Straight to the point implementation of Conway's Game of Life

conway.scala

object Conway {
  type Cell = (Int, Int)
  type World = Set[Cell]
  
  def next(w: World): World = w flatMap expand filter alive(w)
  
  private def expand(c: Cell): Set[Cell] =
    (for (x <- -1 to 1; y <- -1 to 1) yield (c._1 + x, c._2 + y)).toSet
    
  private def alive(w: World)(c: Cell): Boolean = {
    val n = expand(c) count w
    n == 3 || (n == 4 && w(c))
  }
}