.#..####.#..#.#.##....#.#####..
...#.......##..##.##......##....#..#.####.......#..#.#..##.###.#.#.#.#..##.....#
#.##..####....#..#..##..#.#..#..#....#.###.##.....#.....##....#.#..#.##.....##..
...#.#..#.#.....###...#..##.#.....#......#...........###...#.#....#..#.#..##.#.#

Generation: 100
................................................................................
................................................................................
.........................................#......................................
......................#.................#.#.....................................
.##..................#.#................#.#.....................................
.##..................#.#.................#...#..................................
......................#.....................#.#.................................
...........................................#..#.................................
............................................##..................................
.............##.................................................................
............#..#................................................................
.##..........#.#.......................................##..........#............
.##...........#........................................##.........#.#...........
..........##.......................................................##...........
..........##....................................................................

Lambdatalk

Lambdatalk works in any web browsers coming with javascript and canvas.

{center
 {input {@ type="button" value="start random"
           onclick="LIFE.startstop(this,'random')"}}
 {input {@ type="button" value="start cross"
           onclick="LIFE.startstop(this,'cross')"}}
 {canvas {@ id="life" width="330" height="330"
            style="box-shadow:0 0 8px #000"}}
}

calling the following javascript code

{script
var LIFE = (function() {
  var board = [],
      xmax = 8, ymax = 8,
      interval = null,
      delay = 1000;
  
  var isdefined = function(x,y) {
    return typeof board[x]    !== 'undefined'
        && typeof board[x][y] !== 'undefined'
        && board[x][y];
  };

  var alive = function(c,n) {
    if (n < 2 || n > 3) c = 0;
    if (n === 3) c = 1;
    return c
  };

  var neighbours = function(x,y) {
    var n = 0;
    if (isdefined(x-1,y-1)) n++;
    if (isdefined(x  ,y-1)) n++;
    if (isdefined(x+1,y-1)) n++;
    if (isdefined(x-1,y  )) n++;
    if (isdefined(x+1,y  )) n++;
    if (isdefined(x-1,y+1)) n++;
    if (isdefined(x  ,y+1)) n++;
    if (isdefined(x+1,y+1)) n++; 
    return n
  };

  var nextGen = function() {
    var next = [];
    for (var x = 0; x < xmax; x++) {
      next[x] = [];
      for (var y = 0; y < ymax; y++)
        next[x][y] = alive( board[x][y], neighbours(x,y) );
    }
    board = next
  };

  var print = function(ctx,dw,dh) {
    for (var x = 0; x < xmax; x++) {
      for (var y = 0; y < ymax; y++) {
        ctx.fillStyle = (board[x][y])? "#fff" : "#888";
        ctx.fillRect(y*dh+1,x*dw+1,dh-1,dw-1)
      }
    }
  };

  var init = function (type,w,h) {
    xmax = w;
    ymax = h;
    delay = (type === "random")? 100 : 1000;
    for (var x = 0; x < xmax; x++) {
      board[x] = [];
      for (var y = 0; y < ymax; y++) {
        if (type === "random") { 
          board[x][y] = Math.round(Math.random());
        } else {
          board[x][y] = 0;
          if (x === Math.floor(w/2)) board[x][y] = 1;
          if (y === Math.floor(h/2)) board[x][y] = 1;
        }
      }
    }
  };

  var run = function(ctx,dw,dh) {
    print(ctx,dw,dh);
    nextGen()
  };

  var startstop = function(id,type) {
    var can = document.getElementById('life').getContext('2d');
    if (interval === null) {
      id.value = "stop";
      init(type,33,33);
      interval = window.setInterval( run, delay, can, 10, 10 );
    } else {
      id.value = (type === "random")? "start_random" : "start_cross";
      window.clearInterval( interval );
      interval = null;
    }
  };

  return { startstop }
 
}) ();  // end LIFE 
}

Results can be seen in http://lambdaway.free.fr/lambdaspeech/?view=life and in http://lambdaway.free.fr/lambdawalks/?view=conway

Lua

A slight modernization of my original "life.lua" for Lua 3.x circa 2000 -- heck, we didn't even have for loops back then! :D (a copy can be found in the 4.0 source distro if interested in comparing syntax)

local function T2D(w,h) local t={} for y=1,h do t[y]={} for x=1,w do t[y][x]=0 end end return t end

local Life = {
  new = function(self,w,h)
    return setmetatable({ w=w, h=h, gen=1, curr=T2D(w,h), next=T2D(w,h)}, {__index=self})
  end,
  set = function(self, coords)
    for i = 1, #coords, 2 do
      self.curr[coords[i+1]][coords[i]] = 1
    end
  end,
  evolve = function(self)
    local curr, next = self.curr, self.next
    local ym1, y, yp1 = self.h-1, self.h, 1
    for i = 1, self.h do
      local xm1, x, xp1 = self.w-1, self.w, 1
      for j = 1, self.w do
        local sum = curr[ym1][xm1] + curr[ym1][x] + curr[ym1][xp1] +
                    curr[y][xm1] + curr[y][xp1] +
                    curr[yp1][xm1] + curr[yp1][x] + curr[yp1][xp1]
        next[y][x] = ((sum==2) and curr[y][x]) or ((sum==3) and 1) or 0
        xm1, x, xp1 = x, xp1, xp1+1
      end
      ym1, y, yp1 = y, yp1, yp1+1
    end
    self.curr, self.next, self.gen = self.next, self.curr, self.gen+1
  end,
  render = function(self)
    print("Generation "..self.gen..":")
    for y = 1, self.h do
      for x = 1, self.w do
        io.write(self.curr[y][x]==0 and "□ " or "■ ")
      end
      print()
    end
  end
}

Example usage. Coordinates wrap to simulate an infinite universe, so here a glider/lwss are evolved through one complete period, then advanced forward until returning to starting conditions.

print("GLIDER:")
local life = Life:new(5,5)
life:set({ 2,1, 3,2, 1,3, 2,3, 3,3 })
for i = 1, 5 do
  life:render()
  life:evolve()
end
for i = 6,20 do life:evolve() end
life:render()

print()

print("LWSS:")
life = Life:new(10,7)
life:set({ 2,2, 5,2, 6,3, 2,4, 6,4, 3,5, 4,5, 5,5, 6,5 })
for i = 1, 5 do
  life:render()
  life:evolve()
end
for i = 6,20 do life:evolve() end
life:render()
Output:
GLIDER:
Generation 1:
□ ■ □ □ □
□ □ ■ □ □
■ ■ ■ □ □
□ □ □ □ □
□ □ □ □ □
Generation 2:
□ □ □ □ □
■ □ ■ □ □
□ ■ ■ □ □
□ ■ □ □ □
□ □ □ □ □
Generation 3:
□ □ □ □ □
□ □ ■ □ □
■ □ ■ □ □
□ ■ ■ □ □
□ □ □ □ □
Generation 4:
□ □ □ □ □
□ ■ □ □ □
□ □ ■ ■ □
□ ■ ■ □ □
□ □ □ □ □
Generation 5:
□ □ □ □ □
□ □ ■ □ □
□ □ □ ■ □
□ ■ ■ ■ □
□ □ □ □ □
Generation 21:
□ ■ □ □ □
□ □ ■ □ □
■ ■ ■ □ □
□ □ □ □ □
□ □ □ □ □

LWSS:
Generation 1:
□ □ □ □ □ □ □ □ □ □
□ ■ □ □ ■ □ □ □ □ □
□ □ □ □ □ ■ □ □ □ □
□ ■ □ □ □ ■ □ □ □ □
□ □ ■ ■ ■ ■ □ □ □ □
□ □ □ □ □ □ □ □ □ □
□ □ □ □ □ □ □ □ □ □
Generation 2:
□ □ □ □ □ □ □ □ □ □
□ □ □ □ □ □ □ □ □ □
□ □ □ □ ■ ■ □ □ □ □
□ □ ■ ■ □ ■ ■ □ □ □
□ □ ■ ■ ■ ■ □ □ □ □
□ □ □ ■ ■ □ □ □ □ □
□ □ □ □ □ □ □ □ □ □
Generation 3:
□ □ □ □ □ □ □ □ □ □
□ □ □ □ □ □ □ □ □ □
□ □ □ ■ ■ ■ ■ □ □ □
□ □ ■ □ □ □ ■ □ □ □
□ □ □ □ □ □ ■ □ □ □
□ □ ■ □ □ ■ □ □ □ □
□ □ □ □ □ □ □ □ □ □
Generation 4:
□ □ □ □ □ □ □ □ □ □
□ □ □ □ ■ ■ □ □ □ □
□ □ □ ■ ■ ■ ■ □ □ □
□ □ □ ■ ■ □ ■ ■ □ □
□ □ □ □ □ ■ ■ □ □ □
□ □ □ □ □ □ □ □ □ □
□ □ □ □ □ □ □ □ □ □
Generation 5:
□ □ □ □ □ □ □ □ □ □
□ □ □ ■ □ □ ■ □ □ □
□ □ □ □ □ □ □ ■ □ □
□ □ □ ■ □ □ □ ■ □ □
□ □ □ □ ■ ■ ■ ■ □ □
□ □ □ □ □ □ □ □ □ □
□ □ □ □ □ □ □ □ □ □
Generation 21:
□ □ □ □ □ □ □ □ □ □
□ ■ □ □ ■ □ □ □ □ □
□ □ □ □ □ ■ □ □ □ □
□ ■ □ □ □ ■ □ □ □ □
□ □ ■ ■ ■ ■ □ □ □ □
□ □ □ □ □ □ □ □ □ □
□ □ □ □ □ □ □ □ □ □

ksh

#!/bin/ksh
#	# Version AJM 93u+ 2012-08-01

# Conway's Game of Life

#	# Variables:
#
integer RAND_MAX=32767
LIFE="�[07m  �[m"
NULL="  "
typeset -a char=( "$NULL" "$LIFE" )

#	# Input x y or default to 30x30, positive integers only
#
integer h=${1:-30} ; h=$(( h<=0 ? 30 : h ))		# Height (y)
integer w=${2:-30} ; w=$(( w<=0 ? 30 : w ))		# Width  (x)

#	# Functions:
#

#	# Function _display(map, h, w)
#
function _display {
	typeset _dmap ; nameref _dmap="$1"
	typeset _h _w ; integer _h=$2 _w=$3

	typeset _x _y ; integer _x _y

	printf %s "�[H"
	for (( _y=0; _y<_h; _y++ )); do
		for (( _x=0; _x<_w; _x++ )); do
			printf %s "${char[_dmap[_y][_x]]}"
		done
		printf "%s\n"
	done
}

#	# Function _evolve(h, w)
#
_evolve() {
	typeset _h _w ; integer _h=$1 _w=$2

	typeset _x _y _n _y1 _x1 ; integer _x _y _n _y1 _x1
	typeset _new _newdef ; typeset -a _new

	for (( _y=0; _y<_h; _y++ )); do
		for (( _x=0; _x<_w; _x++ )); do
			_n=0
			for (( _y1=_y-1; _y1<=_y+1; _y1++ )); do
				for (( _x1=_x-1; _x1<=_x+1; _x1++ )); do
					(( _map[$(( (_y1 + _h) % _h ))][$(( (_x1 + _w) % _w ))] )) && (( _n++ ))
				done
			done
			(( _map[_y][_x] )) && (( _n-- ))
			_new[_y][_x]=$(( (_n==3) || (_n==2 && _map[_y][_x]) ))
		done
	done
	
	for (( _y=0; _y<_h; _y++ )); do
		for (( _x=0; _x<_w; _x++ )); do
			_map[_y][_x]=${_new[_y][_x]}
		done
	done
}

#	# Function _game(h, w)
#
function _game {
	typeset _h ; integer _h=$1
	typeset _w ; integer _w=$2

	typeset _x _y ; integer _x _y
	typeset -a _map

	for (( _y=0 ; _y<_h ; _y++ )); do
		for (( _x=0 ; _x<_h ; _x++ )); do
			_map[_x][_y]=$(( RANDOM < RAND_MAX / 10 ? 1 : 0 ))	# seed map
		done
	done

	while : ; do
		_display _map ${_h} ${_w}
		_evolve ${_h} ${_w}
		sleep 0.2
	done
}

 ######
# main #
 ######

 _game ${h} ${w}


M2000 Interpreter

Module Life {
	Font "courier new"
	Form 40, 18
	Cls 3,0
	Double
	Report 2,  "Game of Life"
	Normal
	Cls 5, 2
	Const Mx=20, My=10
	Dim A(0 to Mx+1, 0 to My+1)=0
	Flush
REM	Data (2,2),(2,3),(3,3),(4,3),(5,4),(,3,4),(5,3),(6,2),(8,5),(5,8)
	Data (5,3)
	Data (5,4)
	Data (5,5)
	generation=1
	While not empty
		(A, B)=Array
		A(A,B)=1
	End While
	Display()
	Do
		k$=Key$
		If k$=chr$(13) Then exit
		A()=@GetNext()
		refresh 500
		Display()
	Until A()#Sum()=0
	K$=Key$
	Cls, 0
	End
	Function GetNext()
		Local B()
		B()=A()  ' copy array
		Local B=B()  ' get a pointer
		B*=0  ' make all element zero
		Local i, j, tot
		For j=1 to My
			For i=1 to Mx
				tot=-A(i,j)
				For k=j-1 to j+1
					For m=i-1 to i+1
						tot+=A(m, k)
					Next
				Next
				If A(i,j)=1 Then
					If tot=2 or tot=3 Then B(i,j)=1
				Else.if tot=3 Then
					B(i,j)=1
				End If
			Next
		Next
		=B()
	End Function
	Sub Display()
		Cursor 0,2
		move !    ' move graphic to character cursor
		Fill scale.x, scale.y-pos.Y, 1, 5
		Print "Generation:";Generation
		Generation++
		Local i, j
		For j=1 to My
			Print @(width div 2-Mx div 2);
			For i=1 to Mx
				Print If$(A(I,J)=1->"■", "□");
			Next
			Print
		Next
		Print 
		Report 2, "Press enter to exit or any other key for Next generation"
	End Sub
	
}
Life

MANOOL

Straightforward implementation useful for benchmarking:

{ {extern "manool.org.18/std/0.3/all"} in
: let { N = 40; M = 80 } in
: let { G = 99 } in
: let
  { Display =
    { proc { B } as
    : for { I = Range[N]$ } do
    : do Out.WriteLine[] after
    : for { J = Range[M]$ } do
      Out.Write[{if B[I; J] <> 0 then "*" else " "}]
    }
  }
  in
: var { B = {array N of: array M of 0} } in
  -- initialization
  B[19; 41] = 1
  B[20; 40] = 1
  B[21; 40] = 1
  B[22; 40] = 1
  B[22; 41] = 1
  B[22; 42] = 1
  B[22; 43] = 1
  B[19; 44] = 1
  -- end of initialization
  Out.WriteLine["Before:"]; Display[B]
  { var { NextB = B } in
  : repeat G do
  : do {assign B = NextB; NextB = B} after
  : for { I = Range[N]$ } do
  : var { Up = (I - 1).Mod[N]; Down = (I + 1).Mod[N] } in
  : for { J = Range[M]$ } do
  : var { Left = (J - 1).Mod[M]; Right = (J + 1).Mod[M] } in
  : var
    { Count =
      B[Up  ; Left ] +
      B[Up  ; J    ] +
      B[Up  ; Right] +
      B[I   ; Right] +
      B[Down; Right] +
      B[Down; J    ] +
      B[Down; Left ] +
      B[I   ; Left ]
    }
    in
    NextB[I; J] =
    { if Count == 2 then B[I; J] else
    : if Count == 3 then 1 else
      0
    }
  }
  Out.WriteLine["After " G " generations:"]; Display[B]
}

Using comprehension notation:

{ {extern "manool.org.18/std/0.3/all"} in
: let { N = 40; M = 80 } in
: let { G = 99 } in
: let
  { Display =
    { proc { B } as
    : for { I = Range[N]$ } do
    : do Out.WriteLine[] after
    : for { J = Range[M]$ } do
      Out.Write[{if B[I; J] <> 0 then "*" else " "}]
    }
  }
  in
: var { B = {array N of: array M of 0} } in
  -- initialization
  B[19; 41] = 1
  B[20; 40] = 1
  B[21; 40] = 1
  B[22; 40] = 1
  B[22; 41] = 1
  B[22; 42] = 1
  B[22; 43] = 1
  B[19; 44] = 1
  -- end of initialization
  Out.WriteLine["Before:"]; Display[B]
  { repeat G do
    B =
    { array for { I = Range[N]$ } of
    : var { Up = (I - 1).Mod[N]; Down = (I + 1).Mod[N] } in
    : array for { J = Range[M]$ } of
    : var { Left = (J - 1).Mod[M]; Right = (J + 1).Mod[M] } in
    : var
      { Count =
        B[Up  ; Left ] +
        B[Up  ; J    ] +
        B[Up  ; Right] +
        B[I   ; Right] +
        B[Down; Right] +
        B[Down; J    ] +
        B[Down; Left ] +
        B[I   ; Left ]
      }
      in
    : if Count == 2 then B[I; J] else
    : if Count == 3 then 1 else
      0
    }
  }
  Out.WriteLine["After " G " generations:"]; Display[B]
}

Mathematica / Wolfram Language

Mathematica has cellular automaton functionality built in, so implementing Conway's Game of Life is a one-liner:

CellularAutomaton[{224,{2,{{2,2,2},{2,1,2},{2,2,2}}},{1,1}}, startconfiguration, steps];

Example of a glyder progressing 8 steps and showing the 9 frames afterwards as grids of hashes and dots:

results=CellularAutomaton[{224,{2,{{2,2,2},{2,1,2},{2,2,2}}},{1,1}},{{{0,1,0},{0,0,1},{1,1,1}},0},8];
 Do[Print[i-1];Print[Grid[results[[i]]/.{1->"#",0->"."}]];,{i,1,Length[results]}]

gives back:

0
.#...
..#..
###..
.....
.....

1
.....
#.#..
.##..
.#...
.....

2
.....
..#..
#.#..
.##..
.....

3
.....
.#...
..##.
.##..
.....

4
.....
..#..
...#.
.###.
.....

5
.....
.....
.#.#.
..##.
..#..

6
.....
.....
...#.
.#.#.
..##.

7
.....
.....
..#..
...##
..##.

8
.....
.....
...#.
....#
..###

MATLAB

MATLAB has a builtin Game of Life GUI. Type
life
to run it. To view the code, type
open(fullfile(matlabroot, 'toolbox', 'matlab', 'demos', 'life.m'))

Here is an example code, more simple (runs the game of life for N generations in a square of side S) :

function GoL(S, N) %
    colormap copper; whitebg('black');
    G= round(rand(S));
    A = [S 1:S-1]; B = [2:S 1];
    for k=1:N
        Sum = G(A,:)+G(B,:)+G(:,B)+G(:,A)+G(A,B)+G(A,A)+G(B,B)+G(B,A);
        G = double((G & (Sum == 2)) | (Sum == 3));
        surf(G); view([0 90]); pause(0.001)
    end
end

Maxima

life(A) := block(
   [p, q, B: zerofor(A), s],
   [p, q]: matrix_size(A),
   for i thru p do (
      for j thru q do (
         s: 0,
         if j > 1 then s: s + A[i, j - 1],
         if j < q then s: s + A[i, j + 1],
         if i > 1 then (
            s: s + A[i - 1, j],
            if j > 1 then s: s + A[i - 1, j - 1],
            if j < q then s: s + A[i - 1, j + 1]
         ),
         if i < p then (
            s: s + A[i + 1, j],
            if j > 1 then s: s + A[i + 1, j - 1],
            if j < q then s: s + A[i + 1, j + 1]
         ),
         B[i, j]: charfun(s = 3 or (s = 2 and A[i, j] = 1))
      )
   ),
   B
)$


/* a glider */

L: matrix([0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0],
          [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0],
          [0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0],
          [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
          [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
          [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
          [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
          [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
          [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
          [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
          [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])$

gen(A, n) := block(thru n do A: life(A), A)$

gen(L, 4);
matrix([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0],
       [0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])

Blinker over three generations

three_all_alive: matrix([0,1,0],[0,1,0],[0,1,0])$
with_slider_draw(n,makelist(j,j,0,2),image(gen(three_all_alive,n),0,0,30,30));
File:BlinkerMaxima.gif

MiniScript

This GUI implementation is for use with Mini Micro.

// Conway's Game of Life
clear
rows = 64; rowRange = range(0, rows-1)
cols = 96; colRange = range(0, cols-1)
// prepare two tile displays, in display layers 4 and 5
img = Image.create(2, 1); img.setPixel 1, 0, color.white
grids = []
for dispIdx in [4,5]
	display(dispIdx).mode = displayMode.tile
	td = display(dispIdx)
	td.cellSize = 9  // size of cells on screen
	td.extent = [cols, rows]
	td.overlap = -1   // adds a small gap between cells
	td.tileSet = img; td.tileSetTileSize = 1
	td.clear 0
	grids.push td
end for

// initialize to a random state
for x in colRange
	for y in rowRange
		td.setCell x, y, rnd > 0.5
	end for
end for

curIdx = 5
// main loop
while true
	yield
	td = grids[curIdx-4]
	newIdx = 4 + (curIdx == 4)
	newTd = grids[newIdx-4]
	for x in colRange
		for y in rowRange
			// get sum of neighboring states
			sum = 0
			for i in [x-1, x, x+1]
				if i < 0 or i >= cols then continue
				for j in [y-1, y, y+1]
					if j < 0 or j >= rows then continue
					if i==x and j==y then continue
					sum = sum + td.cell(i,j)
				end for
			end for
			// Now, update the cell based on current state
			// and neighboring sum.
			if td.cell(x,y) then
				newTd.setCell x, y, (sum == 2 or sum == 3)
			else
				newTd.setCell x, y, sum == 3
			end if
		end for
	end for
	display(newIdx).mode = displayMode.tile
	display(curIdx).mode = displayMode.off
	curIdx = newIdx
end while

Nim

Translation of: C
import os, strutils, random

randomize()
var w, h: int
if paramCount() >= 2:
  w = parseInt(paramStr(1))
  h = parseInt(paramStr(2))
if w <= 0: w = 30
if h <= 0: h = 30

# Initialize
var univ, utmp = newSeq[seq[bool]](h)
for y in 0..<h:
  univ[y].newSeq w
  utmp[y].newSeq w
  for x in 0 ..< w:
    if rand(9) < 1:
      univ[y][x] = true

while true:
  # Show
  stdout.write "\e[H"
  for y in 0..<h:
    for x in 0..<w:
      stdout.write if univ[y][x]: "\e[07m  \e[m" else: "  "
    stdout.write "\e[E"
  stdout.flushFile

  # Evolve
  for y in 0..<h:
    for x in 0..<w:
      var n = 0
      for y1 in y-1..y+1:
        for x1 in x-1..x+1:
          if univ[(y1+h) mod h][(x1 + w) mod w]:
            inc n

      if univ[y][x]: dec n
      utmp[y][x] = n == 3 or (n == 2 and univ[y][x])
  swap(univ,utmp)

  sleep 200

OCaml

let get g x y =
  try g.(x).(y)
  with _ -> 0

let neighbourhood g x y =
  (get g (x-1) (y-1)) +
  (get g (x-1) (y  )) +
  (get g (x-1) (y+1)) +
  (get g (x  ) (y-1)) +
  (get g (x  ) (y+1)) +
  (get g (x+1) (y-1)) +
  (get g (x+1) (y  )) +
  (get g (x+1) (y+1)) 

let next_cell g x y =
  let n = neighbourhood g x y in
  match g.(x).(y), n with
  | 1, 0 | 1, 1                      -> 0  (* lonely *)
  | 1, 4 | 1, 5 | 1, 6 | 1, 7 | 1, 8 -> 0  (* overcrowded *)
  | 1, 2 | 1, 3                      -> 1  (* lives *)
  | 0, 3                             -> 1  (* get birth *)
  | _ (* 0, (0|1|2|4|5|6|7|8) *)     -> 0  (* barren *)

let copy g = Array.map Array.copy g

let next g =
  let width = Array.length g
  and height = Array.length g.(0)
  and new_g = copy g in
  for x = 0 to pred width do
    for y = 0 to pred height do
      new_g.(x).(y) <- (next_cell g x y)
    done
  done;
  (new_g)

let print g =
  let width = Array.length g
  and height = Array.length g.(0) in
  for x = 0 to pred width do
    for y = 0 to pred height do
      if g.(x).(y) = 0
      then print_char '.'
      else print_char 'o'
    done;
    print_newline ()
  done

put the code above in a file named "life.ml", and then use it in the ocaml toplevel like this:

# #use "life.ml";;
val get : int array array -> int -> int -> int = <fun>
val neighbourhood : int array array -> int -> int -> int = <fun>
val next_cell : int array array -> int -> int -> int = <fun>
val copy : 'a array array -> 'a array array = <fun>
val next : int array array -> int array array = <fun>
val print : int array array -> unit = <fun>

# let g = [|
  [| 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; |];
  [| 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; |];
  [| 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; |];
  [| 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; |];
  [| 0; 0; 0; 0; 1; 1; 1; 0; 0; 0; |];
  [| 0; 0; 0; 1; 1; 1; 0; 0; 0; 0; |];
  [| 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; |];
  [| 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; |];
  [| 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; |];
  [| 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; |];
|] ;;
val g : int array array =
  [|[|0; 0; 0; 0; 0; 0; 0; 0; 0; 0|];
    [|0; 0; 0; 0; 0; 0; 0; 0; 0; 0|];
    [|0; 0; 0; 0; 0; 0; 0; 0; 0; 0|];
    [|0; 0; 0; 0; 0; 0; 0; 0; 0; 0|];
    [|0; 0; 0; 0; 1; 1; 1; 0; 0; 0|];
    [|0; 0; 0; 1; 1; 1; 0; 0; 0; 0|];
    [|0; 0; 0; 0; 0; 0; 0; 0; 0; 0|];
    [|0; 0; 0; 0; 0; 0; 0; 0; 0; 0|];
    [|0; 0; 0; 0; 0; 0; 0; 0; 0; 0|];
    [|0; 0; 0; 0; 0; 0; 0; 0; 0; 0|]|]
# print g;;
..........
..........
..........
..........
....ooo...
...ooo....
..........
..........
..........
..........
- : unit = ()
# print (next g) ;;
..........
..........
..........
.....o....
...o..o...
...o..o...
....o.....
..........
..........
..........
- : unit = ()

A graphical version

This implementation has 6 starting patterns (most get quite large) and a random option, and you can set the grid size.

let alive = 0
let dead = 0xFFFFFF

let iteration ib ob m n =
   let rule = function 3,_ | 2,true -> alive | _ -> dead in
   let f x y =
      if x >= 0 && x < m && y >= 0 && y < n && ib.(x).(y) = alive
      then 1 else 0 in
   let count b q =
      let a, c, p, r = b-1, b+1, q-1, q+1 in
      f a p + f a q + f a r + f b p + f b r + f c p + f c q + f c r in
   for i = 0 to m-1 do
      for j = 0 to n-1 do
         ob.(i).(j) <- rule (count i j, ib.(i).(j) = alive)
      done
   done

let make_random w h bd =
   Random.self_init ();
   for i = 0 to w-1 do
      for j = 0 to h-1 do
         bd.(i).(j) <- if Random.bool () then alive else dead
      done
   done

let set_cells a b cells w h bd =
   let w', h' = w/2 - a, h/2 - b in
   List.iter (fun (i,j) -> bd.(i+w').(j+h') <- alive) cells

let make_blinker = set_cells 1 1 [(1,0); (1,1); (1,2)]

let make_acorn =
   set_cells 1 3 [(0,1); (1,3); (2,0); (2,1); (2,4); (2,5); (2,6)]

let make_growth =
   set_cells 2 3
   [(0,6); (1,4); (1,6); (1,7); (2,4); (2,6); (3,4); (4,2); (5,0); (5,2)]

let make_rabbits =
   set_cells 1 3
   [(0,0); (0,4); (0,5); (0,6); (1,0); (1,1); (1,2); (1,5); (2,1)]

let make_engine =
   set_cells (-100) (-100)
   [(0,1); (0,3); (1,0); (2,1); (2,4); (3,3); (3,4); (3,5); (4,26); (4,27); (5,26); (5,27)]

let make_line w h bd =
   let w', h', l = w/2, h/2, w/3 in
   for i = -l to l do bd.(i+w').(h') <- alive done

let () =
   let argc = Array.length Sys.argv in
   let init =
      let default () = (print_endline "Using random start"; make_random) in
      if argc < 2 then default () else
      match Sys.argv.(1) with
         | "acorn" -> make_acorn
         | "blinker" -> make_blinker
         | "growth" -> make_growth
         | "engine" -> make_engine
         | "line" -> make_line
         | "rabbits" -> make_rabbits
         | "random" -> make_random
         | "-h" -> Printf.printf
            "Usage: %s [acorn|growth|blinker|engine|line|rabbits|random] width height\n" Sys.argv.(0);
            exit 0
         | _ -> default () in
   let width = if argc > 2 then int_of_string Sys.argv.(2) else 300 in
   let height = if argc > 3 then int_of_string Sys.argv.(3) else 300 in
   let bd1 = Array.make_matrix width height dead in
   let bd2 = Array.make_matrix width height dead in
   let border = 5 in
   let disp m = Graphics.draw_image (Graphics.make_image m) border border in
   init width height bd1;
   Graphics.open_graph (Printf.sprintf " %dx%d" (height+2*border) (width+2*border));
   while true do
      disp bd1;
      iteration bd1 bd2 width height;
      disp bd2;
      iteration bd2 bd1 width height
   done
Compile with:
opam install graphics && ocamlopt -o life -I $(ocamlfind query graphics) graphics.cmxa life.ml
and run with
./life acorn 250 250
If you run the blinker it will probably blink too fast to see unless you choose a large grid size.

