Game of Life in Scala

GameOfLife.scala

package de.bripkens

object GameOfLife {
  case class Point(x: Int, y: Int) {
    lazy val neighbours: Seq[Point] = for (
      xDistance <- -1 to 1;
      yDistance <- -1 to 1;
      eachPoint = Point(x + xDistance, y + yDistance);
      if !(eachPoint.x == x && eachPoint.y == y)
    ) yield eachPoint

    def getNumberOfLivingNeighbours(field: Field): Int = {
      (neighbours.toSet -- (neighbours.toSet -- field)).size
    }
  }
  type Field = Set[Point]

  def createField(points: Point*): Field = {
    points.toSet
  }

  def tick(field: Field): Field = {
    val survivors = field.groupBy(identity(_))
      .mapValues(_.head.getNumberOfLivingNeighbours(field))
      .filter(2 to 3 contains _._2)
      .keySet

    val newborns = field.toList
      .flatMap(_.neighbours)
      .groupBy(identity(_))
      .--(field)
      .mapValues(_.size)
      .filter(_._2 == 3)
      .keySet

    survivors ++ newborns
  }

}

GameOfLifeSpec.scala

package de.bripkens

import com.bripkens.GameOfLife
import com.bripkens.GameOfLife.{Point}
import org.scalatest.{FlatSpec, Matchers}

class GameOfLifeSpec extends FlatSpec with Matchers {

  "tick" should "remove living cells when areas are underpopulated with no neighbours" in {
    val field = GameOfLife.createField(Point(1, 1))
    GameOfLife.tick(field) should not contain Point(1, 1)
  }

  it should "remove living cells when areas are underpopulated with one neighbour" in {
    val field = GameOfLife.createField(Point(1, 1), Point(0, 0))
    GameOfLife.tick(field) should not contain Point(1, 1)
  }

  it should "retain cells with two neighbours" in {
    val field = GameOfLife.createField(Point(1, 1), Point(0, 0), Point(0, 1))
    GameOfLife.tick(field) should contain (Point(1, 1))
  }

  it should "retain cells with three neighbours" in {
    val field = GameOfLife.createField(Point(1, 1), Point(0, 0), Point(0, 1), Point(1, 0))
    GameOfLife.tick(field) should contain (Point(1, 1))
  }

  it should "handle reproduction of cells with exactly three neighbours" in {
    val field = GameOfLife.createField(Point(0, 0), Point(0, 1), Point(0, 2))
    GameOfLife.tick(field) should contain (Point(1, 1))
  }

}