board={{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{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},
{0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0},{0,0,0,0,1,1,0,0,1,1,1,0,0,0,0,0},{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}};
board2={{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{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},
{0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0},{0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0},{0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0},
{0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0},{0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0},{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},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}};

initboard=board2;width=16;height=16;
BoardNext[board_]:=Array[Function[{r,c},Transition[board,r,c]],{height,width}];
CellNext[val_,nSum_]:=If[val==0,If[nSum==3,1,0],If[nSum==2||nSum==3,1,0]];
Transition[board_,row_,col_]:=CellNext[GetV[board,row,col],NeighborSum[board,row,col]];
GetV[board_,row_,col_,default_:0]:=If[row<=0||row>height,default,If[col<=0||col>width,default,board[[row]][[col]]]];
NeighborSum[board_,row_,col_]:=Total[{GetV[board,row-1,col-1],GetV[board,row-1,col],GetV[board,row-1,col+1],GetV[board,row,col-1],
     GetV[board,row,col+1],GetV[board,row+1,col-1],GetV[board,row+1,col],GetV[board,row+1,col+1]}];
ToggleCell[board_,row_,col_]:=ReplacePart[board,{row,col}->If[GetV[board,row,col]==1,0,1]];
DrawCell[board_, row_, col_] := {If[GetV[board, row, col] == 1, Black, RGBColor[.9, .9, .9]], Rectangle[{col - 1, height - row}]};
RectArray[board_]:=Array[Function[{r,c},DrawCell[board,r,c]],{height,width}];
DrawBoard[board_]:=Graphics[Flatten[RectArray[board],1],ImageSize->Medium];
ProcessClick[board_,pt_]:=Block[{r=height-Floor[pt[[2]]],c=Floor[pt[[1]]]+1},(z={r,c};ToggleCell[board,r,c])];
DynamicModule[{myboard=initboard},
  Column[{Row[{Button["Next",myboard=BoardNext[myboard]],Button["Reset",myboard=initboard]}],
  Framed@ClickPane[Dynamic[DrawBoard[myboard]],(myboard=ProcessClick[myboard,#])&],Dynamic[z]}]]