Octave

1st order two variable recurrence relation m-file, will also run under MATLAB.

clear all
x=55;                 % Size of the Lattice (same as LAWE)

z(1:1:x^2)=0;         % Initialise the binary lattice
z_prime=z;            % prepare the z prime

idx=7*x+2;             % Origin 
z(idx+4)=1;            % Populate the binary lattice with the Gosper Glider
z(idx+x+4)=1;
z(idx+1+4)=1;
z(idx+x+1+4)=1;

z(idx+14)=1;
z(idx+14+x)=1;
z(idx+14+x+x)=1;
z(idx+15+x+x+x)=1;
z(idx+15-x)=1;
z(idx+16-x-x)=1;
z(idx+16+x+x+x+x)=1;
z(idx+17-x-x)=1;
z(idx+17+x+x+x+x)=1;

z(idx+18+x)=1;
z(idx+19-x)=1;
z(idx+19+x+x+x)=1;
z(idx+20)=1;
z(idx+20+x)=1;
z(idx+20+x+x)=1;
z(idx+21+x)=1;

z(idx+24)=1;
z(idx+25)=1;
z(idx+24-x)=1;
z(idx+25-x)=1;
z(idx+24-x-x)=1;
z(idx+25-x-x)=1;
z(idx+26-x-x-x)=1;
z(idx+26+x)=1;
z(idx+28-x-x-x)=1;
z(idx+28+x)=1;
z(idx+28-x-x-x-x)=1;
z(idx+28+x+x)=1;

z(idx+38)=1;
z(idx+38-x)=1;
z(idx+39)=1;
z(idx-x+39)=1;




for k=1:1:80;                 % Number of frames
for n=x+2:1:x^2-x-1;          % one time pass

theta=0;                      % Sum the surrounding area (top equation)
for c=n-1:1:n+1;
for m=-1:1:1;
theta=theta+z(m*x+c);
endfor
endfor

z_prime(n)= round(1/5*(z(n)*acos(sin(pi/4*(theta-z(n)-9/2)))  +  (1-z(n)) * acos(sin(pi/4*(theta-z(n) + 3)))));        % bottom equation

endfor

figure(2)
title('GOL','FontWeight','bold');
xlabel("X");
ylabel("Y");
imagesc(reshape(z,x,x)')
z=z_prime;
pause                        % each press advances the algorithm one step
endfor

Ol

Library: OpenGL
#!/usr/bin/ol
(import (otus random!))

(define MAX 65536)  ; should be power of two
; size of game board (should be less than MAX)
(define WIDTH 170)
(define HEIGHT 96)

; helper function
(define (hash x y)
   (let ((x (mod (+ x WIDTH) WIDTH))
         (y (mod (+ y HEIGHT) HEIGHT)))
   (+ (* y MAX) x)))

; helper function
(define neighbors '(
   (-1 . -1) ( 0 . -1) ( 1 . -1)
   (-1 .  0)           ( 1 .  0)
   (-1 .  1) ( 0 .  1) ( 1 .  1)
))

; dead-or-alive cell test
(define (alive gen x y)
   (case (fold (lambda (f xy)
                     (+ f (get gen (hash (+ x (car xy)) (+ y (cdr xy))) 0)))
               0 neighbors)
      (2
         (get gen (hash x y) #false))
      (3
         #true)))

; ---------------
(import (lib gl2))
(gl:set-window-title "Convey's The game of Life")

(glShadeModel GL_SMOOTH)
(glClearColor 0.11 0.11 0.11 1)
(glOrtho 0 WIDTH 0 HEIGHT 0 1)

(glPointSize (/ 854 WIDTH))

; generate random field
(gl:set-userdata
   (list->ff (map (lambda (i) (let ((x (rand! WIDTH)) (y (rand! HEIGHT)))
                                 (cons (hash x y) 1))) (iota 2000))))
; main game loop
(gl:set-renderer (lambda (mouse)
(let ((generation (gl:get-userdata)))
   (glClear GL_COLOR_BUFFER_BIT)

   ; draw the cells
   (glColor3f 0.2 0.5 0.2)
   (glBegin GL_POINTS)
      (ff-fold (lambda (st key value)
         (glVertex2f (mod key MAX)
                     (div key MAX))
      ) #f generation)
   (glEnd)

   (gl:set-userdata
      ; next cells generation
      (ff-fold (lambda (st key value)
         (let ((x (mod key MAX))
               (y (div key MAX)))
            (fold (lambda (st key)
                     (let ((x (+ x (car key)))
                           (y (+ y (cdr key))))
                        (if (alive generation x y) (put st (hash x y) 1) st)))
               (if (alive generation x y) (put st (hash x y) 1) st) ; the cell
               neighbors)))
         #empty generation)))))

ooRexx

/* REXX ---------------------------------------------------------------
* 07.08.2014 Walter Pachl Conway's Game of life  graphical
* Input is a file containing the initial pattern.
* The compute area is extended when needed
*   (i.e., when cells are born outside the current compute area)
* When computing the pattern sequence is complete, the graphical
* output starts and continues until Cancel is pressed.
* 10.08.2014 WP fixed the output of what.txt
*--------------------------------------------------------------------*/
 Parse Arg what speed
 If what='?' Then Do
   Say 'Create a file containing the pattern to be processed'
   Say 'named somename.in (octagon.in such as this for the octagon):'
   Say '   **   '
   Say '  *  *  '
   Say ' *    * '
   Say '*      *'
   Say '*      *'
   Say ' *    * '
   Say '  *  *  '
   Say '   **   '
   Say 'Run the program by entering "rexx conlife somename [pause]"',
                                                 'on the command line.'
   Say '(pause is the amount of milliseconds between 2 pictures.',
                                                     'default is 1000)'
   Say 'A file somename.lst will be created.'
   Say 'Hereafter you will see the pattern''s development',
                                                     'in a new window.'
   Say 'Press the Cancel button to end the presentation.'
   Exit
   End
 Parse Version interpreter '_' level '('
 If interpreter<>'REXX-ooRexx' Then Do
   Say interpreter  level
   Say 'This program must be run with object Rexx.'
   Exit
   End
 If what='' Then what='octagon'
 If right(what,3)='.in' then
   what=left(what,length(what)-3)
 infile=what'.in'
 If lines(infile)=0 Then Do
   Say 'Input file' infile 'not found.'
   Say 'Enter conlife ? for help.'
   Exit
   End
 If speed='' Then
   speed=1000
 .local~myspeed=speed

 Call tl what
 --'type' what'.lst'

 .local~title=what
 array=.local~myarrayData
 d = .drawDlg~new
 if d~initCode <> 0 then do
    say 'The Draw dialog was not created correctly.  Aborting.'
    return d~initCode
 end
 d~execute("SHOWTOP")
 return 0

::requires "ooDialog.cls"

::class 'drawDlg' subclass UserDialog

::attribute interrupted unguarded

::method init
   expose walterFont

   forward class (super) continue
   -- colornames:
   --  1 dark red      7 light grey   13 red
   --  2 dark green    8 pale green   14 light green
   --  3 dark yellow   9 light blue   15 yellow
   --  4 dark blue    10 white        16 blue
   --  5 purple       11 grey         17 pink
   --  6 blue grey    12 dark grey    18 turquoise

   self~interrupted = .true

   -- Create a font to write the nice big letters and digits
   opts = .directory~new
   opts~weight = 700
   walterFont = self~createFontEx("Arial",14,opts)
   walterFont = self~createFontEx("Courier",18,opts)

   if \self~createcenter(200, 235,"Walter's Clock", , ,"System",14) then
      self~initCode = 1

::method defineDialog

   self~createPushButton(/*IDC_PB_DRAW*/100,  0,  0,240,200,"DISABLED NOTAB")  -- The drawing surface.

   self~createPushButton(IDCANCEL,160,220, 35, 12,,"&Cancel")

::method initDialog unguarded
   expose x y dc myPen change al. fid nn what array
   change = 0
   x = self~factorx
   y = self~factory
   dc = self~getButtonDC(100)
   myPen   = self~createPen(1,'solid',0)
   t    = .TimeSpan~fromMicroSeconds(500000) -- .5 seconds
   msg  = .Message~new(self,'life')
   alrm = .Alarm~new(t, msg)
   array=.local~myArrayData
   Do s=1 to array~items
     al.s=array[s]
     Parse Var al.s ' == ' al.s
     End
   nn=s-2
   --say 'nn'nn
   Call lineout fid

::method interrupt unguarded

   self~interrupted = .true

::method cancel unguarded   -- Stop the drawing program and quit.
   expose x y
   self~hide
   self~interrupted = .true
   return self~cancel:super

::method leaving unguarded  -- Best place to clean up resources
   expose dc myPen walterFont

   self~deleteObject(myPen)
   self~freeButtonDC(/*IDC_PB_DRAW*/100,dc)
   self~deleteFont(walterFont)

::method life unguarded                           /* draw individual pixels */
   expose x y dc myPen change walterFont al. nn what
   mx = trunc(20*x); my = trunc(20*y); size = 400

   curPen = self~objectToDC(dc, myPen)

   -- Select the nice big letters and digits into the device context to use to
   -- to write with:
   curFont = self~fontToDC(dc, walterFont)

   -- Create a white brush and select it into the device to paint with.
   whiteBrush = self~createBrush(10)
   curBrush   = self~objectToDC(dc, whiteBrush)

   -- Paint the drawing area surface with the white brush
   self~rectangle(dc, 1, 1, 500, 600, 'FILL')
   self~writeDirect(dc,  10, 20,'Conway''s Game of Life')
   self~writeDirect(dc,  10, 40,.local~title)
   self~writeDirect(dc,  10,460,'Walter Pachl, 8 Aug 2014')
   dx=.local~dxval
   dy=.local~dyval
   do s=1 By 1 until self~interrupted
     self~transparentText(dc)
     self~interrupted = .false
     sm=s//nn+1
     If s>1 Then Do
       ali=al.sb
       Do While ali<>''
         Parse Var ali x ',' y ali
         zxa=(x+dx)*10
         zya=(y+dy)*10
         self~draw_square(dc,zxa,zya,3,10)
         End
       End
     self~draw_square(dc, 380, 10,100,10)
     self~writeDirect(dc, 340, 20,time())
     self~writeDirect(dc, 340, 40,right(sm,2) 'of' right(nn,2))
     ali=al.sm
     Do While ali<>''
       Parse Var ali x ',' y ali
       zxa=(x+dx)*10
       zya=(y+dy)*10
       self~draw_square(dc,zxa,zya,3,5)
       End
 --    self~interrupted = .true
     sb=sm
     self~objectToDC(dc, curPen)
     self~objectToDC(dc, curBrush)
     call msSleep .local~myspeed
   --self~pause
     End

::method pause
   j = msSleep(10)

::method draw_square
  Use Arg dc, x, y, d, c
  Do zx=x-d to x+d
    Do zy=y-d to y+d
      self~drawPixel(dc, zx, zy, c)
      End
    End

::method quot
  Parse Arg x,y
  If y=0 Then Return '???'
  Else Return x/y

::routine tl
/* REXX ---------------------------------------------------------------
* 02.08.2014 Walter Pachl
* Input is a file containing the initial pattern
* The compute area is extended when needed
*   (cells are born outside the current compute area)
* The program stops when the picture shown is the same as the first
*   or equal to the previous one
*--------------------------------------------------------------------*/
Parse Arg f
If f='' Then f='bipole'
fid=f'.in'
oid=f'.txt'; 'erase' oid
oil=f'.lst'; 'erase' oil
debug=0
If debug Then Do
  dbg=f'.xxx'; 'erase' dbg
  End
ml=0
l.=''
ol.=''
Parse Value '10 10' With xb yb
xc=copies(' ',xb)
Do ri=yb+1 By 1 While lines(fid)>0
  l.ri=xc||linein(fid)
  ml=max(ml,length(strip(l.ri,'T')))
  End
ri=ri-1
ml=ml+xb
ri=ri+yb
yy=ri
a.=' '
b.=' '
m.=''
x.=''
list.=''
Parse Value 1 ml 1 yy With xmi xma ymi yma
Parse Value '-10 30 -10 30' With xmi xma ymi yma
Parse Value '999 -999  999 -999 999 -999 999 -999',
       With xmin xmax ymin ymax xlo xhi  ylo yhi
Do y=1 To yy
  z=yy-y+1
  l=l.z
  Do x=1 By 1 While l<>''
    Parse Var l c +1 l
    If c='*' Then
      a.x.z='*'
    End
  End
Call show
Do step=1 To  60
  Call store
  If step>1 & is_equal(step,1) Then Leave
  If step>1 & is_equal(step,step-1) Then Leave
  Call show_neighbors
  Do y=yma To ymi By -1
    ol=format(x,3)' '
    Do x=xmi To xma
      neighbors=neighbors(x,y)
      If a.x.y=' ' Then Do             /* dead cell                  */
        If neighbors=3 Then Do
          b.x.y='*'                    /*  gets life                 */
          mmo=xmi xma ymi yma
          xmi=min(xmi,x-1)
          xma=max(xma,x+1)
          ymi=min(ymi,y-1)
          yma=max(yma,y+1)
          mm=xmi xma ymi yma
          If mm<>mmo Then
            Call debug mmo '1->' mm
          End
        Else                           /* life cell                  */
          b.x.y=' '                    /*  remains dead              */
        End
      Else Do                          /* life cell                  */
        If neighbors=2 |,
           neighbors=3 Then Do
          b.x.y='*'  /*  remains life              */
          mmo=xmi xma ymi yma
          xmi=min(xmi,x-1)
          xma=max(xma,x+1)
          ymi=min(ymi,y-1)
          yma=max(yma,y+1)
          mm=xmi xma ymi yma
          If mm<>mmo Then
            Call debug mmo '2->' mm
          End
        Else
          b.x.y=' '  /*  dies                      */
        End
      End
    End
  /* b. is the new state and is now copied to a.                     */
  Do y=yma To ymi By -1
    Do x=xmi To xma
      a.x.y=b.x.y
      End
    End
  End
/* Output name and all states                                        */
Call lineout oid,' 'f
st=' +'                                /* top and bottom border      */
sb=' +'                                /* top and bottom border      */
Do s=1 To step
  st=st||'-'right(s,2,'-')||copies('-',xmax-xmin-2)'+'
  sb=sb||copies('-',xmax-xmin+1)'+'
  End
array=.array~new
Do y=ymin To ymax
  Do s=1 To step
    Do x=xmin To xmax
      If substr(m.s.y,x,1)='*' Then Do
        xlo=min(xlo,x)
        xhi=max(xhi,x)
        ylo=min(ylo,y)
        yhi=max(yhi,y)
        End
      End
    End
  End
Do y=ymin To ymax
  ol=''
  Do s=1 To step
    Do x=xmin To xmax
      If substr(m.s.y,x,1)='*' Then Do
        list.s=list.s (x-xlo+1)','||(y-ylo+1)
        End
      End
    array[s]=s '-' words(list.s) '==' list.s
    End
  --Call lineout oid,ol '|'
  .local~myArrayData=array
  End
height=yhi-ylo+1
width=xhi-xlo+1
.local~dxval=(48-width)%2
.local~dyval=(48-height)%2
Call o st                        /* top border                 */
xl.='|'
Do y=ymax To ymin By -1
  Do s=1 To step
    xl.y=xl.y||substr(ol.s.y,xmin,xmax-xmin+1)'|'
    End
  End
Do y=ymax To ymin By -1
  Call o ' 'xl.y
  End
Call o sb                    /* bottom border              */
Call lineout oid
Say 'frames are shown in' oid
If debug Then Do
  Say 'original area' 1 ml '/' 1 yy
  Say 'compute area ' xmi xma '/' ymi yma
  Say 'used area    ' xlo xhi '/' ylo yhi
  End
Do s=1 To step
  call lineout oil,s '==>' words(list.s) '=='  list.s
  End
Return

o: Parse Arg lili
   Call lineout oid,lili
   Return

set: Parse Arg x,y
     a.x.y='*'
     Return

neighbors: Procedure Expose a. debug
  Parse Arg x,y
  neighbors=0
  do xa=x-1 to x+1
    do ya=y-1 to y+1
      If xa<>x | ya<>y then
        If a.xa.ya='*' Then
          neighbors=neighbors+1
      End
    End
  Return neighbors

store:
/* store current state (a.) in lines m.step.*                        */
Do y=yma To ymi By -1
  ol=''
  Do x=xmi To xma
    z=a.x.y
    ol=ol||z
    End
  x.step.y=ol
  If ol<>'' then Do
    ymin=min(ymin,y)
    ymax=max(ymax,y)
    p=pos('*',ol)
    q=length(strip(ol,'T'))
    If p>0 Then
      xmin=min(xmin,p)
    xmax=max(xmax,q)
    End
  m.step.y=ol
  ol.step.y=ol
  --If pos('*',ol)>0 Then Do
  --  Say '====>' right(step,2) right(y,3) '>'ol'<'  xmin xmax
  --  Say '              'copies('1234567890',3)
  --  End
  End
Return

is_equal:
/* test ist state a.b is equal to state a.a                          */
  Parse Arg a,b
  Do y=yy To 1 By -1
    If x.b.y<>x.a.y Then
      Return 0
    End
  Return 1

show: Procedure Expose dbg a. yy ml debug
Do y=-5 To 13
  ol='>'
  Do x=-5 To 13
    ol=ol||a.x.y
    End
  Call debug ol
  End
Return

show_neighbors: Procedure Expose a. xmi xma ymi yma dbg debug
  Do y=yma To ymi By -1
    ol=format(y,3)' '
    Do x=xmi To xma
      ol=ol||neighbors(x,y)
      End
    Call debug ol
    End
  Return

debug:
  If debug Then
    Return lineout(dbg,arg(1))
  Else
    Return
Output:
blinker.txt
 blinker
 +--1+--2+--3+
 |   | * |   |
 |***| * |***|
 |   | * |   |
 +---+---+---+  
blinker.lst
1 ==> 3 ==  1,2 2,2 3,2
2 ==> 3 ==  2,1 2,2 2,3
3 ==> 3 ==  1,2 2,2 3,2    

Oz

declare
  Rules = [rule(c:1 n:[0 1]             new:0)  %% Lonely
           rule(c:1 n:[4 5 6 7 8]       new:0)  %% Overcrowded
           rule(c:1 n:[2 3]             new:1)  %% Lives
           rule(c:0 n:[3]               new:1)  %% It takes three to give birth!
           rule(c:0 n:[0 1 2 4 5 6 7 8] new:0)  %% Barren
          ]

  Blinker = ["..."
             "###"
             "..."]

  Toad = ["...."
          ".###"
          "###."
          "...."]

  Glider = [".#.........."
            "..#........."
            "###........."
            "............"
            "............"
            "............"
            "............"
            "............"
            "............"
            "............"
            "............"]

  Init = Blinker
  MaxGen = 2

  %% G(i) -> G(i+1)
  fun {Evolve Gi}
     fun {Get X#Y}
        Row = {CondSelect Gi Y unit}
     in
        {CondSelect Row X 0} %% cells beyond boundaries are dead (0)
     end
     fun {GetNeighbors X Y}
        {Map [X-1#Y-1  X#Y-1  X+1#Y-1
              X-1#Y           X+1#Y
              X-1#Y+1  X#Y+1  X+1#Y+1]
         Get}
     end
  in
     {Record.mapInd Gi
      fun {$ Y Row}
         {Record.mapInd Row
          fun {$ X C}
             N = {Sum {GetNeighbors X Y}}
          in
             for Rule in Rules return:Return do
                if C == Rule.c andthen {Member N Rule.n} then
                   {Return Rule.new}
                end
             end
          end}
      end}
  end

  %% For example: [".#"
  %%                "#."] -> grid(1:row(1:0 2:1) 2:row(1:1 2:0))
  fun {ReadG LinesList}
     {List.toTuple grid
      {Map LinesList
       fun {$ Line}
          {List.toTuple row
           {Map Line
            fun {$ C}
               if C == &. then 0
               elseif C == &# then 1
               end
            end}}
       end}}
  end

  %% Inverse to ReadG
  fun {ShowG G}
     {Map {Record.toList G}
      fun {$ Row}
         {Map {Record.toList Row}
          fun {$ C}
             if C == 0 then &.
             elseif C == 1 then &#
             end
          end}
      end}
  end

  %% Helpers
  fun {Sum Xs} {FoldL Xs Number.'+' 0} end
  fun lazy {Iterate F V} V|{Iterate F {F V}} end

  G0 = {ReadG Init}
  Gn = {Iterate Evolve G0}
in
  for
     Gi in Gn
     I in 0..MaxGen
  do
     {System.showInfo "\nGen. "#I}
     {ForAll {ShowG Gi} System.showInfo}
  end

PARI/GP

Basic implementation; prints a matrix representing the state of the game directly. Supports large games but this example uses only the required 3 X 3 blinker.

step(M)={
  my(N=M,W=matsize(M)[1],L=#M,t);
  for(l=1,W,for(w=1,L,
    t=sum(i=l-1,l+1,sum(j=w-1,w+1,if(i<1||j<1||i>W||j>L,0,M[i,j])));
    N[l,w]=(t==3||(M[l,w]&&t==4))
  ));
  N
};
M=[0,1,0;0,1,0;0,1,0];
for(i=1,3,print(M);M=step(M))

Pascal

Uses crt for console output. Can make use of a "torus"-world. Optimized for speed on a Haswell CPU (without PrintGen ~ 8.5 Cpu-cyles/coordinate )

program Gol;
// Game of life
{$IFDEF FPC}
   //save as gol.pp/gol.pas
  {$Mode delphi}
{$ELSE}
  //for Delphi save as gol.dpr
  {$Apptype Console}
{$ENDIF}
uses
  crt;

const
  colMax = 76;
  rowMax = 22;
  dr = colMax+2; // element count of one row

  cDelay = 20;  // delay in ms

(*
expand field by one row/column before and after
for easier access no special treatment of torus
*)

type
  tFldElem  = byte;//0..1
  tpFldElem = ^tFldElem;
  tRow = array[0..colMax+1] of tFldElem;
  tpRow = ^tRow;
  tBoard = array[0..rowMax+1] of tRow;
  tpBoard = ^tBoard;
  tpBoards = array[0..1] of tpBoard;

type
  tIntArr = array[0..2*dr+2] of tFldElem;
  tpIntArr = ^tIntArr;

var
  aBoard,bBoard : tBoard;
  pBoards :tpBoards;
  gblActBoard : byte;
  gblUseTorus :boolean;
  gblGenCnt   : integer;

procedure PrintGen;
const
  cChar: array[0..1] of char = (' ','#');
var
  p0 : tpIntArr;
  col,row: integer;
  s : string[colMax];
begin
  setlength(s,colmax);
  gotoxy(1,1);
  writeln(gblGenCnt:10);
  For row := 1 to rowMax do
  begin
    p0 := @pBoards[gblActBoard]^[row,0];;
    For col := 1 to colMax do
      s[col] := cChar[p0[col]];
    writeln(s);
  end;
  delay(cDelay);
end;

procedure Init0(useTorus:boolean);
begin
  gblUseTorus := useTorus;
  gblGenCnt := 0;
  fillchar(aBoard,SizeOf(aBoard),#0);
  pBoards[0] := @aBoard;
  pBoards[1] := @bBoard;
  gblActBoard := 0;

  clrscr;
end;

procedure InitRandom(useTorus:boolean);
var
  col,row : integer;
begin
  Init0(useTorus);
  For row := 1 to rowMax do
    For col := 1 to colMax do
      aBoard[row,col]:= tFldElem(random>0.9);
end;

procedure InitBlinker(useTorus:boolean);
var
  col,row : integer;
begin
  Init0(useTorus);
  For col := 1 to colMax do
  begin
    IF (col+2) mod 4 = 0 then
      begin
      For row := 1 to rowmax do
        IF row mod 4 <> 0 then
          aBoard[row,col]:= 1;
      end;
  end;
end;

procedure Torus;
var
  p0 : tpIntArr;
  row: integer;
begin
  //copy column 1-> colMax+1 and colMax-> 0
  p0 := @pBoards[gblActBoard]^[1,0];
  For row := 1 to rowMax do
    begin
    p0^[0] := p0^[colMax];
    p0^[colmax+1] := p0^[1];
    //next row
    p0 := Pointer(PtrUint(p0)+SizeOf(tRow));
    end;
  //copy row  1-> rowMax+1
  move(pBoards[gblActBoard]^[1,0],pBoards[gblActBoard]^[rowMax+1,0],sizeof(trow));
  //copy row  rowMax-> 0
  move(pBoards[gblActBoard]^[rowMax,0],pBoards[gblActBoard]^[0,0],sizeof(trow));
end;

function Survive(p: tpIntArr):tFldElem;
//p points to actual_board [row-1,col-1]
//calculates the sum of alive around [row,col] aka p^[dr+1]
//really fast using fpc 2.6.4 no element on stack
const
  cSurvives : array[boolean,0..8] of byte =
              //0,1,2,3,4,5,6,7,8     sum of alive neighbours
              ((0,0,0,1,0,0,0,0,0),   {alive =false 1->born}
               (0,0,1,1,0,0,0,0,0));  {alive =true  0->die }
var
  sum : integer;
begin
  // row above
  // sum := byte(aBoard[row-1,col-1])+byte(aBoard[row-1,col])+byte(aBoard[row-1,col+1]);
  sum :=     integer(p^[     0])+integer(p^[     1])+integer(p^[     2]);
  sum := sum+integer(p^[  dr+0])                    +integer(p^[  dr+2]);
  sum := sum+integer(p^[2*dr+0])+integer(p^[2*dr+1])+integer(p^[2*dr+2]);
  survive := cSurvives[boolean(p^[dr+1]),sum];
end;

procedure NextGen;
var
  p0,p1 : tpFldElem;
  row: NativeInt;
  col :NativeInt;
begin
  if gblUseTorus then
    Torus;
  p1 := @pBoards[1-gblActBoard]^[1,1];
  //One row above and one column before because of survive
  p0 := @pBoards[  gblActBoard]^[0,0];
  For row := rowMax-1 downto 0 do
  begin
    For col := colMax-1 downto 0 do
    begin
      p1^ := survive(tpIntArr(p0));
      inc(p0);
      inc(p1);
    end;
    // jump over the borders
    inc(p1,2);
    inc(p0,2);
  end;
  //aBoard := bBoard;
  gblActBoard :=1-gblActBoard;
  inc(gblGenCnt);
end;

begin
  InitBlinker(false);
  repeat
    PrintGen;
    NextGen;
  until keypressed;
  PrintGen;
end.

