object GameOfLife extends App {

  case class Point(x: Int, y: Int)
  type World = Set[Point]

  val startingWorld = Set(Point(0, 0), Point(0, 1), Point(0, -1), Point(1, 0), Point(-1, 0))
  allGenerations(startingWorld).take(10).map(worldToString).foreach(println)

  def allGenerations(w: World) = Stream.iterate(w)(nextGeneration).takeWhile(_.nonEmpty)

  def nextGeneration(w: World) = w.flatMap(nearbyCluster).filter(isAlive(_, w))

  def nearbyCluster(p: Point) = for {
    x: Int <- (p.x - 1 to p.x + 1).toSet
    y: Int <- (p.y - 1 to p.y + 1).toSet
  } yield Point(x, y)

  def isAlive(p: Point, w: World) = rules(w.contains(p), neighbourCount(p, w))

  def rules(alive: Boolean, nc: Int) = nc == 3 || (alive && nc == 2)

  def neighbourCount(p: Point, w: World) = nearbyCluster(p).intersect(w).filterNot(p.equals).size

  def worldToString(w: World) =
    (w.map(_.y).max to w.map(_.y).min by -1)
      .map(y => (w.map(_.x).min to w.map(_.x).max)
        .map(x => if (w.contains(Point(x, y))) 'x' else '.'))
      .map(_.mkString(" "))
      .mkString("\n") + "\n"
}