Conway's Game of Life

class Life {
 int count(int[][] grid, int x, int y)
 {
  int size = grid.length;
  final int[][] xys = {
   {-1,-1}, {0,-1}, { 1,-1},
   {-1, 0},         { 1, 0},
   {-1, 1}, {0, 1}, { 1, 1}
  };
  int total=0;
  for(int[] xy : xys)
  {
   int nx=(x+xy[0]+size)%size, ny=(y+xy[1]+size)%size;
   total+=grid[ny][nx];
  }
  return total;
 }
 int[][] update(int[][] grid)
 {
  int size = grid.length;
  int[][] output = new int[size][size];
  for(int y=0;y<size;y++)
  {
   for(int x=0;x<size;x++)
   {
    int n = count(grid,x,y);
    int value = grid[y][x];
    output[y][x] = (n==3) ? 1 : (n==2) ? value : 0;
   }
  }
  return output;
 }
 void show(int[][] grid)
 {
  int size = grid.length;
  for(int[] xs : grid)
  {
   String line = "";
   for(int x : xs) line += x;
   System.out.println(line);
  }
 }
 public static void main(String[] args) {
  Life life = new Life();
  int[][] grid = {
   {1,0,0,0,1},
   {0,0,1,1,0},
   {0,1,0,1,0},
   {0,1,1,0,0},
   {1,0,0,0,1}
  };
  life.show(grid);
  for(int i=0;i<3;i++)
  {
    grid = life.update(grid);
    System.out.println();
    life.show(grid);
  }
 }
}