Perl

This a perl example the simulates Conway's life starting with a random grid of the given size for the given number of steps. Example:

life.pl numrows numcols numiterations 
life.pl 5 10 15 

would do 15 iterations over 5 rows and 10 columns.

my ($width, $height, $generations) = @ARGV;

my $printed;

sub generate {
   (map
       {[ (map { rand () < 0.5 } 1 .. $width), 0 ]}
       1 .. $height),
   [(0) x ($width + 1)];
}

sub nexgen {
   my @prev = map {[@$_]} @_;
   my @new = map {[ (0) x ($width + 1) ]} 0 .. $height;
   foreach my $row ( 0 .. $height - 1 ) {
       foreach my $col ( 0 .. $width - 1 ) {
           my $val =
             $prev[ $row - 1 ][ $col - 1 ] +
             $prev[ $row - 1 ][ $col     ] +
             $prev[ $row - 1 ][ $col + 1 ] +
             $prev[ $row     ][ $col - 1 ] +
             $prev[ $row     ][ $col + 1 ] +
             $prev[ $row + 1 ][ $col - 1 ] +
             $prev[ $row + 1 ][ $col     ] +
             $prev[ $row + 1 ][ $col + 1 ];
           $new[$row][$col] =
               ( $prev[$row][$col] && $val == 2 || $val == 3 );
       }
   }
   return @new;
}

sub printlife {
   my @life = @_;
   if ($printed) {
	# Move the cursor up to print over prior generation.
	print "\e[1A" x $height;
   }
   $printed = 1;
   foreach my $row ( 0 .. $height - 1 ) {
       foreach my $col ( 0 .. $width - 1 ) {
           print($life[$row][$col]
             ? "\e[33;45;1m \e[0m"
             : "\e[1;34;1m \e[0m");
       }
       print "\n";
   }
}

my @life = generate;
print "Start\n";
printlife @life;
foreach my $stage ( 1 .. $generations ) {
   sleep 1;
   print "Generation $stage\n\e[1A";
   @life = nexgen @life;
   printlife @life;
}
print "\n";
Another version, takes up the whole area of your terminal. Using warping edges.
my $w = `tput cols` - 1;
my $h = `tput lines` - 1;
my $r = "\033[H";

my @universe = map([ map(rand(1) < .1, 1 .. $w) ], 1 .. $h);
sub iterate {
	my @new = map([ map(0, 1 .. $w) ], 1 .. $h);
	for my $i (0 .. $h - 1) {
	for my $j (0 .. $w - 1) {
		my $neighbor = 0;
		for (	[-1, -1], [-1, 0], [-1, 1],
			[ 0, -1], 	   [ 0, 1],
			[ 1, -1], [ 1, 0], [ 1, 1] )
		{
			my $y = $_->[0] + $i;
			my $x = $_->[1] + $j;
			$neighbor += $universe[$y % $h][$x % $w];
			last if $neighbor > 3;
		}

		$new[$i][$j] = $universe[$i][$j]
			? ($neighbor == 2 or $neighbor == 3)
			: $neighbor == 3;
	}}
	@universe = @new;
}

while(1) {
	print $r;
	print map((map($_ ? "#" : " ", @$_), "\n"), @universe);
	iterate;
}

Next Generation in a Single Substitution Operator

#!/usr/bin/perl

print $_ = <<'' =~ tr/./ /r; # test case, dots only for layout
.....
.....
.###.
.....
.....

my $gap = /..\n/ ? qr/.{$-[0]}/s : die "too small";
my $neighborhood = qr/(?<=(...) $gap (.)) . (?=(.) $gap (...))/x;

for my $generation ( 2 .. 4 )
  {
  s/$neighborhood/ substr "  $&#     ", "$1$2$3$4" =~ tr|#||, 1 /ge;
  print;
  }
Output:


### 
    
    
    
 #  
 #  
 #  
    
    
    
### 
    
    
    
 #  
 #  
 #

Phix

Translation of: basic256
Library: Phix/pGUI
Library: Phix/online

You can run this online here.

--
-- demo\rosetta\Conways_Game_of_Life.exw
-- =====================================
--
with javascript_semantics
include pGUI.e

constant title = "Conway's Game of Life"
Ihandle dlg, canvas
Ihandln hTimer = NULL
cdCanvas cddbuffer

sequence c = {},    -- cells
         cn,        -- new cells
         cl         -- last cells

procedure draw(integer what)
    integer x = floor(length(c)/2)+1,
            y = floor(length(c[1])/2)
    switch what do
        case ' ': c = sq_mul(c,0)                                   -- Clear
        case '+': c[x][y-1..y+1] = repeat(1,3)                      -- Blinker
        case 'G': {                    c[x+1,y+4],
                   c[x+2,y+2],         c[x+2,y+4],
                           c[x+3,y+3], c[x+3,y+4]} = repeat(1,5)    -- Glider
        case 'T': {c[x-1,y+1],c[x,y+1],c[x+1,y+1],
                   c[x  ,y+3],c[x,y+4],c[x  ,y+5]} = repeat(1,6)    -- Thunderbird
        case 'X': for i=0 to min(x,y)-1 do
                    {c[x-i,y+i],c[x+i,y+i],
                     c[x-i,y-i],c[x+i,y-i]} = repeat(1,4)           -- Cross
                  end for
    end switch
end procedure

atom t1 = time()+1
integer fps = 0

function redraw_cb(Ihandle /*ih*/)
    integer {width, height} = IupGetIntInt(canvas, "DRAWSIZE"),
            -- limit to 10K cells (performance target of 10fps)
            -- n here is the cell size in pixels (min of 1x1)
            n = ceil(sqrt(width*height/10000)),
            w = floor(width/n)+2, -- (see cx below)
            h = floor(height/n)+2,
            alive = 0
    -- keep w, h odd for symmetry (plus I suspect the 
    --  "Cross" code above may now crash without this)
    w -= even(w)
    h -= even(h)
    if length(c)!=w
    or length(c[1])!=h then
        c = repeat(repeat(0,h),w)
        cn = deep_copy(c)
        cl = deep_copy(c)
        draw('X')
        if hTimer!=NULL then
            IupStoreAttribute(hTimer, "RUN", "YES")
        end if
    end if
    cdCanvasActivate(cddbuffer)
    --
    -- There is a "dead border" of 1 cell all around the edge of c (etc) which
    -- we never display or update. If we have got this right/an exact fit, then 
    -- w*n should be exactly 2n too wide, whereas in the worst case there is an
    -- (2n-1) pixel border, which we split between left and right, ditto cy.
    --
    integer cx = n+floor((width-w*n)/2)
    for x=2 to w-1 do
        integer cy = n+floor((height-h*n)/2)
        for y=2 to h-1 do
            integer cxy = c[x,y],
                    clxy = cl[x,y],
                    cnxy = -cxy
            for i=x-1 to x+1 do
                for j=y-1 to y+1 do
                    cnxy += c[i,j]
                end for
            end for
            integer live = iff(cxy?cnxy>=2 and cnxy<=3:cnxy==3),
            colour = iff(live?iff(cxy?iff(clxy?CD_PURPLE    -- adult
                                              :CD_GREEN)    -- newborn
                                     :iff(clxy?CD_RED       -- old
                                              :CD_YELLOW))  -- shortlived
                             :CD_BLACK)
            cn[x,y] = live
            alive += live
            cdCanvasSetForeground(cddbuffer,colour)
            cdCanvasBox(cddbuffer, cx, cx+n-1, cy, cy+n-1)
            cy += n
        end for
        cx += n
    end for
    cdCanvasFlush(cddbuffer)
    if not alive then
        IupStoreAttribute(hTimer, "RUN", "NO")
        IupStoreAttribute(dlg, "TITLE", "died")
    elsif c=cn then
        IupStoreAttribute(hTimer, "RUN", "NO")
        IupStoreAttribute(dlg, "TITLE", "stable")
    else
        cl = c
        c = deep_copy(cn)
        fps += 1
        if time()>=t1 then
            IupSetStrAttribute(dlg,"TITLE","%s (%d FPS)",{title,fps})
            t1 = time()+1
            fps = 0
        end if
    end if
    return IUP_DEFAULT
end function

function map_cb(Ihandle ih)
    cdCanvas cdcanvas = cdCreateCanvas(CD_IUP, ih)
    cddbuffer = cdCreateCanvas(CD_DBUFFER, cdcanvas)
    cdCanvasSetBackground(cddbuffer, CD_WHITE)
    cdCanvasSetForeground(cddbuffer, CD_RED)
    return IUP_DEFAULT
end function

function key_cb(Ihandle /*ih*/, atom c)
    if c=K_ESC then return IUP_CLOSE end if -- (standard practice for me)
    if c=K_F5 then return IUP_DEFAULT end if -- (let browser reload work)
    if    find(c," ")   then draw(' ')  -- Clear
    elsif find(c,"+bB") then draw('+')  -- Blinker
    elsif find(c,"gG")  then draw('G')  -- Glider
    elsif find(c,"tT")  then draw('T')  -- Thunderbird
    elsif find(c,"xX")  then draw('X')  -- Cross
    end if
    IupStoreAttribute(hTimer, "RUN", "YES")
    return IUP_CONTINUE
end function

function timer_cb(Ihandle /*ih*/)
    IupUpdate(canvas)
    return IUP_IGNORE
end function

procedure main()
    IupOpen()
    canvas = IupCanvas("RASTERSIZE=390x390")
    IupSetCallbacks(canvas, {"MAP_CB", Icallback("map_cb"),
                             "ACTION", Icallback("redraw_cb")})
    dlg = IupDialog(canvas,`TITLE="%s", MINSIZE=350x55`, {title})
      -- (above MINSIZE prevents the title from getting squished)
    IupSetCallback(dlg, "KEY_CB", Icallback("key_cb"))
    IupShow(dlg)
    IupSetAttribute(canvas,"RASTERSIZE",NULL)
--  hTimer = IupTimer(Icallback("timer_cb"),40) -- 25fps (maybe)
    hTimer = IupTimer(Icallback("timer_cb"),100) -- 10fps
    if platform()!=JS then
        IupMainLoop()
        IupClose()
    end if
end procedure

main()

Picat

Blinker

go => 
   Rows = 3,
   Cols = 3,
   println(blinker),
   pattern(blinker, Pattern,I,J),
   life(fill(Rows,Cols,Pattern,I,J)),
   nl.

fill(Rows, Cols, Obj) = fill(Rows, Cols, Obj,1,1).
fill(Rows, Cols, Obj,OffsetI,OffsetJ) = Grid =>
   Grid = new_array(Rows,Cols), bind_vars(Grid,0),
   foreach(I in 1..Obj.length, J in 1..Obj[1].length) 
     Grid[I+OffsetI-1,J+OffsetJ-1] := Obj[I,J]
   end.

% We stop whenever a fixpoint/cycle is detected
life(S) => 
    Rows = S.length,
    Cols = S[1].length,
    println([rows=Rows, cols=Cols]),
    print_grid(S),
    Seen = new_map(), % detect fixpoint and cycle
    Count = 0,
    while (not Seen.has_key(S))
       Seen.put(S,1),
       T = new_array(Rows,Cols),
       foreach(I in 1..Rows, J in 1..Cols) 
           Sum = sum([S[I+A,J+B] : A in -1..1,B in -1..1, 
                                   I+A > 0, J+B > 0, 
                                   I+A =< Rows, J+B =< Cols]) - S[I,J],
           C = rules(S[I,J], Sum),
           T[I,J] := C
       end,
       print_grid(T),
       S := T,
       Count := Count + 1
    end,
    printf("%d generations\n", Count).

print_grid(G) => 
  foreach(I in 1..G.length) 
     foreach(J in 1..G[1].length) 
        if G[I,J] == 1 then print("#") else print(".") end
     end,
     nl
  end,
  nl.

% The Rules of Life
rules(This,Sum) = 1, (This == 1, member(Sum,[2,3]); This == 0, Sum == 3) => true.
rules(_This, _Sum) = 0 => true.

%
% The patterns
%   pattern(Name, Pattern, OffsetI, OffsetJ)
% where Offset* is the recommended offsets in a grid.
% 

% For the task
pattern(blinker, Pattern,I,J) ?=> 
   Pattern = [[0,0,0],
              [1,1,1],
              [0,0,0]],
   I=1,J=1.
Output:
blinker
[rows = 3,cols = 3]
...
###
...

.#.
.#.
.#.

...
###
...

2 generations

Testing some more forms

go2 => 
   Rows = 20,
   Cols = 20,
   Names = [blinker2, p4, p5, glider, figure_eight], 
   foreach(Name in Names )
     pattern(Name, Pattern,I,J),
     println(Name),     
     life(fill(Rows,Cols,Pattern,I,J)),
     nl
   end,
   nl.

% Increase the recommended offset
pattern(blinker2, Pattern,I,J) ?=> 
   Pattern = [[0,0,0],
              [1,1,1],
              [0,0,0]],
   I=5,J=5.

pattern(p4, Pattern,I,J) ?=> 
   Pattern = [[0,0,0,0],
              [1,1,1,1],
              [1,1,1,1],
              [0,0,0,0]],
   I=10,J=10.

pattern(p5, Pattern,I,J) ?=> 
   Pattern = [[0,0,0,0,0],
              [1,1,1,1,1],
              [1,1,1,1,1],
              [1,1,1,1,1],
              [0,0,0,0,0]],
   I=10,J=10.

pattern(glider, Pattern,I,J) ?=> 
   Pattern = [[0,0,1],
              [1,0,1],
              [0,1,1]],
   I=5,J=5.

pattern(figure_eight, Pattern,I,J) =>
   Pattern = [[1,1,1,0,0,0],
              [1,1,1,0,0,0],
              [1,1,1,0,0,0],
              [0,0,0,1,1,1],
              [0,0,0,1,1,1],
              [0,0,0,1,1,1]],
   I=10,J=10.

PicoLisp

This example uses 'grid' and 'disp' from "lib/simul.l". These functions maintain an array of multiply linked objects, and are also used in the chess program and other games in the distribution.

(load "@lib/simul.l")

(de life (DX DY . Init)
   (let Grid (grid DX DY)
      (for This Init
         (=: life T) )
      (loop
         (disp Grid NIL
            '((This) (if (: life) "X " "  ")) )
         (wait 1000)
         (for Col Grid
            (for This Col
               (let N  # Count neighbors
                  (cnt
                     '((Dir) (get (Dir This) 'life))
                     (quote
                        west east south north
                        ((X) (south (west X)))
                        ((X) (north (west X)))
                        ((X) (south (east X)))
                        ((X) (north (east X))) ) )
                  (=: next  # Next generation
                     (if (: life)
                        (>= 3 N 2)
                        (= N 3) ) ) ) ) )
         (for Col Grid  # Update
            (for This Col
               (=: life (: next)) ) ) ) ) )

(life 5 5  b3 c3 d3)

Output:

 5
 4
 3   X X X
 2
 1
   a b c d e
 5
 4     X
 3     X
 2     X
 1
   a b c d e
 5
 4
 3   X X X
 2
 1
   a b c d e

PL/I

(subscriptrange):
Conway: procedure options (main);        /* 20 November 2013 */
   /* A grid of (1:100, 1:100) is desired; the array GRID is defined as (0:101, 0:101), */
   /* to satisfy the requirement that elements off-grid are zero.                       */
   declare n fixed binary; /* grid size) */

   put ('What grid size do you want?');
   get (n);
   put skip list ('Generating a grid of size ' || trim(n) );

begin;
   declare grid (0:n+1,0:n+1) bit(1) initial ((*) '0'b);
   declare new  (0:n+1,0:n+1) bit(1);
   declare cell(3,3) defined grid(1sub-2+i, 2sub-2+j) bit (1);
   declare (i, j, k) fixed binary;

   /* Initialize some cells. */
   grid(2,2) = '1'b; grid(2,3) = '1'b; grid(2,4) = '1'b;

   /* Print the initial state. */
   put list ('Initial pattern:');
   do i = 1 to n;
      put skip;
      do j = 1 to n;
         put edit (grid(i,j)) (b(1));
      end;
   end;

   do k = 1 to 4;
      /* Do one generation of life */
      new = '0'b;
      /* For each C, the center of a 3 x 3 cell matrix. */
      do i = 1 to n;
         do j = 1 to n;
            if grid(i,j) then
               select (sum(cell)-1);
                  when (0,1)       new(i,j) = '0'b;
                  when (4,5,6,7,8) new(i,j) = '0'b;
                  when (2,3)       new(i,j) = '1'b;
               end;
            else
               select (sum(cell));
                  when (3)         new(i,j) = '1'b;
                  otherwise        new(i,j) = '0'b;
               end;
         end;
      end;
      grid = new; /* Update GRID with the new generation. */

      /* Print the generation. */
      put skip(2) list ('Generation ' || trim(k));
      do i = 1 to n;
         put skip;
         do j = 1 to n;
            put edit (grid(i,j)) (b(1));
         end;
      end;
   end;
end;	
end Conway;

Results:

What grid size do you want? 

Generating a grid of size 5 

Initial conditions: 
00000
01110
00000
00000
00000

Generation 1 
00100
00100
00100
00000
00000

Generation 2 
00000
01110
00000
00000
00000

Generation 3 
00100
00100
00100
00000
00000

Generation 4 
00000
01110
00000
00000
00000

Pointless

-----------------------------------------------------------
-- Print 100 simulated states of conway's game of life
-- for a glider starting pattern on a wrapping grid
-- Print generation number along with cells

output =
  initCells
  |> iterate(updateCells)
  |> take(130)
  |> enumerate
  |> map(showPair)
  |> printFrames

initCells =
 [[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
  [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
  [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
  [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
  [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
  [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
  [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
  [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
  [0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0]
  [0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 0]
  [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
  [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
  [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
  [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
  [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]]

width  = length(initCells[0])
height = length(initCells)

positions = 
  for y in range(0, height - 1)
  for x in range(0, width - 1)
  yield (x, y)

-----------------------------------------------------------
-- Update each cell in the grid according to its position,
-- and convert the resulting list back to a 2D array

updateCells(cells) =
  positions
  |> map(tick(cells))
  |> toNDArray((height, width))

-----------------------------------------------------------
-- Get the new value for a cell at a give position
-- based on the current cell values in the grid

tick(cells, pos) = toInt(survive or birth) where {
  survive = cells[y][x] == 1 and count in {2, 3}
  birth   = cells[y][x] == 0 and count == 3
  count   = getCount(x, y, cells)
  (x, y)  = pos
}

-----------------------------------------------------------
-- Get the number of live neighbors of a given position

getCount(x, y, cells) = sum(
  for dx in [-1, 0, 1] 
  for dy in [-1, 0, 1] 
  when (dx != 0 or dy != 0)
  yield getNeighbor(x + dx, y + dy, cells) 
)

getNeighbor(x, y, cells) = cells[y % height][x % width]   

-----------------------------------------------------------
-- Print the board and generation number given pairs
-- of (gen, cells) from the enumerate function

showPair(pair) =
  format("{}\ngeneration: {}", [showCells(cells), gen])
  where (gen, cells) = pair

showCells(cells) =
  toList(cells)
  |> map(showRow)
  |> join("\n")

showRow(row) =
  format("|{}|", [map(showCell, toList(row)) |> join("")])

showCell(cell) =
  if cell == 1 then "*" else " "

PostScript

%!PS-Adobe-3.0
%%BoundingBox: 0 0 400 400

/size 400 def

realtime srand
/rand1 { rand 2147483647 div } def

/m { moveto } bind def
/l { rlineto} bind def
/drawboard {
        0 1 n 1 sub { /y exch def
        0 1 n 1 sub { /x exch def
                board x get y get 1 eq {
                        x c mul y c mul m
                        c 0 l 0 c l c neg 0 l
                        closepath fill
                } if
        } for } for
} def

/r1n { dup 0 lt { n add } if dup n ge { n sub } if } def
/neighbors { /y exch def /x exch def 0
        y 1 sub 1 y 1 add { r1n /y1 exch def
        x 1 sub 1 x 1 add { r1n /x1 exch def
                board x1 get y1 get add
        } for } for
        board x get y get sub
} def

/iter {
        /board
        [0 1 n 1 sub { /x exch def
        [0 1 n 1 sub { /y exch def
                x y neighbors
                board x get y get
                0 eq    { 3 eq {1}{0} ifelse }
                        { dup 2 eq exch 3 eq or {1}{0} ifelse } ifelse
        } for ]
        } for ] def
} def

/n 200 def
/initprob .15 def
/c size n div def
/board [ n {[ n { rand1 initprob le {1}{0} ifelse } repeat]} repeat ] def

1000 { drawboard showpage iter } repeat
%%EOF

Prolog

%----------------------------------------------------------------------%
% GAME OF LIFE                                                         %
%                                                                      %
% Adapt the prediacte grid_size according to the grid size of the      %
%   start pic.                                                         %
% Modify the number of generations.                                    %
% Run PROLOG and type '[gol].' to compile the source file.             %
% Create a subfolder <subfolder> where your gol.pl resides and place   %
%   your initial PBM '<filename>0.0000.pbm' inside <subfolder>.        %
% You need to adjust the number of zeros after <filename>. The         %
%   sequence of zeros after '0.' must be as long as the number of      %
%   generations. This is important to obtain a propper animation.      %
%   (Maybe someone knows a better solution for this)                   %
% Start PROLOG and run                                                 %
%                                                                      %
%                cellular('./<subloder>/<filename>').                  %
%                                                                      %
% Inside <subfolder> run the following shell command                   %
%                                                                      %
%         convert -delay 25 -loop 0 <filename>* <filename>.gif         %
%                                                                      %
%----------------------------------------------------------------------%

%----------------------------------------------------------------------%
% Special thanks to René Thiemann improving the runtime performance.   %
%----------------------------------------------------------------------%

% Size of the 2D grid
grid_size(300).
% Number of generations
generations(1000).

%----------------------------------------------------------------------%
% Main procedure: generate n generations of life and store each file.  %
%   cellular( +File path )                                             %
%----------------------------------------------------------------------%
cellular(I) :-
	grid_size(GS),
	string_concat(I,'0.0000.pbm',I1),
	read_pbm(I1,GS,M),
	cellular_(I,M,GS,1), !.

cellular_(I,M,GS,N) :-
	N1 is N+1,
	format(atom(N0),'~4d',N),
	string_concat(I,N0,I1),
	string_concat(I1,'.pbm',I2),
	step(M,M1),	
	write_pbm(M1,GS,I2), !,
	cellular_(I,M1,GS,N1).
cellular_(_,_,_,GE) :-
	generations(GE),!.
   
%----------------------------------------------------------------------%
% Apply the Game Of Life rule set to every cell.                       %
%   step( +OldMatrix, +NewMatrix )                                     %
%                                                                      %
%  ss | s | ... | s       ss ... step_ss                               %
% ----+---+-----+---      s  ... step_s                                %
%  ii | i | ... | i       ii ... step_ii                               %
% ----+---+-----+---      i  ... step_i                                %
%   : | : |  :  | :       ee ... step_ee                               %
% ----+---+-----+---      e  ... step_e                                %
%  ii | i | ... | i                                                    %
% ----+---+-----+---                                                   %
%  ee | e | ... | e                                                    %
%                                                                      %
%----------------------------------------------------------------------%
step([R1,R2|M],[H|T]) :- 
	step_ss(R1,R2,H), !,
	step_([R1,R2|M],T).

step_([R1,R2,R3|M],[H|T]) :-
	step_ii(R1,R2,R3,H),
	step_([R2,R3|M],T), !.
step_([R1,R2],[H]) :- 
	step_ee(R1,R2,H).

% Start case
step_ss([A1,A2|R1],[B1,B2|R2],[H|T]) :-
	rule([0,0,0],[0,A1,A2],[0,B1,B2],H),
	step_s([A1,A2|R1],[B1,B2|R2],T).
step_s([A1,A2,A3|R1],[B1,B2,B3|R2],[H|T]) :-	
	rule([0,0,0],[A1,A2,A3],[B1,B2,B3],H),
	step_s([A2,A3|R1],[B2,B3|R2],T).
step_s([A1,A2],[B1,B2],[H]) :-
	rule([0,0,0],[A1,A2,0],[B1,B2,0],H).

% Immediate case
step_ii([A1,A2|R1],[B1,B2|R2],[C1,C2|R3],[H|T]) :-
	rule([0,A1,A2],[0,B1,B2],[0,C1,C2],H),
	step_i([A1,A2|R1],[B1,B2|R2],[C1,C2|R3],T).
step_i([A1,A2,A3|R1],[B1,B2,B3|R2],[C1,C2,C3|R3],[H|T]) :-	
	rule([A1,A2,A3],[B1,B2,B3],[C1,C2,C3],H),
	step_i([A2,A3|R1],[B2,B3|R2],[C2,C3|R3],T).
step_i([A1,A2],[B1,B2],[C1,C2],[H]) :-
	rule([A1,A2,0],[B1,B2,0],[C1,C2,0],H).

% End case
step_ee([A1,A2|R1],[B1,B2|R2],[H|T]) :-
	rule([0,A1,A2],[0,B1,B2],[0,0,0],H),
	step_e([A1,A2|R1],[B1,B2|R2],T).
step_e([A1,A2,A3|R1],[B1,B2,B3|R2],[H|T]) :-	
	rule([A1,A2,A3],[B1,B2,B3],[0,0,0],H),
	step_e([A2,A3|R1],[B2,B3|R2],T).
step_e([A1,A2],[B1,B2],[H]) :-
	rule([A1,A2,0],[B1,B2,0],[0,0,0],H).

%----------------------------------------------------------------------%
% o Any dead cell with exactly three live neighbours becomes a live    %
%   cell, as if by reproduction.                                       %
% o Any other dead cell remains dead.                                  %
% o Any live cell with fewer than two live neighbours dies, as if      %
%   caused by under-population.                                        %
% o Any live cell with two or three live neighbours lives on to the    %
%   next generation.                                                   %
% o Any live cell with more than three live neighbours dies, as if by  %
%   overcrowding.                                                      %
%                                                                      %
% [Source: Wikipedia]                                                  %
%----------------------------------------------------------------------%
rule([A,B,C],[D,0,F],[G,H,I],1) :- A+B+C+D+F+G+H+I =:= 3.
rule([_,_,_],[_,0,_],[_,_,_],0).
rule([A,B,C],[D,1,F],[G,H,I],0) :- A+B+C+D+F+G+H+I < 2.
rule([A,B,C],[D,1,F],[G,H,I],1) :- A+B+C+D+F+G+H+I =:= 2.
rule([A,B,C],[D,1,F],[G,H,I],1) :- A+B+C+D+F+G+H+I =:= 3.
rule([A,B,C],[D,1,F],[G,H,I],0) :- A+B+C+D+F+G+H+I > 3.

%----------------------------------------------------------------------%
% Read a 2bit Protable Bitmap into a GS x GS 2-dimensional list.       %
%   read_pbm( +File path, +Grid size, -List 2D )                       %
%----------------------------------------------------------------------%
read_pbm(F,GS,M) :-
	open(F,read,S),
	skip(S,10),
	skip(S,10),
	get(S,C),
	read_file(S,C,L),
	nest(L,GS,M),
	close(S).

read_file(S,C,[CHR|T]) :-
	CHR is C-48,
	get(S,NC),
	read_file(S,NC,T).
read_file(_,-1,[]) :- !.

%----------------------------------------------------------------------%
% Morph simple list into a 2-dimensional one with size GS x GS         %
%   nest( ?List simple, ?Grid size, ?2D list )                         %
%----------------------------------------------------------------------%
nest(L,GS,[H|T]) :-
	length(H,GS),
	append(H,S,L),
	nest(S,GS,T).
nest(L,GS,[L]) :- 
	length(L,S),
	S =< GS, !.	
   
%----------------------------------------------------------------------%
% Write a GS x GS 2-dimensional list into a 2bit Protable Bitmap.      %
%   write_pbm( +List 2D, +Grid size, +File path )                      %
%----------------------------------------------------------------------%	
write_pbm(L,GS,F) :-
	open(F,write,S),
	write(S,'P1'), nl(S),
	write(S,GS), put(S,' '), write(S,GS), nl(S),
	write_file(S,L),
	close(S).

write_file(S,[H|T]) :-
	write_line(S,H), nl(S),
	write_file(S,T).
write_file(_,[]) :- !.

write_line(S,[H|T]) :-
	write(S,H), put(S,' '),
	write_line(S,T).
write_line(_,[]) :- !.

Sample output:


Processing

Inspired by Daniel Shiffman's book The Nature of Code (http://natureofcode.com)

boolean play = true;
int cellSize = 10;
int cols, rows;
int lastCell = 0;
int sample = 10;
// Game of life board
int[][] grid;

void setup() {
  size(800, 500);
  noStroke();
  // Calculate cols, rows and init array
  cols = width/cellSize;
  rows = height/cellSize;
  grid = new int[cols][rows];
  init(-1); // randomized start

  println("Press 'space' to start/stop");
  println("'e' to clear all cells");
  println("'b' demonstrate 'blinker'");
  println("'g' demonstrate glider");
  println("'r' to randomize grid");
  println("'+'  and '-' to change speed");

}

void draw() {
  background(0);

  for ( int i = 0; i < cols; i++) {
    for ( int j = 0; j < rows; j++) {
      if ((grid[i][j] == 1)) fill(255);
      else fill(0); 
      rect(i*cellSize, j*cellSize, cellSize, cellSize);
    }
  }
  if (play && frameCount%sample==0 && !mousePressed) {
    generate();
  }
}

void generate() {
  int[][] nextGrid = new int[cols][rows];
  for (int x = 0; x < cols; x++) {
    for (int y = 0; y < rows; y++) {
      int ngbs = countNgbs(x, y);
      // the classic Conway rules
      if      ((grid[x][y] == 1) && (ngbs <  2)) nextGrid[x][y] = 0; // solitude
      else if ((grid[x][y] == 1) && (ngbs >  3)) nextGrid[x][y] = 0; // crowded 
      else if ((grid[x][y] == 0) && (ngbs == 3)) nextGrid[x][y] = 1; // cell born
      else                              nextGrid[x][y] = grid[x][y]; // keep
    }
  }
  grid = nextGrid;
}

int countNgbs(int x, int y) {
  int ngbCount = 0;
  for (int i = -1; i <= 1; i++) {
    for (int j = -1; j <= 1; j++) {
      // 'united' borders
      ngbCount += grid[(x+i+cols)%cols][(y+j+rows)%rows];
    }
  }
  // cell taken out of count
  ngbCount -= grid[x][y];
  return ngbCount;
}

void init(int option) {
  int state;
  for (int x = 0; x < cols; x++) {
    for (int y = 0; y < rows; y++) {
      if (option == -1) {
        state = int(random(2));
      } else {
        state = option;
      }
      grid[x][y] = state;
    }
  }
}

void keyReleased() {
  if (key == 'r') {
    init(-1); // randomize grid
  }
  if (key == 'e') {
    init(0); // empty grid
  }
  if (key == 'g') {
    int glider[][] = {
      {0, 1, 0}, 
      {0, 0, 1}, 
      {1, 1, 1}};
    setNine(10, 10, glider);
  }
  if (key == 'b') {
    int blinker[][] = {
      {0, 1, 0}, 
      {0, 1, 0}, 
      {0, 1, 0}};
    setNine(10, 10, blinker);
  }
  if (key == ' ') {
    play = !play;
  }
  if (key == '+' || key == '=') {
    sample=max(sample-1, 1);
  }
  if (key == '-') {
    sample++;
  }
}

void setNine(int x, int y, int nine[][]) {
  for (int i = 0; i <= 2; i++) {
    for (int j = 0; j <= 2; j++) {
      grid[(x+i+cols)%cols][(y+j+rows)%rows] = nine[i][j];
    }
  }
}

void mousePressed() {
  paint();
}
void mouseDragged() {
  paint();
}

void paint() {
  int x = mouseX/cellSize;
  int y = mouseY/cellSize;
  int p = y*cols + x;
  if (p!=lastCell) {
    lastCell=p;
    int states[] = {1, 0};
    grid[x][y] = states[grid[x][y]]; // invert
  }
}

Processing Python mode

cell_size = 10
sample = 10 
play = False   # simulation is running
last_cell = 0

def setup():
    global grid, next_grid, rows, cols
    size(800, 500)

    rows = height / cell_size
    cols = width / cell_size
    grid = empty_grid()
    next_grid = empty_grid()
    randomize_grid()

    println("Press 'space' to start/stop")
    println("'e' to clear all cells")
    println("'b' demonstrate 'blinker'")
    println("'g' demonstrate glider")
    println("'r' to randomize grid")
    println("'+' and '-' to change speed")

def draw():
    background(0)
    for i in range(cols):
        x = i * cell_size
        for j in range(rows):
            y = j * cell_size
            current_state = grid[i][j]
            fill(255)
            noStroke()
            if current_state:
                rect(x, y, cell_size, cell_size)
            if play:
                ngbs_alive = calc_ngbs_alive(i, j)
                result = rule(current_state, ngbs_alive)
                next_grid[i][j] = result
                
    if play and frameCount % sample == 0 and not mousePressed:
        step()

def rule(current, ngbs):
    """ classic Conway's Game of Life rule """
    if ngbs < 2 or ngbs > 3:
        return 0  # dies / dead
    elif ngbs == 3:
        return 1  # born / alive
    else:
        return current  # stays the same (ngbs == 2)

def calc_ngbs_alive(i, j):
    NEIGHBOURS = ((-1, 00), (01, 00),  # a tuple describing the neighbourhood of a cell
                  (-1, -1), (00, -1),
                  (01, -1), (-1, 01),
                  (00, 01), (01, 01))
    alive = 0
    for iv, jv in NEIGHBOURS:
        alive += grid[(i + iv) % cols][(j + jv) % rows]
    return alive

def empty_grid():
    grid = []
    for _ in range(cols):
        grid.append([0] * rows)
    return grid

def randomize_grid():
    from random import choice
    for i in range(cols):
        for j in range(rows):
            grid[i][j] = choice((0, 1))

def step():
    global grid, next_grid
    grid = next_grid
    next_grid = empty_grid()

def keyReleased():
    global grid, play, sample
    if key == "e":
        grid = empty_grid()
    if key == "r":
        randomize_grid()
    if key == "g":
         grid[10][10:13] = [0, 1, 0]       
         grid[11][10:13] = [0, 0, 1]       
         grid[12][10:13] = [1, 1, 1]       
    if key == "b":
         grid[10][10:13] = [0, 1, 0]       
         grid[11][10:13] = [0, 1, 0]       
         grid[12][10:13] = [0, 1, 0]               
    if key == " ":
        play = not play 
    if  str(key) in '+=':
        sample = max(sample - 1, 1);
    if key == '-':
        sample += 1

def mousePressed():
    paint()
    
def mouseDragged():
    paint()

def paint():
    global last_cell
    i, j = mouseX // cell_size, mouseY // cell_size
    p = j * cols + i
    if p != last_cell:
        last_cell = p
        grid[i][j] = (1, 0)[grid[i][j]]

Python

Using defaultdict

This implementation uses defaultdict(int) to create dictionaries that return the result of calling int(), i.e. zero for any key not in the dictionary. This 'trick allows celltable to be initialized to just those keys with a value of 1.

Python allows many types other than strings and ints to be keys in a dictionary. The example uses a dictionary with keys that are a two entry tuple to represent the universe, which also returns a default value of zero. This simplifies the calculation N as out-of-bounds indexing of universe returns zero.

import random
from collections import defaultdict

printdead, printlive = '-#'
maxgenerations = 3
cellcount = 3,3
celltable = defaultdict(int, {
 (1, 2): 1,
 (1, 3): 1,
 (0, 3): 1,
 } ) # Only need to populate with the keys leading to life

##
## Start States
##
# blinker
u = universe = defaultdict(int)
u[(1,0)], u[(1,1)], u[(1,2)] = 1,1,1

## toad
#u = universe = defaultdict(int)
#u[(5,5)], u[(5,6)], u[(5,7)] = 1,1,1
#u[(6,6)], u[(6,7)], u[(6,8)] = 1,1,1

## glider
#u = universe = defaultdict(int)
#maxgenerations = 16
#u[(5,5)], u[(5,6)], u[(5,7)] = 1,1,1
#u[(6,5)] = 1
#u[(7,6)] = 1

## random start
#universe = defaultdict(int, 
#                       # array of random start values
#                       ( ((row, col), random.choice((0,1)))
#                         for col in range(cellcount[0])
#                         for row in range(cellcount[1])
#                       ) )  # returns 0 for out of bounds

for i in range(maxgenerations):
    print("\nGeneration %3i:" % ( i, ))
    for row in range(cellcount[1]):
        print("  ", ''.join(str(universe[(row,col)])
                            for col in range(cellcount[0])).replace(
                                '0', printdead).replace('1', printlive))
    nextgeneration = defaultdict(int)
    for row in range(cellcount[1]):
        for col in range(cellcount[0]):
            nextgeneration[(row,col)] = celltable[
                ( universe[(row,col)],
                  -universe[(row,col)] + sum(universe[(r,c)]
                                             for r in range(row-1,row+2)
                                             for c in range(col-1, col+2) )
                ) ]
    universe = nextgeneration
Output:
(sample)
Generation   0:
   ---
   ###
   ---

Generation   1:
   -#-
   -#-
   -#-

Generation   2:
   ---
   ###
   ---

Boardless approach

A version using the boardless approach. A world is represented as a set of (x, y) coordinates of all the alive cells.

from collections import Counter

def life(world, N):
    "Play Conway's game of life for N generations from initial world."
    for g in range(N+1):
        display(world, g)
        counts = Counter(n for c in world for n in offset(neighboring_cells, c))
        world = {c for c in counts 
                if counts[c] == 3 or (counts[c] == 2 and c in world)}

neighboring_cells = [(-1, -1), (-1, 0), (-1, 1), 
                     ( 0, -1),          ( 0, 1), 
                     ( 1, -1), ( 1, 0), ( 1, 1)]

def offset(cells, delta):
    "Slide/offset all the cells by delta, a (dx, dy) vector."
    (dx, dy) = delta
    return {(x+dx, y+dy) for (x, y) in cells}

def display(world, g):
    "Display the world as a grid of characters."
    print('          GENERATION {}:'.format(g))
    Xs, Ys = zip(*world)
    Xrange = range(min(Xs), max(Xs)+1)
    for y in range(min(Ys), max(Ys)+1):
        print(''.join('#' if (x, y) in world else '.'
                      for x in Xrange))

blinker = {(1, 0), (1, 1), (1, 2)}
block   = {(0, 0), (1, 1), (0, 1), (1, 0)}
toad    = {(1, 2), (0, 1), (0, 0), (0, 2), (1, 3), (1, 1)}
glider  = {(0, 1), (1, 0), (0, 0), (0, 2), (2, 1)}
world   = (block | offset(blinker, (5, 2)) | offset(glider, (15, 5)) | offset(toad, (25, 5))
           | {(18, 2), (19, 2), (20, 2), (21, 2)} | offset(block, (35, 7)))


life(world, 5)
Output:
          GENERATION 0:
##...................................
##...................................
......#...........####...............
......#..............................
......#..............................
...............##........#...........
...............#.#.......##..........
...............#.........##........##
..........................#........##
          GENERATION 1:
##...................................
##.................##................
...................##................
.....###...........##................
.....................................
...............##........##..........
..............##........#............
................#..........#.......##
.........................##........##
          GENERATION 2:
##...................................
##.................##................
......#...........#..#...............
......#............##................
......#..............................
..............###........#...........
..............#..........##..........
...............#.........##........##
..........................#........##
          GENERATION 3:
##...................................
##.................##................
..................#..#...............
.....###...........##................
...............#.....................
..............##.........##..........
..............#.#.......#............
...........................#.......##
.........................##........##
          GENERATION 4:
##...................................
##.................##................
......#...........#..#...............
......#............##................
......#.......##.....................
..............#.#........#...........
..............#..........##..........
.........................##........##
..........................#........##
          GENERATION 5:
##...................................
##.................##................
..................#..#...............
.....###...........##................
..............##.....................
.............##..........##..........
...............#........#............
...........................#.......##
.........................##........##

Using an array to define the world

import numpy as np
from pandas import DataFrame
import matplotlib.pyplot as plt
#import time

def conway_life(len=10, wid=10, gen=5):
     
    curr_gen = DataFrame(np.random.randint(0, 2, (len+2, wid+2)),
                         index = range(len+2), 
                         columns = range(wid+2))
    curr_gen[0] = 0
    curr_gen[wid+1] = 0
    curr_gen[0: 1] = 0
    curr_gen[len+1: len+2] = 0    
    
    for i in range(gen):
        
        fig, ax = plt.subplots()
        draw = curr_gen[1:len+1].drop([0, wid+1], axis=1)
        # 画图
        
        image = draw
        ax.imshow(image, cmap=plt.cm.cool, interpolation='nearest')
        ax.set_title("Conway's game of life.")
        
        # Move left and bottom spines outward by 10 points
        ax.spines['left'].set_position(('outward', 10))
        ax.spines['bottom'].set_position(('outward', 10))
        # Hide the right and top spines
        ax.spines['right'].set_visible(False)
        ax.spines['top'].set_visible(False)
        # Only show ticks on the left and bottom spines
        ax.yaxis.set_ticks_position('left')
        ax.xaxis.set_ticks_position('bottom')

        plt.show()
        # time.sleep(1)         
        
        
        # 初始化空表
        next_gen = DataFrame(np.random.randint(0, 1, (len+2, wid+2)),
                             index = range(len+2), 
                             columns = range(wid+2))
        
        
        # 生成下一代
        for x in range(1, wid+1):
            for y in range(1, len+1):
                env = (curr_gen[x-1][y-1] + curr_gen[x][y-1] + 
                       curr_gen[x+1][y-1]+ curr_gen[x-1][y] + 
                       curr_gen[x+1][y] + curr_gen[x-1][y+1] + 
                       curr_gen[x][y+1] + curr_gen[x+1][y+1])
            
                if (not curr_gen[x][y] and env == 3):
                    next_gen[x][y] = 1
                if (curr_gen[x][y] and env in (2, 3)):
                    next_gen[x][y] = 1
                
        curr_gen = next_gen 
         

conway_life()

Quackery

Uses a Tortoise and Hare algorithm to detect when Life becomes static or repetitive. The tortoise version is displayed, along with five victory laps of the cyclic part once a cycle is detected.

  [ $ "turtleduck.qky" loadfile ]  now!

  [ $ \
import time
now = time.time()
sleepy_time = 5/7-(now%(5/7))
time.sleep(sleepy_time)
\ python ]                                 is wait        (     -->   )

  [ dup 1
    [ 2dup > while + 1 >> 2dup / again ]
    drop nip ]                             is sqrt        (   n --> n )

  [ stack ]                                is width       (     --> s )

  [ tuck witheach
      [ over i^ peek + rot i^ poke swap ]
    drop ]                                 is add         ( [ [ --> [ )

  [ 1 split swap join ]                    is left        (   [ --> [ )

  [ -1 split swap join ]                   is right       (   [ --> [ )

  [ width share split swap join ]          is up          (   [ --> [ )

  [ width share negate split swap join ]   is down        (   [ --> [ )

  [ left dup up tuck add
    swap right tuck add
    swap right tuck add
    swap down tuck add
    swap down tuck add
    swap left tuck add
    swap left add ]                        is neighbours  (   [ --> [ )

  [ [] swap
    width share times
      [ width share split
        dip [ 0 swap 0 join join join ] ]
    drop
    2 width tally
    0 width share of tuck join join ]      is makeborder  (   [ --> [ )

  [ dup size times
      [ 0 swap i^ poke
        0 swap i^ width share + 1 - poke
        width share step ]
     width share times
       [ 0 swap i^ poke
         0 swap i^ 1 + negate poke ] ]     is clearborder (   [ --> [ )

  [ dup neighbours
    witheach
      [ over i^ peek iff
          [ 1 | 3 != if
              [ 0 swap i^ poke ] ]
          done
        3 = if [ 1 swap i^ poke ] ]
    clearborder ]                          is nextgen     (   [ --> [ )

  [ 6 random
    [ table
      [ 200 200 255 ] [ 200 255 200 ]
      [ 255 200 200 ] [ 200 255 255 ]
      [ 255 200 255 ] [ 255 255 200 ] ]
    fill
      [ 4 times
          [ 20 1 walk -1 4 turn ] ] ]      is block       (     -->   )


  [ clear
    width share 10 *
    dup negate
    4 - 1 fly
    -1 4 turn
    16 - 1 fly
    1 4 turn
    20 1 fly
    ' [ 200 200 200 ] colour
    4 times
      [ width share 2 - 20 * 1 walk
        1 4 turn ]
    -20 1 fly
    ' [ 63 63 63 ] colour
    width share times
      [ width share split
        swap witheach
          [ if block
            20 1 fly ]
        width share -20 * 1 fly
        1 4 turn
        20 1 fly
        -1 4 turn ]
    drop wait frame ]                      is draw        (   [ -->   )

  [ turtle 0 frames 2 wide
    dup size sqrt width put
    makeborder
    dup
    [ dup draw nextgen
      dip [ nextgen nextgen ]
      2dup = until ]
    5 times
      [ dup draw nextgen 2dup = until ]
    2drop width release ]                  is life        (   [ -->   )

  ' [ 0 0 0
      1 1 1
      0 0 0 ] life                                 ( task requirement )

  ' [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
      0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
      0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
      0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
      0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
      0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
      0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
      0 0 1 1 1 1 1 0 1 1 1 1 1 0 0
      0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
      0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
      0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
      0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
      0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
      0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
      0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ] life         ( more interesting )

  randomise
  [ []
    1089 times
      [ 2 random join ]
    life
    again ]                                        ( ... runs forever )
Output:

( task requirement )

File:Quackery Life Task.png

( more interesting )

File:Quackery Life.gif

( ... runs forever )

https://youtu.be/U5owgEpxzwg

(The code runs forever, not the video. The accompanying music is also generative, and comes from the Kolakoski Sequence.)

R

# Generates a new board - either a random one, sample blinker or gliders, or user specified.
gen.board <- function(type="random", nrow=3, ncol=3, seeds=NULL)
{
    if(type=="random")
    {
       return(matrix(runif(nrow*ncol) > 0.5, nrow=nrow, ncol=ncol))
    } else if(type=="blinker")
    {
       seeds <- list(c(2,1),c(2,2),c(2,3))
    } else if(type=="glider")
    {
       seeds <- list(c(1,2),c(2,3),c(3,1), c(3,2), c(3,3))
    }
    board <- matrix(FALSE, nrow=nrow, ncol=ncol) 
    for(k in seq_along(seeds))
    {
      board[seeds[[k]][1],seeds[[k]][2]] <- TRUE
    }
    board
}

# Returns the number of living neighbours to a location
count.neighbours <- function(x,i,j) 
{   
   sum(x[max(1,i-1):min(nrow(x),i+1),max(1,j-1):min(ncol(x),j+1)]) - x[i,j]
}

# Implements the rulebase
determine.new.state <- function(board, i, j)
{
   N <- count.neighbours(board,i,j)
   (N == 3 || (N ==2 && board[i,j]))
}

# Generates the next interation of the board from the existing one
evolve <- function(board)
{ 
   newboard <- board
   for(i in seq_len(nrow(board)))
   {
      for(j in seq_len(ncol(board)))
      {
         newboard[i,j] <- determine.new.state(board,i,j)         
      }   
   }
   newboard
}

# Plays the game.  By default, the board is shown in a plot window, though output to the console if possible.
game.of.life <- function(board, nsteps=50, timebetweensteps=0.25, graphicaloutput=TRUE)
{
   if(!require(lattice)) stop("lattice package could not be loaded")   
   nr <- nrow(board)
   
   for(i in seq_len(nsteps))
   {
      if(graphicaloutput) 
      {
         print(levelplot(t(board[nr:1,]), colorkey=FALSE)) 
      } else print(board)  
       
      Sys.sleep(timebetweensteps)
      
      newboard <- evolve(board)
      
      if(all(newboard==board))
      {
         message("board is static")
         break
      } else if(sum(newboard) < 1)
      {
         message("everything is dead")
         break
      } else board <- newboard
   }   
   invisible(board)
}

# Example usage
game.of.life(gen.board("blinker"))
game.of.life(gen.board("glider", 18, 20))
game.of.life(gen.board(, 50, 50))

Racket

#lang racket
(require 2htdp/image 2htdp/universe)

;;;
;;; Grid object
;;;

(define (make-empty-grid m n)
  (build-vector m (lambda (y) (make-vector n 0))))

(define rows vector-length)

(define (cols grid)
  (vector-length (vector-ref grid 0)))

(define (make-grid m n living-cells)
  (let loop ([grid (make-empty-grid m n)]
             [cells living-cells])
    (if (empty? cells)
        grid
        (loop (2d-set! grid (caar cells) (cadar cells) 1) (cdr cells)))))

(define (2d-ref grid i j)
  (cond [(< i 0) 0]
        [(< j 0) 0]
        [(>= i (rows grid)) 0]
        [(>= j (cols grid)) 0]
        [else (vector-ref (vector-ref grid i) j)]))

(define (2d-refs grid indices)
  (map (lambda (ind) (2d-ref grid (car ind) (cadr ind))) indices))

(define (2d-set! grid i j val)
  (vector-set! (vector-ref grid i) j val)
  grid)

;;; cartesian product of 2 lists
(define (cart l1 l2)
  (if (empty? l1)
      '()
      (append (let loop ([n (car l1)] [l l2])
                (if (empty? l) '() (cons (list n (car l)) (loop n (cdr l)))))
              (cart (cdr l1) l2))))

;;; Count living cells in the neighbourhood
(define (n-count grid i j)
  (- (apply + (2d-refs grid (cart (list (- i 1) i (+ i 1))
                                  (list (- j 1) j (+ j 1)))))
     (2d-ref grid i j)))

;;;
;;; Rules and updates of the grid
;;;

;;; rules are stored in a 2d array: r_i,j = new state of a cell
;;; in state i with j neighboors
(define conway-rules
  (list->vector (list (list->vector '(0 0 0 1 0 0 0 0 0))
                      (list->vector '(0 0 1 1 0 0 0 0 0)))))

(define (next-state rules grid i j)
  (let ([current (2d-ref grid i j)]
        [N (n-count grid i j)])
    (2d-ref rules current N)))

(define (next-grid rules grid)
  (let ([new-grid (make-empty-grid (rows grid) (cols grid))])
    (let loop ([i 0] [j 0])
      (if (>= i (rows grid))
          new-grid
          (if (>= j (cols grid))
              (loop (+ i 1) 0)
              (begin (2d-set! new-grid i j (next-state rules grid i j))
                     (loop i (+ j 1))))))))

(define (next-grid! rules grid)
  (let ([new-grid (next-grid rules grid)])
    (let loop ((i 0))
      (if (< i (rows grid))
        (begin (vector-set! grid i (vector-ref new-grid i))
               (loop (+ i 1)))
        grid))))

;;;
;;; Image / Animation
;;;

(define (grid->image grid)
  (let ([m (rows grid)] [n (cols grid)] [size 5])
    (let loop ([img (rectangle (* m size) (* n size) "solid" "white")]
               [i 0] [j 0])
      (if (>= i (rows grid))
          img
          (if (>= j (cols grid))
              (loop img (+ i 1) 0)
              (if (= (2d-ref grid i j) 1)
                  (loop (underlay/xy img (* i (+ 1 size)) (* j (+ 1 size))
                                     (square (- size 2) "solid" "black"))
                        i (+ j 1))
                  (loop img i (+ j 1))))))))



(define (game-of-life grid refresh_time)
  (animate (lambda (n)
             (if (= (modulo n refresh_time) 0)
                 (grid->image (next-grid! conway-rules grid))
                 (grid->image grid)))))

;;;
;;; Examples
;;;

(define (blinker)
  (make-grid 3 3 '((0 1) (1 1) (2 1))))

(define (thunder)
  (make-grid 70 50 '((30 19) (30 20) (30 21) (29 17) (30 17) (31 17))))

(define (cross)
  (let loop ([i 0] [l '()])
    (if (>= i 80)
        (make-grid 80 80 l)
        (loop (+ i 1) (cons (list i i) (cons (list (- 79 i) i) l))))))

;;; To run examples:
;;; (game-of-life (blinker) 30)
;;; (game-of-life (thunder) 2)
;;; (game-of-life (cross) 2)

Output for an 80x80 cross:

Raku

(formerly Perl 6)

class Automaton {
    subset World of Str where {
        .lines>>.chars.unique == 1 and m/^^<[.#\n]>+$$/
    }
    has Int ($.width, $.height);
    has @.a;

    multi method new (World $s) {
        self.new:
            :width(.pick.chars), :height(.elems),
            :a( .map: { [ .comb ] } )
                given $s.lines.cache;
    }

    method gist { join "\n", map { .join }, @!a }

    method C (Int $r, Int $c --> Bool) {
        @!a[$r % $!height][$c % $!width] eq '#';
    }
    method N (Int $r, Int $c --> Int) {
        +grep ?*, map { self.C: |@$_ },
            [ $r - 1, $c - 1], [ $r - 1, $c ], [ $r - 1, $c + 1],
            [ $r    , $c - 1],                 [ $r    , $c + 1],
            [ $r + 1, $c - 1], [ $r + 1, $c ], [ $r + 1, $c + 1];
    }

    method succ {
        self.new: :$!width, :$!height,
            :a(
                gather for ^$.height -> $r {
                    take [
                        gather for ^$.width -> $c {
                            take
                            (self.C($r, $c) == 1 && self.N($r, $c) == 2|3)
                                || (self.C($r, $c) == 0 && self.N($r, $c) == 3)
                            ?? '#' !! '.'
                        }
                    ]
                }
            )
    }
}

my Automaton $glider .= new: q:to/EOF/;
    ............
    ............
    ............
    .......###..
    .###...#....
    ........#...
    ............
    EOF


for ^10 {
    say $glider++;
    say '--';
}

Red

Red [
    Purpose: "Conway's Game of Life"
    Author: "Joe Smith"
]

neigh: [[0 1] [0 -1] [1 0] [-1 0] [1 1] [1 -1] [-1 1] [-1 -1]]
conway: function [petri] [
	new-petri: copy/deep petri
	repeat row length? petri [
		repeat col length? petri [
			live-neigh: 0
			foreach cell neigh [  
				try [
					if petri/(:row + cell/1)/(:col + cell/2) = 1 [live-neigh: live-neigh + 1]	
				]
			] 
			switch petri/:row/:col [
				1	[if any [live-neigh < 2 live-neigh > 3] 
						[new-petri/:row/:col: 0]
					]	
				0	[if live-neigh = 3 [new-petri/:row/:col: 1]]
	]]]
	clear insert petri new-petri
]

*3-3: [
	[0 1 0]
	[0 1 0]
	[0 1 0]
]

*8-8: [
	[0 0 1 0 0 0 0 0]
	[0 0 0 1 0 0 0 0]
	[0 1 1 1 0 0 0 0]
	[0 0 0 0 0 0 0 0]
	[0 0 0 0 0 0 0 0]
	[0 0 0 0 0 0 0 0]
	[0 0 0 0 0 0 0 0]
	[0 0 0 0 0 0 0 0]
]

display: function [table] [
	foreach row table [
		print replace/all (replace/all to-string row "0" "_") "1" "#"	
	] print ""
]

loop 5 [
	display *3-3
	conway *3-3 
]
loop 23 [
	display *8-8
	conway *8-8
]
Output:
 
_#_
_#_
_#_

___
###
___

_#_
_#_
_#_

___
###
___

_#_
_#_
_#_

__#_____
___#____
_###____
________
________
________
________
________

________
_#_#____
__##____
__#_____
________
________
________
________

________
___#____
_#_#____
__##____
________
________
________
________

________
__#_____
___##___
__##____
________
________
________
________

________
___#____
____#___
__###___
________
________
________
________

________
________
__#_#___
___##___
___#____
________
________
________

________
________
____#___
__#_#___
___##___
________
________
________

________
________
___#____
____##__
___##___
________
________
________

________
________
____#___
_____#__
___###__
________
________
________

________
________
________
___#_#__
____##__
____#___
________
________

________
________
________
_____#__
___#_#__
____##__
________
________

________
________
________
____#___
_____##_
____##__
________
________

________
________
________
_____#__
______#_
____###_
________
________

________
________
________
________
____#_#_
_____##_
_____#__
________

________
________
________
________
______#_
____#_#_
_____##_
________

________
________
________
________
_____#__
______##
_____##_
________

________
________
________
________
______#_
_______#
_____###
________

________
________
________
________
________
_____#_#
______##
______#_

________
________
________
________
________
_______#
_____#_#
______##

________
________
________
________
________
______#_
_______#
______##

________
________
________
________
________
________
_______#
______##

________
________
________
________
________
________
______##
______##

________
________
________
________
________
________
______##
______##

Retro

:w/l [ $. eq? [ #0 ] [ #1 ] choose , ] s:for-each ;

'World d:create
  '.................... w/l
  '.................... w/l
  '.................... w/l
  '..ooo............... w/l
  '....o............... w/l
  '...o................ w/l
  '.................... w/l
  '.................... w/l
  '.................... w/l
  '.................... w/l
  '.................... w/l
  '....ooo............. w/l
  '.................... w/l
  '.................... w/l
  '.................... w/l
  '........ooo......... w/l
  '.......ooo.......... w/l
  '.................... w/l
  '.................... w/l
  '.................... w/l

'Next d:create
  #20 #20 * allot

{{
  'Surrounding var
  :get (rc-v)
    dup-pair [ #0 #19 n:between? 
] bi@ and
    [ &World + [ #20 * ] dip + fetch ] [ drop-pair #0 ] choose ;
  :neighbor?  (rc-) get &Surrounding v:inc-by ;
  :NW (rc-rc) dup-pair [ n:dec ] bi@       neighbor? ;
  :NN (rc-rc) dup-pair [ n:dec ] dip       neighbor? ;
  :NE (rc-rc) dup-pair [ n:dec ] dip n:inc neighbor? ;  
  :WW (rc-rc) dup-pair   n:dec             neighbor? ;
  :EE (rc-rc) dup-pair   n:inc             neighbor? ;
  :SW (rc-rc) dup-pair [ n:inc ] dip n:dec neighbor? ;
  :SS (rc-rc) dup-pair [ n:inc ] dip       neighbor? ;
  :SE (rc-rc) dup-pair [ n:inc ] bi@       neighbor? ;
  :count (rc-rcn)
    #0 !Surrounding NW NN NE
                    WW    EE
                    SW SS SE @Surrounding ;
  :alive (rc-n)
    count #2 #3 n:between? [ #1 ] if; #0 ;
  :dead (rc-n)
    count #3 eq? [ #1 ] if; #0 ;
  :new-state (rc-n)
    dup-pair get #1 eq? &alive &dead choose ;
  :set   (nrc-)  &Next + [ #20 * ] dip + store ;
  :cols (r-)
    #20 [ I over swap new-state rot rot set ] times<with-index> drop ;
  :output (n-) n:-zero? [ $o ] [ $. ] choose c:put sp ;
---reveal---
  :display (-)
    nl &World #20 [ #20 [ fetch-next output ] times nl ] times drop ;
  :gen (-)
    #20 [ I cols ] times<with-index> &Next &World #20 #20 * copy ;
}}
 
{{
  :divide #20 [ $- c:put ] times sp 'Gen:_ s:put dup n:put nl ;
---reveal---
  :gens (n-)  #0 swap [ display divide  n:inc gen ] times drop ;
}}
 
#12 gens

REXX

version 1

This version has been trimmed down from the original REXX program, otherwise the size of the program (with all its options and optional formatting)
would probably be on the large side for general viewing,   and maybe a wee bit complex to demonstrate how to program for this task.

/*REXX program runs and displays the Conway's game of life, it stops after  N  repeats. */
signal on halt                                   /*handle a  cell growth  interruptus.  */
parse arg peeps  '(' rows  cols  empty  life!  clearScreen  repeats  generations .
       rows =        p(rows               3)     /*the maximum number of cell  rows.    */
       cols =        p(cols               3)     /* "     "       "    "   "  columns.  */
        emp = pickChar(empty        'blank')     /*an empty cell character  (glyph).    */
   clearScr =        p(clearScreen        0)     /* "1"   indicates to clear the screen.*/
      life! = pickChar(life!            '☼')     /*the gylph kinda looks like an amoeba.*/
       reps =        p(repeats            2)     /*stop pgm  if there are  two  repeats.*/
generations =        p(generations      100)     /*the number of  generations  allowed. */
sw= max(linesize() - 1,  cols)                   /*usable screen width for the display. */
#reps= 0;        $.= emp                         /*the universe is new,  ··· and barren.*/
gens=abs(generations)                            /*used for a  programming  convenience.*/
x= space(peeps); upper x                         /*elide superfluous spaces; uppercase. */
if x==''         then x= "BLINKER"               /*if nothing specified,  use  BLINKER. */
if x=='BLINKER'  then x= "2,1 2,2 2,3"
if x=='OCTAGON'  then x= "1,5 1,6 2,4 2,7 3,3 3,8 4,2 4,9 5,2 5,9 6,3 6,8 7,4 7,7 8,5 8,6"
call assign.                                     /*assign the initial state of all cells*/
call showCells                                   /*show the  initial state of the cells.*/
     do life=1  for gens;      call assign@      /*construct  next  generation of cells.*/
     if generations>0 | life==gens  then call showCells    /*should cells be displayed? */
     end   /*life*/                              /* [↑]  cell colony grows, lives, dies.*/
exit                                             /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
showCells: if clearScr  then 'CLS'               /*  ◄───  change 'command' for your OS.*/
           call showRows                         /*show the rows in the proper order.   */
           say right(copies('▒', sw)  life, sw)  /*show a fence between the generations.*/
           if _==''  then exit                   /*if there's no life, then stop the run*/
           if !._    then #reps= #reps + 1       /*we detected a repeated cell pattern. */
           !._= 1                                /*existence  state and compare  later. */
           if reps\==0 & #reps<=reps then return /*so far, so good,   regarding repeats.*/
           say
           say center('"Life" repeated itself' reps "times, simulation has ended.",sw,'▒')
           exit                                  /*stick a fork in it,  we're all done. */
/*───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────*/
$:         parse arg _row,_col;                    return $._row._col==life!
assign$:   do r=1  for rows;   do c=1  for cols;   $.r.c= @.r.c;                                    end;    end;       return
assign.:   do while x\==''; parse var x r "," c x; $.r.c=life!; rows=max(rows,r); cols=max(cols,c); end; life=0; !.=0; return
assign?:   ?=$.r.c; n=neighbors(); if ?==emp then do;if n==3 then ?=life!; end; else if n<2 | n>3 then ?=emp; @.r.c=?; return
assign@:   @.=emp;      do r=1  for rows;  do c=1  for cols;  call assign?;  end;  end;            call assign$;       return
halt:      say;         say "REXX program  (Conway's Life)  halted.";    say;      exit 0
neighbors: return $(r-1,c-1)  +  $(r-1,c)  +  $(r-1,c+1)  +  $(r,c-1)  +  $(r,c+1)  +  $(r+1,c-1)  +  $(r+1,c)  +  $(r+1,c+1)
p:         return word(arg(1), 1)
pickChar:  _=p(arg(1)); arg u .; if u=='BLANK' then _=" "; L=length(_); if L==3 then _=d2c(_); if L==2 then _=x2c(_);  return _
showRows:  _=; do r=rows by -1 for rows; z=; do c=1 for cols; z=z||$.r.c; end; z=strip(z,'T',emp); say z; _=_||z; end; return

This REXX program makes use of   linesize   REXX program (or BIF)   which is used to determine the screen width (or linesize) of the terminal (console);   not all REXXes have this BIF.

The   LINESIZE.REX   REXX program is included here   ──►   LINESIZE.REX.

output   when using the default inputs:
☼☼☼

▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒ 0
 ☼
 ☼
 ☼
▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒ 1

☼☼☼

▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒ 2
 ☼
 ☼
 ☼
▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒ 3

☼☼☼

▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒ 4

▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒ "Life" repeated itself 2 times, simulation has ended. ▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒

version 2

/* REXX ---------------------------------------------------------------
* 02.08.2014 Walter Pachl
* Input is a file containing the initial pattern
* The compute area is extended when needed
*   (cells are born outside the current compute area)
* The program stops when the picture shown is the same as the first
*   or equal to the previous one
*--------------------------------------------------------------------*/
Parse Arg f
If f='' Then f='bipole'
fid=f'.in'
oid=f'.txt'; 'erase' oid
debug=0
If debug Then Do
  dbg=f'.xxx'; 'erase' dbg
  End
ml=0
l.=''
Do ri=3 By 1 While lines(fid)>0
  l.ri='  'linein(fid)
  ml=max(ml,length(strip(l.ri,'T')))
  End
ml=ml+2
ri=ri+1
yy=ri
If debug Then
  say 'ml='ml 'yy='yy
yb=1
a.=' '
b.=' '
m.=''
x.=''
Parse Value 1 ml 1 yy With xmi xma ymi yma
Parse Value '999 0' With xmin xmax
Parse Value '999 0' With ymin ymax

Do y=1 To yy
  z=yy-y-1
  l=l.z
  Do x=1 By 1 While l<>''
    Parse Var l c +1 l
    If c='*' Then Do
      a.x.z='*'
      End
    End
  End
Call show
Do step=1 To 60
  Call store
  If step>1 & is_equal(step,1) Then Leave
  If step>1 & is_equal(step,step-1) Then Leave
    Call show_neighbors
  Do y=yma To ymi By -1
    ol=format(x,2)' '
    Do x=xmi To xma
      neighbors=neighbors(x,y)
      If a.x.y=' ' Then Do             /* dead cell                  */
        If neighbors=3 Then Do
          b.x.y='*'                    /*  gets life                 */
          mmo=xmi xma ymi yma
          xmi=min(xmi,x-1)
          xma=max(xma,x+1)
          ymi=min(ymi,y-1)
          yma=max(yma,y+1)
          mm=xmi xma ymi yma
          If mm<>mmo Then
            Call debug mmo '->' mm
          End
        Else                           /* life cell                  */
          b.x.y=' '                    /*  remains dead              */

        End
      Else Do                          /* life cell                  */
        If neighbors=2 |,
           neighbors=3 Then b.x.y='*'  /*  remains life              */
                       Else b.x.y=' '  /*  dies                      */
        End
      End
    End
  /* b. is the new state and is now copied to a.                     */
  Do y=yma To ymi By -1
    Do x=xmi To xma
      a.x.y=b.x.y
      End
    End
  End
/* Output name and all states                                        */
Call lineout oid,' 'f
st=' +'                                /* top and bottom border      */
sb=' +'                                /* top and bottom border      */
Do s=1 To step
  st=st||'-'right(s,2,'-')||copies('-',xmax-xmin)'+'
  sb=sb||copies('-',xmax-xmin+3)'+'
  End
Call lineout oid,st                    /* top border                 */
Do y=ymin To ymax
  ol=''
  Do s=1 To step
    ol=ol '|' substr(m.s.y,xmin,xmax-xmin+1)
    End
  Call lineout oid,ol '|'
  End
Call lineout oid,sb                    /* bottom border              */
Call lineout oid
'type' oid
If debug Then Do
  Say 'original area' 1 ml '/' 1 yy
  Say 'compute area ' xmi xma '/' ymi yma
  End
Exit

set: Parse Arg x,y
     a.x.y='*'
     Return

neighbors: Procedure Expose a. debug
  Parse Arg x,y
  neighbors=0
  do xa=x-1 to x+1
    do ya=y-1 to y+1
      If xa<>x | ya<>y then
        If a.xa.ya='*' Then
          neighbors=neighbors+1
      End
    End
  Return neighbors

store:
/* store current state (a.) in lines m.step.*                        */
Do y=yy To 1 By -1
  ol=''
  Do x=1 To ml
    z=a.x.y
    ol=ol||z
    End
  x.step.y=ol
  If ol<>'' then Do
    ymin=min(ymin,y)
    ymax=max(ymax,y)
    p=pos('*',ol)
    q=length(strip(ol,'T'))
    If p>0 Then
      xmin=min(xmin,p)
    xmax=max(xmax,q)
    End
  m.step.y=ol
  Call debug '====>' right(step,2) y ol  xmin xmax
  End
Return

is_equal:
/* test ist state a.b is equal to state a.a                          */
  Parse Arg a,b
  Do y=yy To 1 By -1
    If x.b.y<>x.a.y Then
      Return 0
    End
  Return 1

show: Procedure Expose dbg a. yy ml debug
Do y=1 To yy
  ol='>'
  Do x=1 To ml
    ol=ol||a.x.y
    End
  Call debug ol
  End
Return

show_neighbors: Procedure Expose a. xmi xma ymi yma dbg debug
  Do y=yma To ymi By -1
    ol=format(y,2)' '

    Do x=xmi To xma
      ol=ol||neighbors(x,y)
      End
    Call debug ol
    End
  Return

debug:
  If debug Then
    Return lineout(dbg,arg(1))
  Else
    Return
Output:
 blinker
+--1--+--2--+--3--+
|     |  *  |     |
| *** |  *  | *** |
|     |  *  |     |
+-----+-----+-----+ 
oktagon
*--1-------*--2-------*--3-------*--4-------*--5-------*--6-------*
|    **    |    **    |   *  *   |          |          |    **    |
|   *  *   |   ****   |   *  *   |   *  *   |   ****   |   *  *   |
|  *    *  |  *    *  | ** ** ** |  * ** *  |  * ** *  |  *    *  |
| *      * | **    ** |   *  *   |   *  *   |  **  **  | *      * |
| *      * | **    ** |   *  *   |   *  *   |  **  **  | *      * |
|  *    *  |  *    *  | ** ** ** |  * ** *  |  * ** *  |  *    *  |
|   *  *   |   ****   |   *  *   |   *  *   |   ****   |   *  *   |
|    **    |    **    |   *  *   |          |          |    **    |
*----------*----------*----------*----------*----------*----------*

Ruby

def game_of_life(name, size, generations, initial_life=nil)
  board = new_board size
  seed board, size, initial_life
  print_board board, name, 0
  reason = generations.times do |gen|
    new = evolve board, size
    print_board new, name, gen+1
    break :all_dead if barren? new, size
    break :static   if board == new
    board = new
  end
  if    reason == :all_dead then puts "no more life."
  elsif reason == :static   then puts "no movement"
  else                           puts "specified lifetime ended"
  end
  puts
end

def new_board(n)
  Array.new(n) {Array.new(n, 0)}
end

def seed(board, n, points=nil)
  if points.nil?
    # randomly seed board
    indices = []
    n.times {|x| n.times {|y| indices << [x,y] }}
    indices.shuffle[0,10].each {|x,y| board[y][x] = 1}
  else
    points.each {|x, y| board[y][x] = 1}
  end
end

def evolve(board, n)
  new = new_board n
  n.times {|i| n.times {|j| new[i][j] = fate board, i, j, n}}
  new
end

def fate(board, i, j, n)
  i1 = [0, i-1].max; i2 = [i+1, n-1].min
  j1 = [0, j-1].max; j2 = [j+1, n-1].min
  sum = 0
  for ii in (i1..i2)
    for jj in (j1..j2)
      sum += board[ii][jj] if not (ii == i and jj == j)
    end
  end
  (sum == 3 or (sum == 2 and board[i][j] == 1)) ? 1 : 0
end

def barren?(board, n)
  n.times {|i| n.times {|j| return false if board[i][j] == 1}}
  true
end

def print_board(m, name, generation)
  puts "#{name}: generation #{generation}"
  m.each {|row| row.each {|val| print "#{val == 1 ? '#' : '.'} "}; puts}
end

game_of_life "blinker", 3, 2, [[1,0],[1,1],[1,2]]
game_of_life "glider", 4, 4, [[1,0],[2,1],[0,2],[1,2],[2,2]]
game_of_life "random", 5, 10
Output:
blinker: generation 0
. # . 
. # . 
. # . 
blinker: generation 1
. . . 
# # # 
. . . 
blinker: generation 2
. # . 
. # . 
. # . 
specified lifetime ended

glider: generation 0
. # . . 
. . # . 
# # # . 
. . . . 
glider: generation 1
. . . . 
# . # . 
. # # . 
. # . . 
glider: generation 2
. . . . 
. . # . 
# . # . 
. # # . 
glider: generation 3
. . . . 
. # . . 
. . # # 
. # # . 
glider: generation 4
. . . . 
. . # . 
. . . # 
. # # # 
specified lifetime ended

random: generation 0
. . . # # 
. . . # . 
. . . # . 
# . . . # 
# . # # # 
random: generation 1
. . . # # 
. . # # . 
. . . # # 
. # # . # 
. # . # # 
random: generation 2
. . # # # 
. . # . . 
. # . . # 
. # . . . 
. # . # # 
random: generation 3
. . # # . 
. # # . # 
. # # . . 
# # . # # 
. . # . . 
random: generation 4
. # # # . 
. . . . . 
. . . . # 
# . . # . 
. # # # . 
random: generation 5
. . # . . 
. . # # . 
. . . . . 
. # . # # 
. # # # . 
random: generation 6
. . # # . 
. . # # . 
. . . . # 
. # . # # 
. # . # # 
random: generation 7
. . # # . 
. . # . # 
. . . . # 
. . . . . 
. . . # # 
random: generation 8
. . # # . 
. . # . # 
. . . # . 
. . . # # 
. . . . . 
random: generation 9
. . # # . 
. . # . # 
. . # . . 
. . . # # 
. . . . . 
random: generation 10
. . # # . 
. # # . . 
. . # . # 
. . . # . 
. . . . . 
specified lifetime ended

Class version

The above implementation uses only methods. Below is one that is object-oriented and feels perhaps a bit more Ruby-ish.

class Game
  def initialize(name, size, generations, initial_life=nil)
    @size = size
    @board = GameBoard.new size, initial_life
    @board.display name, 0
    
    reason = generations.times do |gen|
      new_board = evolve
      new_board.display name, gen+1
      break :all_dead if new_board.barren?
      break :static   if @board == new_board
      @board = new_board
    end
    
    case reason
    when :all_dead  then puts "No more life."
    when :static    then puts "No movement."
    else                 puts "Specified lifetime ended."
    end
    puts
  end
  
  def evolve
    life = @board.each_index.select {|i,j| cell_fate(i,j)}
    GameBoard.new @size, life
  end
  
  def cell_fate(i, j)
    left_right = [0, i-1].max .. [i+1, @size-1].min
    top_bottom = [0, j-1].max .. [j+1, @size-1].min
    sum = 0
    for x in left_right
      for y in top_bottom
        sum += @board[x,y].value if x != i or y != j
      end
    end
    sum == 3 or (sum == 2 and @board[i,j].alive?)
  end
end

class GameBoard
  include Enumerable
  
  def initialize(size, initial_life=nil)
    @size = size
    @board = Array.new(size) {Array.new(size) {Cell.new false}}
    seed_board initial_life
  end
  
  def seed_board(life)
    if life.nil?
      # randomly seed board
      each_index.to_a.sample(10).each {|x,y| @board[y][x].live}
    else
      life.each {|x,y| @board[y][x].live}
    end
  end
  
  def each
    @size.times {|x| @size.times {|y| yield @board[y][x] }}
  end
  
  def each_index
    return to_enum(__method__) unless block_given?
    @size.times {|x| @size.times {|y| yield x,y }}
  end
  
  def [](x, y)
    @board[y][x]
  end
  
  def ==(board)
    self.life == board.life
  end
  
  def barren?
    none? {|cell| cell.alive?}
  end
  
  def life
    each_index.select {|x,y| @board[y][x].alive?}
  end
  
  def display(name, generation)
    puts "#{name}: generation #{generation}"
    puts @board.map {|row| row.map {|cell| cell.alive? ? '#' : '.'}.join(' ')}
  end
  
  def apocalypse
    # utility function to entirely clear the game board
    each {|cell| cell.die}
  end
end

class Cell
  def initialize(alive) @alive = alive  end
  def alive?;           @alive          end
  def value;            @alive ? 1 : 0  end
  def live;             @alive = true   end
  def die;              @alive = false  end
end

Game.new "blinker", 3, 2, [[1,0],[1,1],[1,2]]
Game.new "glider", 4, 4, [[1,0],[2,1],[0,2],[1,2],[2,2]]
Game.new "random", 5, 10

Rust

use std::collections::HashMap;
use std::collections::HashSet;

type Cell = (i32, i32);
type Colony = HashSet<Cell>;

fn print_colony(col: &Colony, width: i32, height: i32) {
    for y in 0..height {
        for x in 0..width {
            print!("{} ",
                if col.contains(&(x, y)) {"O"}
                else {"."}
            );
        }
        println!();
    }
}

fn neighbours(&(x,y): &Cell) -> Vec<Cell> {
    vec![
        (x-1,y-1), (x,y-1), (x+1,y-1),
        (x-1,y),            (x+1,y),
        (x-1,y+1), (x,y+1), (x+1,y+1),
    ]
}

fn neighbour_counts(col: &Colony) -> HashMap<Cell, i32> {
    let mut ncnts = HashMap::new();
    for cell in col.iter().flat_map(neighbours) {
        *ncnts.entry(cell).or_insert(0) += 1;
    }
    ncnts
}

fn generation(col: Colony) -> Colony {
    neighbour_counts(&col)
        .into_iter()
        .filter_map(|(cell, cnt)|
            match (cnt, col.contains(&cell)) {
                (2, true) |
                (3, ..) => Some(cell),
                _ => None
        })
        .collect()
}

fn life(init: Vec<Cell>, iters: i32, width: i32, height: i32) {
    let mut col: Colony = init.into_iter().collect(); 
    for i in 0..iters+1
    {
        println!("({})", &i);
        if i != 0 {
            col = generation(col);
        }
        print_colony(&col, width, height);
    }
}

fn main() {
    let blinker = vec![
        (1,0),
        (1,1),
        (1,2)];

    life(blinker, 3, 3, 3);

    let glider = vec![
                (1,0),
                        (2,1),
        (0,2),  (1,2),  (2,2)];

    life(glider, 20, 8, 8);
}

Scala

See Conway's Game of Life/Scala, Scala/Spark distributed

Scheme

Works with: Scheme version implementing R6RS (tested with PLT Scheme, Petite Chez Scheme)
;;An R6RS Scheme implementation of Conway's Game of Life --- assumes
;;all cells outside the defined grid are dead

;if n is outside bounds of list, return 0 else value at n
(define (nth n lst)
  (cond ((> n (length lst)) 0)
        ((< n 1) 0)
        ((= n 1) (car lst))
        (else (nth (- n 1) (cdr lst)))))

;return the next state of the supplied universe
(define (next-universe universe)
  ;value at (x, y)
  (define (cell x y)
    (if (list? (nth y universe))
        (nth x (nth y universe))
        0))
  ;sum of the values of the cells surrounding (x, y)
  (define (neighbor-sum x y)
    (+ (cell (- x 1) (- y 1))
       (cell (- x 1) y)
       (cell (- x 1) (+ y 1))
       (cell x (- y 1))
       (cell x (+ y 1))
       (cell (+ x 1) (- y 1))
       (cell (+ x 1) y)
       (cell (+ x 1) (+ y 1))))
  ;next state of the cell at (x, y)
  (define (next-cell x y)
    (let ((cur (cell x y))
          (ns (neighbor-sum x y)))
      (cond ((and (= cur 1)
                  (or (< ns 2) (> ns 3)))
             0)
            ((and (= cur 0) (= ns 3))
             1)
            (else cur))))
  ;next state of row n
  (define (row n out)
    (let ((w (length (car universe))))
      (if (= (length out) w)
          out
          (row n
               (cons (next-cell (- w (length out)) n)
                     out)))))
  ;a range of ints from bot to top
  (define (int-range bot top)
    (if (> bot top) '()
        (cons bot (int-range (+ bot 1) top))))
  (map (lambda (n)
         (row n '()))
       (int-range 1 (length universe))))

;represent the universe as a string
(define (universe->string universe)
  (define (prettify row)
    (apply string-append
           (map (lambda (b)
                  (if (= b 1) "#" "-"))
                row)))
  (if (null? universe)
      ""
      (string-append (prettify (car universe))
                     "\n"
                     (universe->string (cdr universe)))))

;starting with seed, show reps states of the universe
(define (conway seed reps)
  (when (> reps 0)
    (display (universe->string seed))
    (newline)
    (conway (next-universe seed) (- reps 1))))

;; --- Example Universes --- ;;

;blinker in a 3x3 universe
(conway '((0 1 0)
          (0 1 0)
          (0 1 0)) 5)

;glider in an 8x8 universe
(conway '((0 0 1 0 0 0 0 0)
          (0 0 0 1 0 0 0 0)
          (0 1 1 1 0 0 0 0)
          (0 0 0 0 0 0 0 0)
          (0 0 0 0 0 0 0 0)
          (0 0 0 0 0 0 0 0)
          (0 0 0 0 0 0 0 0)
          (0 0 0 0 0 0 0 0)) 30)
Output:
-#-
-#-
-#-

---
###
---

-#-
-#-
-#-

---
###
---

-#-
-#-
-#-

--#-----
---#----
-###----
--------
--------
--------
--------
--------

--------
-#-#----
--##----
--#-----
--------
--------
--------
--------

--------
---#----
-#-#----
--##----
--------
--------
--------
--------

--------
--#-----
---##---
--##----
--------
--------
--------
--------

--------
---#----
----#---
--###---
--------
--------
--------
--------

--------
--------
--#-#---
---##---
---#----
--------
--------
--------

--------
--------
----#---
--#-#---
---##---
--------
--------
--------

--------
--------
---#----
----##--
---##---
--------
--------
--------

--------
--------
----#---
-----#--
---###--
--------
--------
--------

--------
--------
--------
---#-#--
----##--
----#---
--------
--------

--------
--------
--------
-----#--
---#-#--
----##--
--------
--------

--------
--------
--------
----#---
-----##-
----##--
--------
--------

--------
--------
--------
-----#--
------#-
----###-
--------
--------

--------
--------
--------
--------
----#-#-
-----##-
-----#--
--------

--------
--------
--------
--------
------#-
----#-#-
-----##-
--------

--------
--------
--------
--------
-----#--
------##
-----##-
--------

--------
--------
--------
--------
------#-
-------#
-----###
--------

--------
--------
--------
--------
--------
-----#-#
------##
------#-

--------
--------
--------
--------
--------
-------#
-----#-#
------##

--------
--------
--------
--------
--------
------#-
-------#
------##

--------
--------
--------
--------
--------
--------
-------#
------##

--------
--------
--------
--------
--------
--------
------##
------##

--------
--------
--------
--------
--------
--------
------##
------##

--------
--------
--------
--------
--------
--------
------##
------##

--------
--------
--------
--------
--------
--------
------##
------##

--------
--------
--------
--------
--------
--------
------##
------##

--------
--------
--------
--------
--------
--------
------##
------##

--------
--------
--------
--------
--------
--------
------##
------##

--------
--------
--------
--------
--------
--------
------##
------##

--------
--------
--------
--------
--------
--------
------##
------##

Scilab

The game's initial state can be input manually by setting the values of Init_state, or using a bitmap image (or other supported formats). The output can be either printed on Scilab's console, or on a graphic window. For both image input and graphic output, either SIVP or IPCV modules are required, and console_output should be set to false.

Init_state=[0 0 0;...
            1 1 1;...
            0 0 0];
console_output=%T;

if (atomsIsLoaded('IPCV') | atomsIsLoaded('SIVP')) & ~console_output then
    Input=imread('initial_state.bmp');  //Comment this three lines in case
    Init_state=~im2bw(Input,0.1);       //there is no input image but
    Init_state=1.0.*Init_state;         //you still want the graphic window
    scf(0); clf();
    imshow(~Init_state);
    set(gca(),"isoview","on");
end

Curr_state=1.0.*Init_state;
Grid_size=size(Init_state);
Gens=4;

function varargout=neighbourhood(A,i,j)
    R_top=i-1;
    if i==1 then
        R_top=1;
    end
    
    R_bottom=i+1;
    if i==Grid_size(1) then
        R_bottom=Grid_size(1);
    end
    
    R_left=j-1;
    if j==1 then
        R_left=1;
    end
    
    C_right=j+1;
    if j==Grid_size(2) then
        C_right=Grid_size(2);
    end
    
    varargout=list(A(R_top:R_bottom,R_left:C_right));
endfunction

function []=console_print(Grid)
    String_grid=string(Grid);
    for i=1:size(Grid,'r')
        for j=1:size(Grid,'c')
            if Grid(i,j) then
                String_grid(i,j)="#";
            else
                String_grid(i,j)=" ";
            end
        end
    end
    disp(String_grid);
endfunction

neighbours=[];
Next_state=[];

for gen=1:Gens
    Next_state=zeros(Init_state);
    
    for i=1:Grid_size(1)
        for j=1:Grid_size(2)
            neighbours=zeros(3,3);
            neighbours=neighbourhood(Curr_state,i,j);
            
            Sum_neighbours=sum(neighbours)-1*Curr_state(i,j);
            
            Alive=Curr_state(i,j);
            if Alive then
                if Sum_neighbours<2 then
                    Next_state(i,j)=0;
                elseif Sum_neighbours==2 | Sum_neighbours==3 then
                    Next_state(i,j)=1;
                elseif Sum_neighbours>3 then
                    Next_state(i,j)=0;
                end
            else
                if Sum_neighbours==3 then
                    Next_state(i,j)=1;
                end
            end
        end
    end
    
    if (atomsIsLoaded('IPCV') | atomsIsLoaded('SIVP')) & ~console_output then
        imshow(~Next_state);
        sleep(50);
    else
        sleep(50);
        disp("Generation "+string(gen)+":")
        console_print(Next_state);
    end
    
    if sum(Next_state)==0 | Curr_state==Next_state then
        disp('ALL CELLS HAVE DIED OR BECAME INERT');
        disp('No. of Generations: '+string(gen))
        break
    end
    
    Curr_state=Next_state;
end
Output:

Output when console_output=%T.

 Generation 1:

!   #     !
!         !
!   #     !
!         !
!   #     !

 Generation 2:

!         !
!         !
!#  #  #  !
!         !
!         !

 Generation 3:

!   #     !
!         !
!   #     !
!         !
!   #     !

 Generation 4:

!         !
!         !
!#  #  #  !
!         !
!         !

SenseTalk

set starting_condition to ((0, 0), (1, 0), (2, 0), (-1, -1), (0, -1), (1, -1))

RunGameOfLife starting_condition

to printColony colonies
    set xCoords to the first item of each item of colonies
    set yCoords to the second item of each item of colonies
    set min_x to the min of xCoords
    set max_x to the max of xCoords
    set min_y to the min of yCoords
    set max_y to the max of yCoords
    repeat for y in min_y..max_y
        set row to ()
        repeat for x in min_x..max_x
            if (x, y) is in colonies
                push "#" into row
            else
                push "-" into row
            end if
        end repeat
        join row using ""
        put row
    end repeat
end printColony

to neighboursOf coordinate
    return ( \
            coordinate + (-1, 1), \
            coordinate + (0, 1), \
            coordinate + (1, 1), \
            coordinate + (-1, 0), \
            coordinate + (1, 0), \
            coordinate + (-1, -1), \
            coordinate + (0, -1), \
            coordinate + (1, -1), \
            )
end neighboursOf

to WillNextGenHaveCell colony, coordinate
    set neighbour_count to the number of items in (each item of neighboursOf(coordinate) where each is in colony)
    if coordinate is in colony
        return neighbour_count is in (2, 3)
    else
        return neighbour_count equals 3
    end if
end WillNextGenHaveCell

to RunGameOfLife colony
    printColony colony
    set the listInsertionMode to "nested"
    repeat 10 times
        set new_colony to ()

        set xCoords to the first item of each item of colony
        set yCoords to the second item of each item of colony

        set min_x to (the min of xCoords) - 1
        set max_x to (the max of xCoords) + 1
        set min_y to (the min of yCoords) - 1
        set max_y to (the max of yCoords) + 1

        repeat for y in min_y..max_y
            repeat for x in min_x..max_x
                if WillNextGenHaveCell(colony, (x, y))
                    insert (x, y) into new_colony
                end if
            end repeat
        end repeat
        set colony to new_colony
        printColony colony
        wait 1 second
    end repeat
end RunGameOfLife

SequenceL

Library: CImg

SequenceL Code:

life(Cells(2))[I, J] := 
	let
		numNeighbors := Cells[I-1,J-1] + Cells[I-1,J] + Cells[I-1,J+1] +
				Cells[I,J-1]   +/*current cell*/Cells[I,J+1] +
				Cells[I+1,J-1] + Cells[I+1,J] + Cells[I+1,J+1];
	in
		0 when I=1 or J=1 or I=size(Cells) or J=size(Cells[I]) //On Border
	else
		0 when numNeighbors < 2 or numNeighbors > 3 //Cell Dies
	else
		1 when Cells[I,J] = 1 and numNeighbors = 2 or numNeighbors = 3 //Cell lives on or is born.
	else
		Cells[I,J]; //No Change
		
		
stressTestInput(n(0))[y,x] :=
		0 when not y = n / 2
	else
		1
	foreach y within 1 ... n,
		x within 1 ... n;

C++ Driver Code:

#include <iostream>
#include <string>
#include <vector>
#include <fstream>
#include <cerrno>

#include "Cimg.h"

#include "SL_Generated.h"

using namespace std;
using namespace cimg_library;

char titleBuffer[200];

std::string get_file_contents(const char*);

int main(int argc, char ** argv)
{
	int cores = 0;
	int maxSize = 700;

	int drawSkip = 1;
	int drawWait = 0;

	string inputFile = "test";

	if(argc > 1)
	{
		inputFile = argv[1];
	}
	if(argc > 2)
	{
		cores = atoi(argv[2]);
	}

	if(argc > 3)
	{
		maxSize = atoi(argv[3]);
	}

	if(argc > 4)
	{
		drawSkip = atoi(argv[4]);

		if(drawSkip < 0)
		{
			drawWait = abs(drawSkip);
			drawSkip = 1;
		}
	}

	sl_init(cores);

	SLTimer drawTimer;

	sprintf(titleBuffer, "Conway's Game of Life in SequenceL: %d Cores", cores);

	int width = 0;
	int height = 0;

	//Read input file--------------
	Sequence<Sequence<int>> initialGrid;

	if(inputFile != "test")
	{
		stringstream ss(get_file_contents(inputFile.c_str()));
		string stringItem;
		vector<int> elems;
		char delim = ',';

		getline(ss, stringItem, delim);
		width = atoi(stringItem.c_str());
		getline(ss, stringItem, delim);
		height = atoi(stringItem.c_str());

		while(getline(ss, stringItem, delim))
		{
			elems.push_back(atoi(stringItem.c_str()));
		}

		//Sequence Pointer Constructor----
		int gridDims[] = {height, width, 0};
		Sequence<Sequence<int>> tempGrid( (void*)&elems[0], gridDims);
		initialGrid.hard_copy(tempGrid, 0);
		//-----------------------------
	}
	else
	{
		width = maxSize;
		height = maxSize;
		sl_stressTestInput(maxSize, cores, initialGrid);
	}
	//--------

	Sequence<Sequence<int>>  result;

	const unsigned char black[] = {0};

	CImg<unsigned char> visu(width * 4, height * 4, 1, 1, 0);
	CImgDisplay draw_disp(visu, titleBuffer);
	cout << "Conway's Game of Life in SequenceL" << endl << "Cores: " << cores << endl;

	int generations = 0;
	double compTime = 0;
	double drawTime = 0;
	SLTimer t;

	while(!draw_disp.is_closed())
	{
		t.start();
		sl_life(initialGrid, cores, result);
		generations++;
		initialGrid.hard_copy(result, 0);
		t.stop();
		compTime += t.getTime();

		drawTimer.start();

		if(drawSkip > 0 && generations % drawSkip == 0)
		{

			visu.fill(255);

			for(int i = 1; i <= result.size(); i++)
			{
				for(int j = 1; j <= result[i].size(); j++)
				{
					if(result[i][j] == 1) visu.draw_circle((j-1) * 4, (i - 1) * 4, 2, black, 1);
				}
			}

			visu.display(draw_disp);

			int drawWidth = maxSize;
			int drawHeight = maxSize;

			if(width < height)
			{
				drawWidth = ((double)drawHeight * ((double)width / (double)height));
			}
			else
			{
				drawHeight = ((double)drawWidth * ((double)height / (double)width));
			}

			draw_disp.resize(drawWidth, drawHeight, false);

			draw_disp.wait(drawWait);
			drawTimer.stop();
			drawTime += drawTimer.getTime();
		}
	}

	cout << "Total Generations: " << generations << endl;

	cout << "Average Compute Time: " << compTime / generations << " seconds" << endl;

	cout << "Average Draw Time: " << drawTime / generations << " seconds" << endl;

	sl_done();

	return 0;
}

std::string get_file_contents(const char *filename)
{
  std::ifstream in(filename, std::ios::in | std::ios::binary);
  if (in)
  {
    std::string contents;
    in.seekg(0, std::ios::end);
    contents.resize(in.tellg());
    in.seekg(0, std::ios::beg);
    in.read(&contents[0], contents.size());
    in.close();
    return(contents);
  }
  throw(errno);
}

Usage:

SequenceL Intended Use:

life(int(2)); stressTestInput(int(0))

Running the program:

  • If no inputs are provided, a 700 element stress test is performed.
  • Argument 1 is the input file ("test" to run stress test).
  • Argument 2 is the optional number of cores which defaults to 0(all cores).
  • Argument 3 is the size to make the largest dimension of the display window.
  • Argument 4 is the number of frames to skip when drawing.

Sample Input:

Blinker:

5,5,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0

Output: http://i.imgur.com/9ZtKw1X.gifv

Stress Test Output:

This is the output for the 700 element stress test, which is an input of a 700X700 grid with a single line of live cells horizontally in the center.

Output: http://i.imgur.com/yKTrszV.gifv

SETL

Compiler: GNU SETL

This version uses a live cell set representation (set of coordinate pairs.) This example first appeared here.

program life;

const
  initialMatrix =
    [".....",
     "..#..",
     "...#.",
     ".###.",
     "....."];

loop
init
  s := initialLiveSet();
do
  output(s);
  nm := {[[x+dx, y+dy], [x, y]]: [x, y] in s, dx in {-1..1}, dy in {-1..1}};
  s := {c: t = nm{c} | 3 in {#t, #(t less c)}};
end;

proc output(s);
  system("clear");
  (for y in [0..24])
    (for x in [0..78])
      nprint(if [x, y] in s then "#" else " " end);
    end;
    print();
  end;
  select([], 250);
end proc;

proc initialLiveSet();
  return {[x,y]: row = initialMatrix(y), c = row(x) | c = '#'};
end proc;

end program;

Shen

Somewhat verbose but functional and type-checked implementation (tested with chibi-scheme and Shen/SBCL). Running this shows ten iterations of a toad.

(tc +)

(datatype subtype
  (subtype B A); X : B;
  _____________________
  X : A;)

(datatype integer
  if (integer? X)
  ___________
  X: integer;

  ________________________
  (subtype integer number);)

(datatype bit
  if (< X 2)
  _______
  X: bit;

  _____________________
  (subtype bit integer);)

(datatype row

  _________
  [] : row;
  
  C : bit; Row : row;
  ===================
  [C | Row] : row;)
  
(datatype universe

  ______________
  [] : universe;
  
  R : row; Uni : universe;
  ========================
  [R | Uni] : universe;)

(define conway-nth
  \\ returns value of x from row if it exists, else 0
  { number --> row --> bit }
  _ [] -> 0
  N _ -> 0 where (< N 0)
  0 [A|B] -> A
  N [A|B] -> (conway-nth (- N 1) B))

(define row-retrieve
  { number --> universe --> row }
  _ [] -> []
  0 [] -> []
  0 [A|B] -> A
  N [A|B] -> (row-retrieve (- N 1) B))

(define cell-retrieve
  { number --> number --> universe --> bit }
  X Y Universe -> (conway-nth X (row-retrieve Y Universe)))

(define neighbors
  \\ takes an X and Y, retrieves the number of neighbors
  { number --> number --> universe --> number }
  X Y Universe -> (let ++ (+ 1)
                       -- (/. X (- X 1))
                    (+ (cell-retrieve (++ X) Y Universe)
                       (cell-retrieve (++ X) (++ Y) Universe)
                       (cell-retrieve (++ X) (-- Y) Universe)
                       (cell-retrieve (-- X) Y Universe)
                       (cell-retrieve (-- X) (++ Y) Universe)
                       (cell-retrieve (-- X) (-- Y) Universe)
                       (cell-retrieve X (++ Y) Universe)
                       (cell-retrieve X (-- Y) Universe))))

(define handle-alive
  { number --> number --> universe --> bit }
  X Y Universe -> (if (or (= (neighbors X Y Universe) 2)
                          (= (neighbors X Y Universe) 3))
                      1 0))

(define handle-dead
  { number --> number --> universe --> bit }
  X Y Universe -> (if (= (neighbors X Y Universe) 3)
                      1 0))

(define next-row
  \\ first argument must be a previous row, second must be 0 when
  \\ first called, third must be a Y value and the final must be the
  \\ current universe
  { row --> number --> number --> universe --> row }
  [] _ _ _ -> []
  [1|B] X Y Universe -> (cons (handle-alive X Y Universe)
                              (next-row B (+ X 1) Y Universe))
  [_|B] X Y Universe -> (cons (handle-dead X Y Universe)
                              (next-row B (+ X 1) Y Universe)))

(define next-universe
  \\ both the first and second arguments must be the same universe,
  \\ the third must be 0 upon first call
  { universe --> number --> universe --> universe }
  [] _ _ -> []
  [Row|Rest] Y Universe -> (cons (next-row Row 0 Y Universe)
                                 (next-universe Rest (+ Y 1) Universe)))

(define display-row
  { row --> number }
  [] -> (nl)
  [1|Rest] -> (do (output "* ")
                  (display-row Rest))
  [_|Rest] -> (do (output "  ")
                  (display-row Rest)))

(define display-universe
  { universe --> number }
  [] -> (nl 2)
  [Row|Rest] -> (do (display-row Row)
                    (display-universe Rest)))

(define iterate-universe
  { number --> universe --> number }
  0 _ -> (nl)
  N Universe -> (do (display-universe Universe)
                    (iterate-universe (- N 1)
                                      (next-universe Universe 0 Universe))))

(iterate-universe
 10
 [[0 0 0 0 0 0]
  [0 0 0 0 0 0]
  [0 0 1 1 1 0]
  [0 1 1 1 0 0]
  [0 0 0 0 0 0]
  [0 0 0 0 0 0]])

Sidef

Translation of: Perl
var w = Num(`tput cols`)
var h = Num(`tput lines`)
var r = "\033[H"

var dirs = [[-1,-1], [-1, 0], [-1, 1], [ 0,-1],
            [ 0, 1], [ 1,-1], [ 1, 0], [ 1, 1]]

var universe = h.of { w.of {1.rand < 0.1} }

func iterate {
    var new = h.of { w.of(false) }
    static rx = (^h ~X ^w)
    for i,j in rx {
        var neighbor = 0
        for y,x in (dirs.map {|dir| dir »+« [i, j] }) {
            universe[y % h][x % w] && ++neighbor
            neighbor > 3 && break
        }
        new[i][j] = (universe[i][j]
                        ? (neighbor==2 || neighbor==3)
                        : (neighbor==3))
    }
    universe = new
}

STDOUT.autoflush(true)

loop {
    print r
    say universe.map{|row| row.map{|cell| cell ? '#' : ' '}.join }.join("\n")
    iterate()
}

Simula

Translation of: Scheme
COMMENT A PORT OF AN R6RS SCHEME IMPLEMENTATION OF CONWAY'S GAME OF LIFE TO SIMULA --- ASSUMES ;
COMMENT ALL CELLS OUTSIDE THE DEFINED GRID ARE DEAD ;

BEGIN


COMMENT FIRST WE NEED CONS, CAR, CDR, LENGTH AND MAP TO SIMULATE SCHEME ;

CLASS ATOM;;

ATOM CLASS CELL(ALIVE); INTEGER ALIVE;;

ATOM CLASS LIST(A1, A2); REF(ATOM) A1, A2;;

REF(LIST) PROCEDURE CONS(A1, A2); REF(ATOM) A1, A2;
    CONS :- NEW LIST(A1, A2);

REF(ATOM) PROCEDURE CAR(LST); REF(LIST) LST;
    CAR :- LST.A1;

REF(ATOM) PROCEDURE CDR(LST); REF(LIST) LST;
    CDR :- LST.A2;

INTEGER PROCEDURE LENGTH(LST); REF(LIST) LST;
    LENGTH := IF LST == NONE THEN 0 ELSE 1 + LENGTH(CDR(LST));

REF(LIST) PROCEDURE MAP(F, LST); PROCEDURE F IS REF(ATOM) PROCEDURE F(ARG); REF(ATOM) ARG;; REF(LIST) LST;
    MAP :- IF LST == NONE THEN NONE ELSE CONS(F(CAR(LST)), MAP(F, CDR(LST)));



COMMENT NOW FOLLOWS THE PROBLEM SPECIFIC PART ;


COMMENT IF N IS OUTSIDE BOUNDS OF LIST, RETURN 0 ELSE VALUE AT N ;
REF(ATOM) PROCEDURE NTH(N, LST); INTEGER N; REF(LIST) LST;
    NTH :- IF N > LENGTH(LST) THEN NEW CELL(0) ELSE
           IF N < 1 THEN NEW CELL(0) ELSE
           IF N = 1 THEN CAR(LST) ELSE NTH(N - 1, CDR(LST));


COMMENT RETURN THE NEXT STATE OF THE SUPPLIED UNIVERSE ;
REF(LIST) PROCEDURE NEXTUNIVERSE(UNIVERSE); REF(LIST) UNIVERSE;
BEGIN

    COMMENT VALUE AT (X, Y) ;
    INTEGER PROCEDURE VALUEAT(X, Y); INTEGER X, Y;
    BEGIN
        REF(ATOM) A;
        A :- NTH(Y, UNIVERSE);
        INSPECT A
            WHEN LIST DO
                VALUEAT := NTH(X, THIS LIST) QUA CELL.ALIVE
            OTHERWISE
                VALUEAT := 0;
    END VALUEAT;

    COMMENT SUM OF THE VALUES OF THE CELLS SURROUNDING (X, Y) ;
    INTEGER PROCEDURE NEIGHBORSUM(X, Y); INTEGER X, Y;
        NEIGHBORSUM :=
            VALUEAT(X - 1, Y - 1)
          + VALUEAT(X - 1, Y    )
          + VALUEAT(X - 1, Y + 1)
          + VALUEAT(X,     Y - 1)
          + VALUEAT(X,     Y + 1)
          + VALUEAT(X + 1, Y - 1)
          + VALUEAT(X + 1, Y    )
          + VALUEAT(X + 1, Y + 1);

    COMMENT NEXT STATE OF THE CELL AT (X, Y) ;
    INTEGER PROCEDURE NEXTCELL(X, Y); INTEGER X, Y;
    BEGIN
        INTEGER CUR, NS;
        CUR := VALUEAT(X, Y);
        NS := NEIGHBORSUM(X, Y);
        NEXTCELL := IF CUR = 1 AND (NS < 2 OR NS > 3) THEN 0 ELSE
                    IF CUR = 0 AND NS = 3 THEN 1 ELSE CUR;
    END NEXTCELL;

    COMMENT NEXT STATE OF ROW N ;
    REF(LIST) PROCEDURE ROW(N, OUT); INTEGER N; REF(LIST) OUT;
    BEGIN
        INTEGER W, O;
        W := LENGTH(CAR(UNIVERSE));
        O := LENGTH(OUT);
        ROW :- IF W = O THEN OUT ELSE ROW(N, CONS(NEW CELL(NEXTCELL(W - O, N)), OUT));
    END ROW;


    COMMENT A RANGE OF INTS FROM BOT TO TOP ;
    REF(LIST) PROCEDURE INTRANGE(BOT, TOP); INTEGER BOT, TOP;
        INTRANGE :- IF BOT > TOP THEN NONE ELSE CONS(NEW CELL(BOT), INTRANGE(BOT + 1, TOP));

    REF(ATOM) PROCEDURE LAMBDA(N); REF(ATOM) N;
        LAMBDA :- ROW(N QUA CELL.ALIVE, NONE);

    NEXTUNIVERSE :- MAP(LAMBDA, INTRANGE(1, LENGTH(UNIVERSE)));

END NEXTUNIVERSE;

COMMENT DISPLAY THE UNIVERSE ;
PROCEDURE DISPLAY(LST); REF(LIST) LST;
BEGIN
    WHILE LST =/= NONE DO
    BEGIN
        REF(LIST) LI;
        LI :- CAR(LST);
        WHILE LI =/= NONE DO
        BEGIN
            REF(CELL) CE;
            CE :- CAR(LI);
            OUTCHAR(IF CE.ALIVE = 1 THEN '#' ELSE '-');
            LI :- CDR(LI);
        END;
        OUTIMAGE;
        LST :- CDR(LST);
    END;
END DISPLAY;

COMMENT STARTING WITH SEED, SHOW REPS STATES OF THE UNIVERSE ;
PROCEDURE CONWAY(SEED, REPS); REF(LIST) SEED; INTEGER REPS;
BEGIN
    IF REPS > 0 THEN
    BEGIN
        DISPLAY(SEED);
        OUTIMAGE;
        CONWAY(NEXTUNIVERSE(SEED), REPS - 1);
    END;
END CONWAY;

REF(CELL) O, L;
O :- NEW CELL(0);
L :- NEW CELL(1);

COMMENT BLINKER IN A 3X3 UNIVERSE ;
! (CONWAY '((0 1 0)
            (0 1 0)
            (0 1 0)) 5) ;
CONWAY(CONS(CONS(O, CONS(L, CONS(O, NONE))),
       CONS(CONS(O, CONS(L, CONS(O, NONE))),
       CONS(CONS(O, CONS(L, CONS(O, NONE))),
       NONE))), 5);

COMMENT GLIDER IN AN 8X8 UNIVERSE ;
!(CONWAY '((0 0 1 0 0 0 0 0)
           (0 0 0 1 0 0 0 0)
           (0 1 1 1 0 0 0 0)
           (0 0 0 0 0 0 0 0)
           (0 0 0 0 0 0 0 0)
           (0 0 0 0 0 0 0 0)
           (0 0 0 0 0 0 0 0)
           (0 0 0 0 0 0 0 0)) 30) ;
OUTIMAGE;

CONWAY(CONS(CONS(O, CONS(O, CONS(L, CONS(O, CONS(O, CONS(O, CONS(O, CONS(O, NONE)))))))),
       CONS(CONS(O, CONS(O, CONS(O, CONS(L, CONS(O, CONS(O, CONS(O, CONS(O, NONE)))))))),
       CONS(CONS(O, CONS(L, CONS(L, CONS(L, CONS(O, CONS(O, CONS(O, CONS(O, NONE)))))))),
       CONS(CONS(O, CONS(O, CONS(O, CONS(O, CONS(O, CONS(O, CONS(O, CONS(O, NONE)))))))),
       CONS(CONS(O, CONS(O, CONS(O, CONS(O, CONS(O, CONS(O, CONS(O, CONS(O, NONE)))))))),
       CONS(CONS(O, CONS(O, CONS(O, CONS(O, CONS(O, CONS(O, CONS(O, CONS(O, NONE)))))))),
       CONS(CONS(O, CONS(O, CONS(O, CONS(O, CONS(O, CONS(O, CONS(O, CONS(O, NONE)))))))),
       CONS(CONS(O, CONS(O, CONS(O, CONS(O, CONS(O, CONS(O, CONS(O, CONS(O, NONE)))))))),
       NONE)))))))), 30);

END.
Output:
-#-
-#-
-#-

---
###
---

-#-
-#-
-#-

---
###
---

-#-
-#-
-#-


--#-----
---#----
-###----
--------
--------
--------
--------
--------

--------
-#-#----
--##----
--#-----
--------
--------
--------
--------

--------
---#----
-#-#----
--##----
--------
--------
--------
--------

--------
--#-----
---##---
--##----
--------
--------
--------
--------

--------
---#----
----#---
--###---
--------
--------
--------
--------

--------
--------
--#-#---
---##---
---#----
--------
--------
--------

--------
--------
----#---
--#-#---
---##---
--------
--------
--------

--------
--------
---#----
----##--
---##---
--------
--------
--------

--------
--------
----#---
-----#--
---###--
--------
--------
--------

--------
--------
--------
---#-#--
----##--
----#---
--------
--------

--------
--------
--------
-----#--
---#-#--
----##--
--------
--------

--------
--------
--------
----#---
-----##-
----##--
--------
--------

--------
--------
--------
-----#--
------#-
----###-
--------
--------

--------
--------
--------
--------
----#-#-
-----##-
-----#--
--------

--------
--------
--------
--------
------#-
----#-#-
-----##-
--------

--------
--------
--------
--------
-----#--
------##
-----##-
--------

--------
--------
--------
--------
------#-
-------#
-----###
--------

--------
--------
--------
--------
--------
-----#-#
------##
------#-

--------
--------
--------
--------
--------
-------#
-----#-#
------##

--------
--------
--------
--------
--------
------#-
-------#
------##

--------
--------
--------
--------
--------
--------
-------#
------##

--------
--------
--------
--------
--------
--------
------##
------##

--------
--------
--------
--------
--------
--------
------##
------##

--------
--------
--------
--------
--------
--------
------##
------##

--------
--------
--------
--------
--------
--------
------##
------##

--------
--------
--------
--------
--------
--------
------##
------##

--------
--------
--------
--------
--------
--------
------##
------##

--------
--------
--------
--------
--------
--------
------##
------##

--------
--------
--------
--------
--------
--------
------##
------##

--------
--------
--------
--------
--------
--------
------##
------##


180 garbage collection(s) in 0.1 seconds.

Smalltalk

This implementation has been developed using Cuis Smalltalk [1]. Here are different configurations:

"Blinker"
GameOfLife withAliveCells: { 4@2. 4@3. 4@4. 3@3. 4@3. 5@3 } ofSize: 10@10.

"Toad"
GameOfLife withAliveCells: { 2@4. 3@4. 4@4. 3@3. 4@3. 5@3 } ofSize: 10@10

This is the implementation:

Object subclass: #GameOfLife
  instanceVariableNames: 'aliveCells boardSize'
  classVariableNames: ''
  poolDictionaries: ''
  category: 'GameOfLife'

GameOfLife class>>withAliveCells: aCollectionOfCells ofSize: aBoardSize      
  self assertAll: aCollectionOfCells areInside: aBoardSize.
  ^self new initializeWithAliveCells: aCollectionOfCells ofSize: aBoardSize
  
GameOfLife class>>assertAll: aCollectionOfAliveCells areInside: aSize
  | origin |	
  origin := 0@0.
  aCollectionOfAliveCells do: [:aCell |
  (aCell between: origin and: aSize) ifFalse: [ self error: 'Cell ', aCell printString,' out of range' ]]

initializeWithAliveCells: aCollectionOfCells ofSize: aBoardSize
  aliveCells := aCollectionOfCells asSet.
  boardSize := aBoardSize

calculateNextGeneration
  aliveCells := self boardCellsSelect: [ :aCell | self shouldBeAliveOnNextGeneration: aCell ]

shouldBeAliveOnNextGeneration: aCell
  | numberOfAliveNeighbors |
  numberOfAliveNeighbors := self numberOfAliveNeighborsOf: aCell.
  ^numberOfAliveNeighbors = 3 or: [ self shouldSurvive: aCell with: numberOfAliveNeighbors]

shouldSurvive: aCell with: numberOfAliveNeighbors
  ^ (self isAlive: aCell) and: [ numberOfAliveNeighbors = 2 ]

isAlive: aCell
  ^aliveCells includes: aCell

isDead: aCell
  ^(self isAlive: aCell) not

boardCellsDo: aClosure
  0 to: boardSize x do: [ :x |
    0 to: boardSize y do: [ :y | aClosure value: x@y ]]

boardCellsSelect: aCondition
  | selectedCells |
  selectedCells := Set new.
  self boardCellsDo: [ :aCell | (aCondition value: aCell)  ifTrue: [ selectedCells add: aCell ]].
  ^selectedCells
  
numberOfAliveNeighborsOf: aCell
  ^aCell eightNeighbors count: [ :aNeighbor | self isAlive: aNeighbor ]

The implementation was developed using TDD. This are the tests used to implement it.

TestCase subclass: #GameOfLifeTest
  instanceVariableNames: ''
  classVariableNames: ''
  poolDictionaries: ''
  category: 'GameOfLife'

test01AliveCellWithLessThatTwoAliveCellsDies
  | gameOfLife |
  gameOfLife := GameOfLife withAliveCells: {1@1} ofSize: 3@3.
  gameOfLife calculateNextGeneration.
  self assert: (gameOfLife isDead: 1@1)

test02AliveCellWithTwoAliveNeighborsSurvives
  | gameOfLife |
  gameOfLife := GameOfLife withAliveCells: {1@1. 1@2. 2@1} ofSize: 3@3.
  gameOfLife calculateNextGeneration.
  self assert: (gameOfLife isAlive: 1@1).

test03AliveCellWithThreeAliveNeighborsSurvives
  | gameOfLife |
  gameOfLife := GameOfLife withAliveCells: {1@1. 1@2. 2@1. 2@2} ofSize: 3@3.
  gameOfLife calculateNextGeneration.
  self assert: (gameOfLife isAlive: 1@1).

test04DeadCellWithThreeAliveNeighborsBecomesAlive
  | gameOfLife |
  gameOfLife := GameOfLife withAliveCells: {1@1. 1@2. 2@1} ofSize: 3@3.
  gameOfLife calculateNextGeneration.
  self assert: (gameOfLife isAlive: 2@2).

test05DeadCellWithAliveNeighborsDifferentToThreeKeepsDead
  | gameOfLife |
  gameOfLife := GameOfLife withAliveCells: {1@2. 2@2. 3@2. 1@3} ofSize: 3@3.
  gameOfLife calculateNextGeneration.
  self assert: (gameOfLife isDead: 1@1).
  self assert: (gameOfLife isDead: 2@3).

test06CanNotCreateGameWithCellOutsideXOrigin
  self 
    should: [ GameOfLife withAliveCells: { 2@0. 1@0. -1@1 } ofSize: 3@3 ]
    raise: Error - MessageNotUnderstood 
    withMessageText: 'Cell -1@1 out of range'

test07CanNotCreateGameWithCellOutsideYOrigin
  self 
    should: [ GameOfLife withAliveCells: { 2@0. 1@0. 1@-1 } ofSize: 3@3 ]
    raise: Error - MessageNotUnderstood 
    withMessageText: 'Cell 1@-1 out of range'

test08CanNotCreateGameWithCellOutsideXLimit
  self 
    should: [ GameOfLife withAliveCells: { 2@0. 1@0. 4@1 } ofSize: 3@3 ]
    raise: Error - MessageNotUnderstood 
    withMessageText: 'Cell 4@1 out of range'

test09CanNotCreateGameWithCellOutsideYLimit
  self 
    should: [ GameOfLife withAliveCells: { 2@0. 1@0. 1@4 } ofSize: 3@3 ]
    raise: Error - MessageNotUnderstood 
    withMessageText: 'Cell 1@4 out of range'

If you want to have a visual representation, here is a view for it:

ImageMorph subclass: #GameOfLifeView
  instanceVariableNames: 'game'
  classVariableNames: ''
  poolDictionaries: ''
  category: 'GameOfLife'

GameOfLifeView class>>for: aGameOfLife
  ^self new initializeFor: aGameOfLife

GameOfLifeView class>>openFor: aGameOfLife
  ^(self for: aGameOfLife) open

GameOfLifeView class>>blinker
  ^GameOfLife withAliveCells: { 4@2. 4@3. 4@4. 3@3. 4@3. 5@3 } ofSize: 10@10
  	
GameOfLifeView class>>toad
  ^GameOfLife withAliveCells: { 2@4. 3@4. 4@4. 3@3. 4@3. 5@3 } ofSize: 10@10

GameOfLifeView class>>openBlinker
  ^self openFor: self blinker

GameOfLifeView class>>openToad
  ^self openFor: self toad  	

initializeFor: aGameOfLife
  game := aGameOfLife.
  self image: (Form extent: game boardSize * 5 depth: 2).

open
  self showBoard.
  self openInWorld.
  self startSteppingStepTime: 500

showBoard
  game boardCellsDo: [ :aPoint | 
    (game isAlive: aPoint)
      ifTrue: [ self form fillBlack: (aPoint*5 extent: 5@5) ]
      ifFalse: [ self form fillWhite: (aPoint*5 extent: 5@5) ]].

step
  game calculateNextGeneration.
  self showBoard.
  self redrawNeeded.

SQL

Microsoft SQL here: http://www.sqlservercentral.com/articles/CTE/130407/

Works with: Oracle
-- save these lines in a file called
-- setupworld.sql

-- turn off feedback for cleaner display

set feedback off

-- 3 x 3 world

-- alive has coordinates of living cells

drop table alive;

create table alive (x number,y number);

-- three alive up the middle
--  * 
--  * 
--  *

insert into alive values (2,1);
insert into alive values (2,2);
insert into alive values (2,3);

commit;

-- save these lines in a file called
newgeneration.sql

-- adjact contains one row for each pair of 
-- coordinates that is adjacent to a living cell

drop table adjacent;

create table adjacent (x number,y number);

-- add row for each of the 8 adjacent squares

insert into adjacent select x-1,y-1 from alive; 
insert into adjacent select x-1,y from alive;
insert into adjacent select x-1,y+1 from alive;
insert into adjacent select x,y-1 from alive; 
insert into adjacent select x,y+1 from alive;
insert into adjacent select x+1,y-1 from alive; 
insert into adjacent select x+1,y from alive;
insert into adjacent select x+1,y+1 from alive;

commit;

-- delete rows for squares that are outside the world

delete from adjacent where x<1 or y<1 or x>3 or y>3;

commit;

-- table counts is the number of live cells
-- adjacent to that point

drop table counts;

create table counts as 
select x,y,count(*) n
from adjacent a
group by x,y;

--    C   N                 new C
--    1   0,1             ->  0  # Lonely
--    1   4,5,6,7,8       ->  0  # Overcrowded
--    1   2,3             ->  1  # Lives
--    0   3               ->  1  # It takes three to give birth!
--    0   0,1,2,4,5,6,7,8 ->  0  # Barren

-- delete the ones who die

delete from alive a
where
((a.x,a.y) not in (select x,y from counts)) or
((select c.n from counts c where a.x=c.x and a.y=c.y) in 
(1,4,5,6,7,8));

-- insert the ones that are born

insert into alive a
select x,y from counts c
where c.n=3 and
((c.x,c.y) not in (select x,y from alive));

commit;

-- create output table

drop table output;

create table output as
select rownum y,' ' x1,' ' x2,' ' x3
from dba_tables where rownum < 4;

update output set x1='*'
where (1,y) in
(select x,y from alive);

update output set x2='*'
where (2,y) in
(select x,y from alive);

update output set x3='*'
where (3,y) in
(select x,y from alive);

commit

-- output configuration

select x1||x2||x3 WLD
from output
order by y desc;
Running in sqlplus:

SQL> @setupworld
SQL> @newgeneration

WLD
---

***

SQL> @newgeneration

WLD
---
 *
 *
 *
SQL> @newgeneration

WLD
---

***

Swift

Translation of: Rust
struct Cell: Hashable {
  var x: Int
  var y: Int
}

struct Colony {
  private var height: Int
  private var width: Int
  private var cells: Set<Cell>

  init(cells: Set<Cell>, height: Int, width: Int) {
    self.cells = cells
    self.height = height
    self.width = width
  }

  private func neighborCounts() -> [Cell: Int] {
    var counts = [Cell: Int]()

    for cell in cells.flatMap(Colony.neighbors(for:)) {
      counts[cell, default: 0] += 1
    }

    return counts
  }

  private static func neighbors(for cell: Cell) -> [Cell] {
    return [
      Cell(x: cell.x - 1, y: cell.y - 1),
      Cell(x: cell.x,     y: cell.y - 1),
      Cell(x: cell.x + 1, y: cell.y - 1),
      Cell(x: cell.x - 1, y: cell.y),
      Cell(x: cell.x + 1, y: cell.y),
      Cell(x: cell.x - 1, y: cell.y + 1),
      Cell(x: cell.x,     y: cell.y + 1),
      Cell(x: cell.x + 1, y: cell.y + 1),
    ]
  }

  func printColony() {
    for y in 0..<height {
      for x in 0..<width {
        let char = cells.contains(Cell(x: x, y: y)) ? "0" : "."

        print("\(char) ", terminator: "")
      }

      print()
    }
  }

  mutating func run(iterations: Int) {
    print("(0)")
    printColony()
    print()

    for i in 1...iterations {
      print("(\(i))")
      runGeneration()
      printColony()
      print()
    }
  }

  private mutating func runGeneration() {
    cells = Set(neighborCounts().compactMap({keyValue in
      switch (keyValue.value, cells.contains(keyValue.key)) {
      case (2, true), (3, _):
        return keyValue.key
      case _:
        return nil
      }
    }))
  }
}

let blinker = [Cell(x: 1, y: 0), Cell(x: 1, y: 1), Cell(x: 1, y: 2)] as Set

var col = Colony(cells: blinker, height: 3, width: 3)

print("Blinker: ")
col.run(iterations: 3)

let glider = [
  Cell(x: 1, y: 0),
  Cell(x: 2, y: 1),
  Cell(x: 0, y: 2),
  Cell(x: 1, y: 2),
  Cell(x: 2, y: 2)
] as Set

col = Colony(cells: glider, height: 8, width: 8)

print("Glider: ")
col.run(iterations: 20)
Output:
Blinker: 
(0)
. 0 . 
. 0 . 
. 0 . 

(1)
. . . 
0 0 0 
. . . 

(2)
. 0 . 
. 0 . 
. 0 . 

(3)
. . . 
0 0 0 
. . . 

Glider: 
(0)
. 0 . . . . . . 
. . 0 . . . . . 
0 0 0 . . . . . 
. . . . . . . . 
. . . . . . . . 
. . . . . . . . 
. . . . . . . . 
. . . . . . . . 

(1)
. . . . . . . . 
0 . 0 . . . . . 
. 0 0 . . . . . 
. 0 . . . . . . 
. . . . . . . . 
. . . . . . . . 
. . . . . . . . 
. . . . . . . . 

(2)
. . . . . . . . 
. . 0 . . . . . 
0 . 0 . . . . . 
. 0 0 . . . . . 
. . . . . . . . 
. . . . . . . . 
. . . . . . . . 
. . . . . . . . 

(3)
. . . . . . . . 
. 0 . . . . . . 
. . 0 0 . . . . 
. 0 0 . . . . . 
. . . . . . . . 
. . . . . . . . 
. . . . . . . . 
. . . . . . . . 

(4)
. . . . . . . . 
. . 0 . . . . . 
. . . 0 . . . . 
. 0 0 0 . . . . 
. . . . . . . . 
. . . . . . . . 
. . . . . . . . 
. . . . . . . . 

(5)
. . . . . . . . 
. . . . . . . . 
. 0 . 0 . . . . 
. . 0 0 . . . . 
. . 0 . . . . . 
. . . . . . . . 
. . . . . . . . 
. . . . . . . . 

(6)
. . . . . . . . 
. . . . . . . . 
. . . 0 . . . . 
. 0 . 0 . . . . 
. . 0 0 . . . . 
. . . . . . . . 
. . . . . . . . 
. . . . . . . . 

(7)
. . . . . . . . 
. . . . . . . . 
. . 0 . . . . . 
. . . 0 0 . . . 
. . 0 0 . . . . 
. . . . . . . . 
. . . . . . . . 
. . . . . . . . 

(8)
. . . . . . . . 
. . . . . . . . 
. . . 0 . . . . 
. . . . 0 . . . 
. . 0 0 0 . . . 
. . . . . . . . 
. . . . . . . . 
. . . . . . . . 

(9)
. . . . . . . . 
. . . . . . . . 
. . . . . . . . 
. . 0 . 0 . . . 
. . . 0 0 . . . 
. . . 0 . . . . 
. . . . . . . . 
. . . . . . . . 

(10)
. . . . . . . . 
. . . . . . . . 
. . . . . . . . 
. . . . 0 . . . 
. . 0 . 0 . . . 
. . . 0 0 . . . 
. . . . . . . . 
. . . . . . . . 

(11)
. . . . . . . . 
. . . . . . . . 
. . . . . . . . 
. . . 0 . . . . 
. . . . 0 0 . . 
. . . 0 0 . . . 
. . . . . . . . 
. . . . . . . . 

(12)
. . . . . . . . 
. . . . . . . . 
. . . . . . . . 
. . . . 0 . . . 
. . . . . 0 . . 
. . . 0 0 0 . . 
. . . . . . . . 
. . . . . . . . 

(13)
. . . . . . . . 
. . . . . . . . 
. . . . . . . . 
. . . . . . . . 
. . . 0 . 0 . . 
. . . . 0 0 . . 
. . . . 0 . . . 
. . . . . . . . 

(14)
. . . . . . . . 
. . . . . . . . 
. . . . . . . . 
. . . . . . . . 
. . . . . 0 . . 
. . . 0 . 0 . . 
. . . . 0 0 . . 
. . . . . . . . 

(15)
. . . . . . . . 
. . . . . . . . 
. . . . . . . . 
. . . . . . . . 
. . . . 0 . . . 
. . . . . 0 0 . 
. . . . 0 0 . . 
. . . . . . . . 

(16)
. . . . . . . . 
. . . . . . . . 
. . . . . . . . 
. . . . . . . . 
. . . . . 0 . . 
. . . . . . 0 . 
. . . . 0 0 0 . 
. . . . . . . . 

(17)
. . . . . . . . 
. . . . . . . . 
. . . . . . . . 
. . . . . . . . 
. . . . . . . . 
. . . . 0 . 0 . 
. . . . . 0 0 . 
. . . . . 0 . . 

(18)
. . . . . . . . 
. . . . . . . . 
. . . . . . . . 
. . . . . . . . 
. . . . . . . . 
. . . . . . 0 . 
. . . . 0 . 0 . 
. . . . . 0 0 . 

(19)
. . . . . . . . 
. . . . . . . . 
. . . . . . . . 
. . . . . . . . 
. . . . . . . . 
. . . . . 0 . . 
. . . . . . 0 0 
. . . . . 0 0 . 

(20)
. . . . . . . . 
. . . . . . . . 
. . . . . . . . 
. . . . . . . . 
. . . . . . . . 
. . . . . . 0 . 
. . . . . . . 0 
. . . . . 0 0 0

SystemVerilog

Note using non-blocking assignments, so that the code behaves as if every cell is updated in parallel on each clock edge. (I didn't need to use a clock here, but doing so looks more like standard verilog coding that is familiar to hardware designers).

module gol;

  parameter NUM_ROWS = 20;
  parameter NUM_COLS = 32;

  bit [NUM_COLS:1] cell[1:NUM_ROWS];
  bit clk;

  initial begin
    cell[10][10:8] = 3'b111;
    cell[11][10:8] = 3'b100;
    cell[12][10:8] = 3'b010;
    repeat(8) #5 clk = ~clk;
  end

  always @(posedge clk) begin
    foreach (cell[y,x]) begin
      automatic int count = $countones({ cell[y-1][x-1+:3], cell[y][x-1], cell[y][x+1], cell[y+1][x-1+:3] });
      if (count == 3) cell[y][x] <= 1'b1;
      else if (count != 2) cell[y][x] <= 1'b0;
    end
  end

  always @(negedge clk) begin
    $display("--");
    foreach (cell[y]) $display( "  %b", cell[y] );
  end

endmodule

Tcl

Works with: Tcl version 8.5
package require Tcl 8.5 

proc main {} {
    evolve 3 blinker [initialize_tableau {3 3} {{0 1} {1 1} {2 1}}]
    evolve 5 glider  [initialize_tableau {4 4} {{0 1} {1 2} {2 0} {2 1} {2 2}}]
}

proc evolve {generations name tableau} {
    for {set gen 1} {$gen <= $generations} {incr gen} {
        puts "$name generation $gen:"
        print $tableau
        set tableau [next_generation $tableau]
    }
    puts ""
}

proc initialize_tableau {size initial_life} {
    lassign $size ::max_x ::max_y 
    set tableau [blank_tableau]
    foreach point $initial_life {
        lset tableau {*}$point 1
    }
    return $tableau
}

proc blank_tableau {} {
    return [lrepeat $::max_x [lrepeat $::max_y 0]]
}

proc print {tableau} {
    foreach row $tableau {puts [string map {0 . 1 #} [join $row]]}
}

proc next_generation {tableau} {
    set new [blank_tableau]
    for {set x 0} {$x < $::max_x} {incr x} {
        for {set y 0} {$y < $::max_y} {incr y} {
            lset new $x $y [fate [list $x $y] $tableau]
        }
    }
    return $new
}

proc fate {point tableau} {
    set current [value $point $tableau]
    set neighbours [sum_neighbours $point $tableau]
    return [expr {($neighbours == 3) || ($neighbours == 2 && $current == 1)}]
}

proc value {point tableau} {
    return [lindex $tableau {*}$point]
}

proc sum_neighbours {point tableau} {
    set sum 0
    foreach neighbour [get_neighbours $point] {
        incr sum [value $neighbour $tableau]
    }
    return $sum
}

proc get_neighbours {point} {
    lassign $point x y
    set results [list]
    foreach x_off {-1 0 1} {
        foreach y_off {-1 0 1} {
            if { ! ($x_off == 0 && $y_off == 0)} {
                set i [expr {$x + $x_off}] 
                set j [expr {$y + $y_off}]
                if {(0 <= $i && $i < $::max_x) && (0 <= $j && $j < $::max_y)} {
                    lappend results [list $i $j]
                }
            }
        }
    }
    return $results
}

main
blinker generation 1:
. # .
. # .
. # .
blinker generation 2:
. . .
# # #
. . .
blinker generation 3:
. # .
. # .
. # .

glider generation 1:
. # . .
. . # .
# # # .
. . . .
glider generation 2:
. . . .
# . # .
. # # .
. # . .
glider generation 3:
. . . .
. . # .
# . # .
. # # .
glider generation 4:
. . . .
. # . .
. . # #
. # # .
glider generation 5:
. . . .
. . # .
. . . #
. # # #

UNIX Shell

Works with: Bourne Again SHell
Works with: Korn Shell
Works with: Z Shell
# Shells only have 1-dimensional arrays, so each row is one string
function main {
  typeset blinker=(000 111 000)
  run list 4 "${blinker[@]}"
}

function run { 
  typeset mode=$1 # screen or list
  shift
  typeset -i limit=0
  if (( $1 > 1 )); then
    limit=$1
    shift
  fi
  if [[ mode == screen ]]; then
    clear
  fi
  typeset universe=("$@")
  typeset -i generation=0
  while (( !limit || generation < limit )); do
    if [[ mode == screen ]]; then
      printf '\e[H'
    else
      printf '\n'
    fi
    printf 'Generation %d\n' "$generation"
    disp "${universe[@]}" | tr '01' '.@'
    universe=($(next_generation "${universe[@]}"))
    (( generation += 1 ))
    sleep 0.125
  done
}

# display a matrix
function disp {
  # remove sed for more compact display
  printf '%s\n' "$@" | sed 's/./ &/g'
}

# center a matrix within a given size by padding with 0s
function center {
  typeset height=$1 width=$2
  shift 2
  typeset -i offset_i offset_j i j
  if (( $# > height || ${#1} > width )); then
    printf >&2 'Source larger than target.\n'
    return 1
  fi
  (( offset_i = (height - $#) / 2 ))
  (( offset_j = (width - ${#1}) / 2 ))
  typeset prefix zeroes suffix
  for (( j=0; j<width; ++j )); do
    zeroes+=0
    if (( j < offset_j )); then
      prefix+=0
    elif (( j >= offset_j+${#1} )); then
      suffix+=0
    fi
  done
  for (( i=0; i<offset_i; ++i )); do
    printf '%s\n' "$zeroes"
  done
  while (( $# )); do
    printf '%s%s%s\n' "$prefix" "$1" "$suffix"
    shift
    (( i++ ))
  done
  while (( i++ < height )); do
    printf '%s\n' "$zeroes"
  done
}

# compute the next generation
# the grid is finite; pass -t to treat as torus (wraparound), otherwise it's
# bounded by always-dead cells
next_generation() {
  typeset -i torus=0
  if [[ $1 == -t ]]; then
    torus=1
    shift
  fi
  # cache cells in an associative array
  # (for fast lookup when counting neighbors)
  typeset -A cells
  typeset -i i=0 j=0 height=$# width=${#1}
  while (( $# )); do
    row=$1
    shift
    for (( j=0; j<${#row}; ++j )); do
      cells[$i,$j]=${row:$j:1}
    done
    (( i+=1 ))
  done
  typeset -i di dj ni nj n cell
  for (( i=0; i<height; ++i )); do
    for (( j=0; j<width; ++j )); do
      n=0
      for (( di=-1; di<2; ++di )); do
        (( ni = i + di ))
        if (( torus )); then
          (( ni = (ni + height) % height ))
        fi
        for (( dj=-1; dj<2; ++dj )); do
          (( nj = j + dj ))
          if (( torus )); then
            (( nj = (nj + width) % width ))
          fi
          if (( (di || dj) && ni >= 0 && nj >= 0 && ni < height && nj < width  )); then
            (( n += ${cells[$ni,$nj]} ))
          fi
        done
      done
      printf '%d' "$(( ( n == 3 ) || ( ${cells[$i,$j]} && n==2 ) ))"
    done
    printf '\n'
  done
}

main "$@"
Output:
Generation 0
 . . .
 @ @ @
 . . .

Generation 1
 . @ .
 . @ .
 . @ .

Generation 2
 . . .
 @ @ @
 . . .

Generation 3
 . @ .
 . @ .
 . @ .

Ursala

Three functions are defined: rule takes a pair (c,<n..>) representing a cell and its list of neighboring cells to the new cell, neighborhoods takes board of cells <<c..>..> to a structure <<(c,<n..>)..>..> explicitly pairing each cell with its neighborhood, and evolve(n) takes a board <<c..>..> to a sequence of n boards evolving from it.

#import std
#import nat

rule = -: ^(~&,~&l?(~&r-={2,3},~&r-={3})^|/~& length@F)* pad0 iota512

neighborhoods = ~&thth3hthhttPCPthPTPTX**K7S+ swin3**+ swin3@hNSPiCihNCT+ --<0>*+ 0-*

evolve "n" = next"n" rule**+ neighborhoods

test program:

blinker =

(==`O)**t -[
+++
OOO
+++]-

glider =

(==`O)**t -[
+O++++
++O+++
OOO+++
++++++
++++++]-

#show+

examples = mat0 ~&?(`O!,`+!)*** evolve3(blinker)-- evolve5(glider)
Output:
+++
OOO
+++

+O+
+O+
+O+

+++
OOO
+++

+O++++
++O+++
OOO+++
++++++
++++++

++++++
O+O+++
+OO+++
+O++++
++++++

++++++
++O+++
O+O+++
+OO+++
++++++

++++++
+O++++
++OO++
+OO+++
++++++

++++++
++O+++
+++O++
+OOO++
++++++

Vedit macro language

This implementation uses an edit buffer for data storage and to show results. For purpose of this task, the macro writes the initial pattern in the buffer. However, easier way to enter patterns would be by editing them directly in the edit buffer before starting the macro (in which case the Ins_Text commands would be omitted).

The macro calculates one generation and then waits for a key press before calculating the next generation.

The algorithm used is kind of reverse to the one normally used in Life implementations. Instead of counting cells around each location, this implementation finds each living cell and then increments the values of the 8 surrounding cells. After going through all the living cells, each location of the grid contains an unique ascii value depending on the original value (dead or alive) and the number of living cells in surrounding positions. Two Replace commands are then used to change characters into '.' or 'O' to represent dead and living cells in the new generation.

IT("Generation 0    ") IN
IT(".O.") IN
IT(".O.") IN
IT(".O.")

#9  = 2		  // number of generations to calculate
#10 = Cur_Line
#11 = Cur_Col-1
for (#2 = 1; #2 <= #9; #2++) {
    Update()
    Get_Key("Next gen...", STATLINE)
    Call("calculate")
    itoa(#2, 20, LEFT)
    GL(1) GC(12) Reg_Ins(20, OVERWRITE)
}
EOF
Return

// Calculate one generation
:calculate:
Goto_Line(2)
While (At_EOF == 0) {
  Search("|A",ERRBREAK)		// find next living cell
  #3 = Cur_Line
  #4 = #7 = #8 = Cur_Col
  if (#4 > 1) {			// increment cell at left
      #7 = #4-1
      Goto_Col(#7)
      Ins_Char(Cur_Char+1,OVERWRITE)
  }
  if (#4 < #11) {		// increment cell at right
      #8 = #4+1
      Goto_Col(#8)
      Ins_Char(Cur_Char+1,OVERWRITE)
  }
  if (#3 > 2) {			// increment 3 cells above
      Goto_Line(#3-1)
      Call("inc_3")
  }
  if (#3 < #10) {		// increment 3 cells below
      Goto_Line(#3+1)
      Call("inc_3")
  }
  Goto_Line(#3)
  Goto_Col(#4+1)
}

Replace("[1QR]", "O", REGEXP+BEGIN+ALL)	    // these cells alive
Replace("[/-7P-X]", ".", REGEXP+BEGIN+ALL)  // these cells dead
Return

// increment values of 3 characters in a row
:inc_3:
for (#1 = #7; #1 <= #8; #1++) {
  Goto_Col(#1)
  Ins_Char(Cur_Char+1,OVERWRITE)
}
Return
Output:
Generation 0    
.O.
.O.
.O.

Generation 1    
...
OOO
...

Generation 2    
.O.
.O.
.O.

Wortel

Mapping over a matrix.

@let {
  life &m ~!* m &[a y] ~!* a &[v x] @let {
    neigh @sum [
      @`-x 1 @`-y 1 m  @`x @`-y 1 m  @`+x 1 @`-y 1 m
      @`-x 1 @`y    m                @`+x 1 @`y    m
      @`-x 1 @`+y 1 m  @`x @`+y 1 m  @`+x 1 @`+y 1 m
    ]
    @+ || = neigh 3 && v = neigh 2
  }

  blinker [
    [0 0 0 0 0]
    [0 0 0 0 0]
    [0 1 1 1 0]
    [0 0 0 0 0]
    [0 0 0 0 0]
  ]

  [[
    !^life 0 blinker
    !^life 1 blinker
    !^life 2 blinker
  ]]
}
Output:
[
 [[0 0 0 0 0]
  [0 0 0 0 0]
  [0 1 1 1 0]
  [0 0 0 0 0]
  [0 0 0 0 0]]
 [[0 0 0 0 0]
  [0 0 1 0 0]
  [0 0 1 0 0]
  [0 0 1 0 0]
  [0 0 0 0 0]]
 [[0 0 0 0 0]
  [0 0 0 0 0]
  [0 1 1 1 0]
  [0 0 0 0 0]
  [0 0 0 0 0]]
]

Different solution by using functions that operate on matrices.

@let {
  ; Translation of the APL game of life (http://catpad.net/michael/apl/).
  life &m @let {
    ; create functions that work on two matrices
    makemf  &f @[\@mapm @[\@mapm f ^@,] ^@,]
    addm    !makemf ^+
    orm     !makemf ^||
    andm    !makemf ^&&
    eqm     !makemf ^=

    ; bool matrix to number matrix
    tonum   *^*^@+
    
    ; create a matrix of value v in the shape of matrix m
    repm    &[v m] @rep #m &,@rep #m.0 v

    ; move a matrix in directions by padding zeroes
    movel   \!*~t0j
    mover   \!*~i0SO
    moveu   &m ~, &,@rep #m.0 0 !~t m
    moved   &m  , &,@rep #m.0 0 !~i m

    ; cache up and down
    mu      !moveu m
    md      !moved m

    ; calculate the neighbours
    neigh   !/addm [
      !movel mu  mu  !mover mu
      !movel m       !mover m
      !movel md  md  !mover md
    ]
 
    ; ((neigh = 2) AND m) OR (neigh = 3)
    ; (2 neighbours AND alive) OR (3 neighbours)
    !tonum !!orm !!andm m !!eqm neigh !!repm 2 m
                 !!eqm neigh !!repm 3 m
  }

  blinker [
    [0 0 0 0 0]
    [0 0 0 0 0]
    [0 1 1 1 0]
    [0 0 0 0 0]
    [0 0 0 0 0]
  ]

  [[
    !^life 0 blinker
    !^life 1 blinker
    !^life 2 blinker
  ]]
}
Output:
[
 [[0 0 0 0 0]
  [0 0 0 0 0]
  [0 1 1 1 0]
  [0 0 0 0 0]
  [0 0 0 0 0]]
 [[0 0 0 0 0]
  [0 0 1 0 0]
  [0 0 1 0 0]
  [0 0 1 0 0]
  [0 0 0 0 0]]
 [[0 0 0 0 0]
  [0 0 0 0 0]
  [0 1 1 1 0]
  [0 0 0 0 0]
  [0 0 0 0 0]]
]

VBScript

I have used ANSI escape codes, so the program will not whork from W2000 to W8.1, where Microsoft did see fit to remove support to these codes. The game wraps around at borders, so the gliders are always alive. Must be invoked from cscript.

option explicit
const tlcr=3, tlcc=3
const maxdim=15

dim a(15,15)
dim b(15,15)
dim ans0:ans0=chr(27)&"["
dim gen,n

erase a
'glider
a(0,1)=true:a(1,2)=true:a(2,0)=true:a(2,1)=true:a(2,2)=true
'blinker
a(3,13)=true:a(4,13)=true:a(5,13)=true
'beacon
a(11,1)=true:a(11,2)=true: a(12,1)=true:a(12,2)=true
a(13,3)=true:a(13,4)=true: a(14,3)=true:a(14,4)=true

gen=0
doframe

do
  display 
  wscript.sleep(100)
  n=newgen
loop until n=0
display 

sub cls()  wscript.StdOut.Write ans0 &"2J"&ans0 &"?25l":end sub 'hide cursor too
sub toxy(r,c,s)  wscript.StdOut.Write ans0 & r & ";" & c & "f"  & s :end sub
function iif(a,b,c) if a then iif=b else iif=c end if :end function

sub doframe
  dim r,c,s
	const frame="@"
	cls
	toxy 1,tlcc-1, "Conway's Game of Life"
	toxy tlcr-1,tlcc-1,string(maxdim+3,frame)
	s=frame&space(maxdim+1)&frame
	for r=0 to maxdim
		toxy tlcr+r,tlcc-1,s
	next
	toxy tlcr+maxdim+1,tlcc-1,string(maxdim+3,frame)
end sub

sub display 
dim r,c
const pix="#"
for r=0 to maxdim
   for c=0 to maxdim
	   toxy tlcr+r,tlcc+c,iif (a(r,c),pix," ") 
	 next
next
toxy tlcr+maxdim+2,tlcc-1,gen & " " & n
toxy tlcr+maxdim+3,tlcc-1,""
gen=gen+1
end sub

function newgen
  dim r,c,cnt,cp,cm,rp,rm
	for r=0 to maxdim
	  for c=0 to maxdim
			cp=(c+1) and maxdim    'wrap around
			cm=(c-1) and maxdim
			rp=(r+1) and maxdim
			rm=(r-1) and maxdim
			cnt=0
			cnt=- a(rp,cp) - a(rp,c) - a(rp,cm)  'true =-1
			cnt=cnt- a(r,cp)-	 a(r,cm)	
			cnt=cnt- a(rm,cp)- a(rm,c) - a(rm,cm)  
			 
			if a(r,c) then 
				b(r,c)=iif (cnt=2 or cnt=3,true,false)
			else
				b(r,c)=iif (cnt=3,true,false)					
			end if
	  next 
	next
	for r=0 to maxdim
	  for c=0 to maxdim
		  a(r,c)=b(r,c)
		  newgen=newgen- b(r,c)
	  next
	next
end function
 Conway's Game of Life
 @@@@@@@@@@@@@@@@@@
 @                @
 @                @
 @                @
 @    #        #  @
 @  # #        #  @
 @   ##        #  @
 @                @
 @                @
 @                @
 @                @
 @                @
 @ ##             @
 @ #              @
 @    #           @
 @   ##           @
 @                @
 @@@@@@@@@@@@@@@@@@
 9 14

A fast version using a thechnique from Abrash's Black Book. Set your console to 34 rows minimum, as it uses a 32x32 cells world

option explicit
const pix="##"
const cl_on=16
const cl_mnum=15
randomize timer
const tlcr=2, tlcc=2
const maxdim =31
settitle "Conway's game of life"

dim a(31,31)

dim ans0:ans0=chr(27)&"["
dim gen,n
gen=0
paintframe
'init1      'objects 
init2 400   'random

do
  n=nextgen
  toxy tlcr-1,tlcc+maxdim*2+4,gen & " " & n
  toxy tlcr,tlcc+maxdim*2+3,""
  gen=gen+1
loop until n=0

sub pause() wscript.stdout.write vbcrlf & "Press Enter":wscript.stdin.readline: end sub
sub settitle(s)  wscript.StdOut.Write chr(27)&"]0;"& s &chr(7):end sub
sub cls()  wscript.StdOut.Write ans0 &"2J"&ans0 &"?25l":end sub
sub toxy(r,c,s)  wscript.StdOut.Write ans0 & r & ";" & c & "f"  & s :end sub
function iif(a,b,c) if a then iif=b else iif=c end if :end function

sub init1 
dim x
update 0,1,1,x:update 1,2,1,x:update 2,0,1,x:update 2,1,1,x:update 2,2,1,x
update 3,13,1,x:update 4,13,1,x:update 5,13,1,x
update 11,1,1,x:update 11,2,1,x: update 12,1,1,x:update 12,2,1,x
update 13,3,1,x:update 13,4,1,x: update 14,3,1,x:update 14,4,1,x
end sub

sub init2 (n)
dim i,r,c,x
for i=1 to n
   do
     r=cint(rnd*maxdim)
     c=cint(rnd*maxdim)
   loop until (a(r,c) and cl_on)=0
   update r,c,1,x
next
end sub

sub paintframe
  dim r,c,s
  const frame="@"
  cls
  'toxy 1,tlcc-1, "Conway's Game of Life"
  toxy tlcr-1,tlcc-1,string(maxdim*2+4,frame)
  s=frame&space(maxdim*2+2)&frame
  for r=0 to maxdim
    toxy tlcr+r,tlcc-1,s
  next
  toxy tlcr+maxdim+1,tlcc-1,string(maxdim*2+4,frame)
end sub

function nextgen()
  dim r,c,pre,cnt,a1,onoff,chg
  nextgen=0
  a1=a                                 'does a hard a copy of a
  for r=0 to maxdim
    for c=0 to maxdim
      if a1(r,c)then                'check only cells alive or having neighbors
        pre=a1(r,c) and cl_on
        cnt=a1(r,c) and cl_mnum
        'check life condition and update cell
        if pre<>0  and  (cnt<2 or cnt>3)  then
          update r,c,0,nextgen
        elseif pre=0  and cnt=3 then
          update r,c,1,nextgen
        end if
      end if
    next
   next
end function

sub update(r,c,onoff,nextgen)
'displays cell and update neighbors count in neighbors
dim cp,cm,rp,rm,inc,mask
   mask=iif(onoff,cl_on,0)
   a(r,c)= (a(r,c) and cl_mnum) or mask       'update cell
   toxy tlcr+r,tlcc+c*2,iif (onoff,pix,"  ")  'display cell
   cp=(c+1) and maxdim                 'wrap around
   cm=(c-1) and maxdim
   rp=(r+1) and maxdim
   rm=(r-1) and maxdim
   if onoff then inc=1 else inc=-1
   'update count in neighbors
   a(rp,cp)=(a(rp,cp) and cl_on) or ((a(rp,cp) and cl_mnum)+inc)
   a(rp,c)=(a(rp,c) and cl_on) or ((a(rp,c) and cl_mnum)+inc)
   a(rp,cm)=(a(rp,cm) and cl_on) or ((a(rp,cm) and cl_mnum)+inc)
   a(r,cp)=(a(r,cp) and cl_on) or ((a(r,cp) and cl_mnum)+inc)
   a(r,cm)=(a(r,cm) and cl_on) or ((a(r,cm) and cl_mnum)+inc)
   a(rm,cp)=(a(rm,cp) and cl_on) or ((a(rm,cp) and cl_mnum)+inc)
   a(rm,c)=(a(rm,c) and cl_on) or ((a(rm,c) and cl_mnum)+inc)
   a(rm,cm)=(a(rm,cm) and cl_on) or ((a(rm,cm) and cl_mnum)+inc)
   nextgen=nextgen+1
end sub

V (Vlang)

Translation of: Go
import rand
import strings
import time

struct Field {
mut:
	s    [][]bool
	w int
	h int
}
 
fn new_field(w int, h int) Field {
	s := [][]bool{len: h, init: []bool{len: w}}
	return Field{s, w, h}
}
 
fn (mut f Field) set(x int, y int, b bool) {
	f.s[y][x] = b
}
 
fn (f Field) next(x int, y int) bool {
	mut on := 0
	for i := -1; i <= 1; i++ {
		for j := -1; j <= 1; j++ {
			if f.state(x+i, y+j) && !(j == 0 && i == 0) {
				on++
			}
		}
	}
	return on == 3 || (on == 2 && f.state(x, y))
}
 
fn (f Field) state(xx int, yy int) bool {
	mut x, mut y := xx, yy
	for y < 0 {
		y += f.h
	}
	for x < 0 {
		x += f.w
	}
	return f.s[y%f.h][x%f.w]
}
 
struct Life {
mut:
	w int
	h int
	a Field
	b Field
}
 
fn new_life(w int, h int) Life {
	mut a := new_field(w, h)
	for _ in 0..(w * h / 2) {
		a.set(rand.intn(w) or {0}, rand.intn(h) or {0}, true)
	}
	return Life{
		a: a,
		b: new_field(w, h),
		w: w
		h: h,
	}
}
 
fn (mut l Life) step() {
	for y in 0..l.h {
		for x in 0.. l.w {
			l.b.set(x, y, l.a.next(x, y))
		}
	}
	l.a, l.b = l.b, l.a
}
 
fn (l Life) str() string {
	mut buf := strings.new_builder(128)
	for y in 0..l.h {
		for x in 0..l.w {
			mut b := ' '
			if l.a.state(x, y) {
				b = '*'
			}
			buf.write_string(b)
		}
		buf.write_string('\n')
	}
	return buf.str()
}
 
fn main() {
	mut l := new_life(80, 15)
	for i := 0; i < 300; i++ {
		l.step()
		//println("------------------------------------------------")
		print('\x0c')
		println(l)
		time.sleep(time.second / 30)
	}
}
Output:

Generation 300:

               **                                                   ***   *     
                *                                                         **    
                *           *                                             **    
                           ** **              **                           *    
                              **              **                                
                       ** *** * *                                               
                   ******  *                                                    
                   * *                                          **              
                   * * **                                      *  *             
                    **                                          * *      **     
             **      * *     *                                   *       **     
            *  *           ** **                                                
            * *            ** *                                                 
              **             *  

Wren

Translation of: Kotlin
import "random" for Random
import "timer" for Timer

var Rand = Random.new(0) // using a constant seed to produce same output on each run

// patterns
var BLINKER = 0
var GLIDER  = 1
var RANDOM  = 2

class Field {
    construct new(w, h) {
        _w = w
        _h = h
        _s = List.filled(h, null)
        for (i in 0...h) _s[i] = List.filled(w, false)
    }

    [x, y]=(b) { _s[y][x] = b }

    state(x, y) {
        if (!(0..._w).contains(x) || !(0..._h).contains(y)) return false
        return _s[y][x]
    }

    next(x, y) {
        var on = 0
        for (i in -1..1) {
            for (j in -1..1) {
                 if (state(x + i, y + j) && !(j == 0 && i == 0)) on = on + 1
            }
        }
        return on == 3 || (on == 2 && state(x, y))
    }
}

class Life {
    construct new(pattern) {
        if (pattern == BLINKER) {
            _w = 3
            _h = 3
            _a = Field.new(_w, _h)
            _b = Field.new(_w, _h)
            _a[0, 1] = true
            _a[1, 1] = true
            _a[2, 1] = true
        } else if (pattern == GLIDER) {
            _w = 4
            _h = 4
            _a = Field.new(_w, _h)
            _b = Field.new(_w, _h)
            _a[1, 0] = true
            _a[2, 1] = true
            for (i in 0..2) _a[i, 2] = true
        } else if(pattern == RANDOM) {
             _w = 80
             _h = 15
             _a = Field.new(_w, _h)
             _b = Field.new(_w, _h)
            for (i in 0...(_w * _h).floor / 2) {
                _a[Rand.int(_w), Rand.int(_h)] = true
            }
        }
    }

    step() {
        for (y in 0..._h) {
            for (x in 0..._w) _b[x, y] = _a.next(x, y)
        }
        var t = _a
        _a = _b
        _b = t
    }

    toString {
        var sb = ""
        for (y in 0..._h) {
            for (x in 0..._w) {
                var c = _a.state(x, y) ? "#" : "."
                sb = sb + c
            }
            sb = sb + "\n"
        }
        return sb
    }
}

var lives = [
    [Life.new(BLINKER),  3, "BLINKER"],
    [Life.new(GLIDER),   4, "GLIDER" ],
    [Life.new(RANDOM), 100, "RANDOM" ]
]

for (t in lives) {
    var game  = t[0]
    var gens  = t[1]
    var title = t[2]
    System.print("%(title):\n")
    for (i in 0..gens) {
        System.print("Generation: %(i)\n%(game)")
        Timer.sleep(30)
        game.step()
    }
    System.print()
}
Output:

Just shows generations 0 and 100 for RANDOM pattern:

BLINKER:

Generation: 0
...
###
...

Generation: 1
.#.
.#.
.#.

Generation: 2
...
###
...

Generation: 3
.#.
.#.
.#.


GLIDER:

Generation: 0
.#..
..#.
###.
....

Generation: 1
....
#.#.
.##.
.#..

Generation: 2
....
..#.
#.#.
.##.

Generation: 3
....
.#..
..##
.##.

Generation: 4
....
..#.
...#
.###


RANDOM:

Generation: 0
#.#.###.#...#...#..##.....#......#....#...#.....#...#..#..#.....##.##....#..####
..#...#....#.##..#..#...##.#.....#....#..##.#.###..#.#.#.#..#.##..#.#.......#.#.
###.###..##...#......#.#.#............#.......##.#..#...###.##..#...###...#..#..
.#.....#.#.#.#.#..###.#.#.######...##..##.###.####....#....#####..##...####.#..#
..##.###.#..###...#..#..##....##...#..##.##.#..###.#..#..#.#...##..#..###.......
.####..###.##..#..#...#..#..#.##..#..........##.#..#.....#.###.#...######.#..#..
...##...#.....##.....##.##..#..#####...##.###.#.###..#..#.#.....##.#..##....##.#
##...##.#...#.#...##.##..#.#..##.#....###.##.#.....#.##..#..#.##..#....##......#
....#.#..##.#..####..#..##....#####.#....#.#...#.#.###.#.#.#.#.#.....#...#.....#
..#..####..###..###..##.####.#....#.....#.###.#.#.###.####..#...#...#...#.##....
#.........##..#..##...###...#..#....#.###...#.##.....###..###..##....###.#..#...
.#..#..#......#...##.###.#...#.#...##.#.....#...#......##..#.....###...##..#.#..
.#.#.....##..#.##.....#.#.#..#.#..######.#....#..##...##.##.....#..##...#.##.##.
.#......###..#...###..........................##......#....####.#...#..#...#..#.
#..#.#......#...#...#...#..#..##...#.##...#.####.##......#....#..#.##.....#####.

Generation: 100
...............####......#......................................................
...............#..#.....#.#...................#.................................
........................#.#.................##..................................
.........................#..................##............##....................
............................................#.....#.......##....................
.............................................#.###..............................
...................................##...###.....#####...........................
........................##........#..#..###........#............................
.......................#..#...........#....##...................................
.......................#....#.......#....###....................................
........................######.....##....##.....................................
...........................#.##.....#..#..........................##.##.........
...........................#.#.......##...........................##.##.........
......##...................##...................................................
......##........................................................................

XPL0

def     M=3;                    \array size
char    NowGen(M+2, M+2),       \size with surrounding borders
        NewGen(M+2, M+2);
int     X, Y, I, J, N, Gen;
code    ChOut=8, CrLf=9;

[for Y:= 0 to M+1 do            \set up initial state
    for X:= 0 to M+1 do
        [NowGen(X,Y):= ^ ;  NewGen(X,Y):= ^ ];
NowGen(1,2):= ^#;  NowGen(2,2):= ^#;  NowGen(3,2):= ^#;

for Gen:= 1 to 3 do
        [for Y:= 1 to M do                      \show current generation
            [for X:= 1 to M do [ChOut(0, NowGen(X,Y));  ChOut(0,^ )];
            CrLf(0);
            ];
        CrLf(0);

        for Y:= 1 to M do                       \determine next generation
            for X:= 1 to M do
                [N:= 0;                         \count adjacent live (#) cells
                for J:= Y-1 to Y+1 do
                    for I:= X-1 to X+1 do
                        if NowGen(I,J) = ^# then N:= N+1;
                if NowGen(X,Y) = ^# then N:= N-1;       \don't count center
                NewGen(X,Y):= ^ ;                       \assume death
                if N=2 then NewGen(X,Y):= NowGen(X,Y)   \actually no change
                else if N=3 then NewGen(X,Y):= ^#;      \actually birth
                ];
        I:= NowGen;  NowGen:= NewGen;  NewGen:= I;      \swap arrays
        ];
]
Output:
      
# # # 
      

  #   
  #   
  #   

      
# # #

XSLT

So when the following templates

<xsl:template match="/table">
    <table>
        <xsl:apply-templates />
    </table>
</xsl:template>

<xsl:template match="tr">
    <tr><xsl:apply-templates /></tr>
</xsl:template>

<xsl:template match="td">
    <xsl:variable name="liveNeighbours">
        <xsl:apply-templates select="current()" mode="countLiveNeighbours" />
    </xsl:variable>

    <xsl:choose>
        <xsl:when test="(current() = 'X' and $liveNeighbours = 2) or $liveNeighbours = 3">
            <xsl:call-template name="live" />
        </xsl:when>
        <xsl:otherwise>
            <xsl:call-template name="die" />
        </xsl:otherwise>
    </xsl:choose>
</xsl:template>

<xsl:template match="td" mode="countLiveNeighbours">
    <xsl:variable name="currentX" select="count(preceding-sibling::td) + 1" />
    <xsl:variable name="precedingRow" select="parent::tr/preceding-sibling::tr[1]" />
    <xsl:variable name="followingRow" select="parent::tr/following-sibling::tr[1]" />

    <xsl:variable name="neighbours" select="$precedingRow/td[$currentX - 1] |
                                            $precedingRow/td[$currentX] |
                                            $precedingRow/td[$currentX + 1] |
                                            preceding-sibling::td[1] |
                                            following-sibling::td[1] |
                                            $followingRow/td[$currentX - 1] |
                                            $followingRow/td[$currentX] |
                                            $followingRow/td[$currentX + 1]" />

    <xsl:value-of select="count($neighbours[text() = 'X'])" />
</xsl:template>

<xsl:template name="die">
    <td>_</td>
</xsl:template>

<xsl:template name="live">
    <td>X</td>
</xsl:template>

are applied against the document

<table>
    <tr><td>_</td><td>X</td><td>_</td></tr>
    <tr><td>_</td><td>X</td><td>_</td></tr>
    <tr><td>_</td><td>X</td><td>_</td></tr>
</table>

then the transformed XML document contains the new universe evolved by one tick:

<table>
    <tr><td>_</td><td>_</td><td>_</td></tr>
    <tr><td>X</td><td>X</td><td>X</td></tr>
    <tr><td>_</td><td>_</td><td>_</td></tr>
</table>

Z80 Assembly

Works with: zmac version 5nov2016

This code will run on an MSX computer if progammed on a cartride or on an emulator (like openMSX) if loaded as a .rom file

The code below will show the Gosper glider gun, but if INITLINES is set to 0 the code will show the blinker

;MSX Bios calls
CHPUT     equ 000A2H          ;print character A
CHGET     equ 0009FH          ;wait for keyboard input
INITXT    equ 0006CH          ;init TEXT1 mode (40 x 24), based on TXTNAM,TXTCGP and LINL40
LDIRVM    equ 0005CH          ;write BC times MEM(HL++) to VRAM(DE++) 

;MSX system variables
TXTNAM    equ 0F3B3H          ;pattern name table
TXTCGP    equ 0F3B7H          ;pattern generator table
LINL40    equ 0F3AEH          ;line length

;defines
LIFE_CHAR equ 0xDB            ;MSX all-pixels-on character

;variables
screen    equ 0E000H          ;40x24 bytes
scratch   equ screen+(40*24)  ;table for calculations


          org 04000H
;*********************************************************************
HEADER    ;first 16 bytes of the rom. (as specified by MSX standard)
;*********************************************************************
          db "AB"             ;id
          dw Main             ;init
          dw 0                ;statement
          dw 0                ;device
          dw 0                ;text
          dw 0                ;reserved
          dw 0                ;reserved
          dw 0                ;reserved

init_tab1 db 0x18
          dc 7, 0x17 
          db " Conway's Game Of Life "
          dc 8, 0x17
          db 0x19
          db 0x16
          dc 38, " "
          db 0x16, 0x1A
          dc 38, 0x17
          db 0x1B
init_tab2 dc 41, 0x80
          dc 38, 0
          dc 41, 0x80

INITLINES equ 10
init_tab3 db "                                        "
          db "                          X             "
          db "                        X X             "
          db "              XX      XX            XX  "
          db "             X   X    XX            XX  "
          db "  XX        X     X   XX                "
          db "  XX        X   X XX    X X             "
          db "            X     X       X             "
          db "             X   X                      "
          db "              XX                        "

Expand    ld bc, 40
          ldir                ;copy top line
          push de
          ld bc, 40
          ldir                ;copy first middle line
          ex (sp), hl
          ld bc, 40*21
          ldir                ;repeat middle line
          pop hl
          ld bc, 40           ;copy bottom line
          ldir
          ret

InitGOL   ;create empty screen
          ld hl, init_tab1
          ld de, screen
          call Expand
          ;Now add intial pattern
if INITLINES
          ld hl, init_tab3    ;glider gun start pattern
          ld de, init_tab3    ;de=hl, so ldi does not change RAM
          ld bc, 40*INITLINES
          ld ix, screen+40
InitGOLl  ld a, (hl)
          cp 'X'
          jr nz, InitGOLe
          ld (ix), LIFE_CHAR
InitGOLe  inc ix
          ldi                 ;hl++ and bc-- (with flag!)
          jp pe, InitGOLl          
else
          ld hl, screen+(4*40)+18
          ld a, LIFE_CHAR     ;blinker start pattern
          ld (hl), a
          inc hl
          ld (hl), a
          inc hl
          ld (hl), a
endif
          ret
          
DoGOL     ld hl, init_tab2    ;initialize scratchpad (sums to zero, borders marked)
          ld de, scratch
          call Expand
          ;first loop: create sums in scratchpad
          ld bc, 40*24
          ld hl, screen
          ld de, screen       ;de=hl, so ldi does not change RAM
          ld ix, scratch          
DoGOLsuml ld a, (hl)
          cp LIFE_CHAR        ;if cell is alive increase sums of all surrounding cells
          jr nz, DoGOLsume
          inc (ix-41)
          inc (ix-40)
          inc (ix-39)
          inc (ix-1)
          inc (ix+1)
          inc (ix+39)
          inc (ix+40)
          inc (ix+41)
DoGOLsume inc ix
          ldi                 ;hl++, bc-- (with flag!)
          jp pe, DoGOLsuml
          ;second loop: update cell based on current state and sum
          ld bc, 40*24
          ld hl, screen
          ld de, screen       ;de=hl, so ldi does not change RAM
          ld ix, scratch
DoGOLupdl ld a, (ix)
          cp 0x7f             ;border -> keep the same
          jr nc, DoGOLupde
          cp 3                ;3 neighbors-> always live
          jr z, DoGOLlive
          cp 2
          jr z, DoGOLupde     ;2 -> stay the same          
DoGOLdie  ld (hl), 0x20       ;1,4,5,6,7,8 -> always die
          jr DoGoLupde
DoGOLlive ld (hl), LIFE_CHAR
DoGOLupde inc ix
          ldi                 ;hl++, bc-- (with flag!)
          jp pe, DoGOLupdl
          ret

;*********************************************************************
Main
;*********************************************************************
          call INITXT
          call InitGOL          
Mainloop  ld hl, screen
          ld de, (TXTNAM)
          ld bc, 40*24
          call LDIRVM
          ;call CHGET
          call DoGOL
          jr Mainloop
          
          ;force 16k ROM size binary output
EndOfCode dc 0x8000 - EndOfCode, 0xFF
          end

Yabasic

This example does not show the output mentioned in the task description on this page (or a page linked to from here). Please ensure that it meets all task requirements and remove this message.
Note that phrases in task descriptions such as "print and display" and "print and show" for example, indicate that (reasonable length) output be a part of a language's solution.


Translation of: BASIC256
// Conway's_Game_of_Life
 
X = 59 : Y = 35 : H = 4
 
open window X*H,Y*H
backcolor 0, 0, 0
 
dim c(X,Y) : dim cn(X,Y) : dim cl(X,Y)

// Thunderbird methuselah
c(X/2-1,Y/3+1) = 1 : c(X/2,Y/3+1) = 1 : c(X/2+1,Y/3+1) = 1  
c(X/2,Y/3+3) = 1 : c(X/2,Y/3+4) = 1 : c(X/2,Y/3+5) = 1
 
s = 0
repeat
    clear window
    alive = 0 : stable = 1
    s = s + 1
    for y = 0 to Y-1 
        for x = 0 to X-1
            xm1 = mod(x-1+X, X) : xp1 = mod(x+1+X, X)
            ym1 = mod(y-1+Y, Y) : yp1 = mod(y+1+Y, Y)
            cn(x,y) = c(xm1,y) + c(xp1,y)
            cn(x,y) = c(xm1,ym1) + c(x,ym1) + c(xp1,ym1) + cn(x,y)
            cn(x,y) = c(xm1,yp1) + c(x,yp1) + c(xp1,yp1) + cn(x,y)
            if c(x,y) = 1 then
                if cn(x,y) < 2 or cn(x,y) > 3 then 
                    cn(x,y) = 0
                else 
                    cn(x,y) = 1
                    alive = alive + 1
                end if
            else 
                if cn(x,y) = 3 then 
                    cn(x,y) = 1
                    alive = alive + 1
                else
                    cn(x,y) = 0
                end if
            end if
            if c(x,y) then
                if cn(x,y) then
                    if cl(x,y) color 0, 0, 255          // adult
                    if not cl(x,y) color 0, 255, 0      // newborn
                else 
                    if cl(x,y) color 255, 0, 0          // old
                    if not cl(x,y) color 255, 255, 0    // shortlived
                end if 
                fill rect x*H,y*H,x*H+H,y*H+H
            end if
        next x
    next y

    pause 0.06
    // Copy arrays
    for i = 0 to X-1
        for j = 0 to Y-1
            if cl(i,j)<>cn(i,j) stable = 0
            cl(i,j) = c(i,j)
            c(i,j) = cn(i,j)
        next j
    next i  
until(not alive or stable)
 
if not alive then
    print "Died in ", s, " iterations"
    clear window
else 
    print "Stabilized in ", s-2, " iterations"  
end if

zkl

class Life{
   fcn init(n, r1,c1, r2,c2, etc){
      var N=n, cells=Data(n*n), tmp=Data(n*n),
        ds=T(T(-1,-1),T(-1,0),T(-1,1), T(0,-1),T(0,1), T(1,-1),T(1,0),T(1,1));
      icells:=vm.arglist[1,*];
      (N*N).pump(Void,cells.append.fpM("1-",0));	// clear board
      icells.pump(Void,Void.Read,fcn(row,col){ cells[row*N+col]=1 });
   }
   fcn get(row,col){
      if((0<=row<N) and (0<=col<N)) return(cells[row*N+col]);
      return(0);
   }
   fcn postToastie(row,col){
      n:=ds.reduce('wrap(n,[(r,c)]){n+get(r+row,c+col)},0);
      c:=get(row,col);
      ((n==2 and c==1) or n==3).toInt()
   }
   fcn cycle{
      tmp.clear();
      foreach row in (N){ foreach col in (N) { 
         tmp.append(postToastie(row,col)) } }
      t:=cells; cells=tmp; tmp=t;
   }
   fcn toString{
      cells.pump(0,String,fcn(c,rn){
         (if(c)"*" else "-") + (if(rn.inc()%N) "" else "\n")
      }.fp1(Ref(1)));
   }
   fcn toAnsi{
      cells.pump(0,"\e[H",fcn(c,rn){
         (if(c)"\e[07m  \e[m" else "  ") + (if(rn.inc()%N) "" else "\e[E")
      }.fp1(Ref(1)));
   }
   fcn dance(n=300){ do(n){ toAnsi().print(); Atomic.sleep(0.2); cycle(); } }
}

The data structure is a Data, which is a linear block of bytes.

cells:=Life(4, 0,1, 1,1, 2,1);		  // blinker
do(3){ cells.println("="*4); cells.cycle(); }

cells:=Life(30, 0,1, 1,2, 2,0, 2,1, 2,2);  // glider
cells.dance(100);
Output:

Just the glider (reformatted), if you have an ANSI terminal (eg xterm), you'll see the glider moving down the screen.

-*--    ----   -*--
-*--    ***-   -*--
-*--    ----   -*--
----    ----   ----
====    ====   ====

ZPL

program Life;

config var
     n : integer = 100;

region 
     BigR = [0 .. n+1, 0 .. n+1];
     R    = [1 .. n,   1 .. n  ];

direction
     nw   = [-1, -1]; north = [-1, 0]; ne   = [-1, 1];
     west = [ 0, -1];                  east = [ 0, 1];
     sw   = [ 1, -1]; south = [ 1, 0]; se   = [ 1, 1];

var 
     TW   : [BigR] boolean; -- The World
     NN   : [R]    integer; -- Number of Neighbours

procedure Life();
begin
     -- Initialize world
     [R]  repeat
          NN := TW@nw   + TW@north + TW@ne   +
                TW@west +            TW@east + 
                TW@sw   + TW@south + TW@se;
          TW := (TW & NN = 2) | ( NN = 3);
     until !(|<< TW);
end;

ZX Spectrum Basic

Play on emulator at full speed for reasonable performance.

The ZX Spectrum was shipped with a demo tape called Horizons, which included an implementation of Life; however, it relied on machine code.

10 REM Initialize
20 LET w=32*22
30 DIM w$(w): DIM n$(w)
40 FOR n=1 TO 100
50 LET w$(RND*w+1)="O"
60 NEXT n
70 REM Loop
80 FOR i=34 TO w-34
90 LET p$="": LET d=0
100 LET p$=p$+w$(i-1)+w$(i+1)+w$(i-33)+w$(i-32)+w$(i-31)+w$(i+31)+w$(i+32)+w$(i+33)
110 LET n$(i)=w$(i)
120 FOR n=1 TO LEN p$
130 IF p$(n)="O" THEN LET d=d+1
140 NEXT n
150 IF (w$(i)=" ") AND (d=3) THEN LET n$(i)="O": GO TO 180
160 IF (w$(i)="O") AND (d<2) THEN LET n$(i)=" ": GO TO 180
170 IF (w$(i)="O") AND (d>3) THEN LET n$(i)=" "
180 NEXT i
190 PRINT AT 0,0;w$
200 LET w$=n$
210 GO TO 80