The Chaos Game is a method of generating the attractor of an iterated function system (IFS).

One of the best-known and simplest examples creates a fractal, using a polygon and an initial point selected at random.



Task
Play the Chaos Game using the corners of an equilateral triangle as the reference points.   Add a starting point at random (preferably inside the triangle).   Then add the next point halfway between the starting point and one of the reference points.   This reference point is chosen at random.

After a sufficient number of iterations, the image of a Sierpinski Triangle should emerge.



See also
 The Game of Chaos


import javax.swing._
import java.awt._
import java.awt.event.ActionEvent
 
import scala.collection.mutable
import scala.util.Random
 
object ChaosGame extends App {
  SwingUtilities.invokeLater(() =>
    new JFrame("Chaos Game") {
 
      class ChaosGame extends JPanel {
        private val (dim, margin)= (new Dimension(640, 640), 60)
        private val sizez: Int = dim.width - 2 * margin
        private val (stack, r) = (new mutable.Stack[ColoredPoint], new Random)
        private val points = Seq(new Point(dim.width / 2, margin),
          new Point(margin, sizez),
          new Point(margin + sizez, sizez)
        )
        private val colors = Seq(Color.red, Color.green, Color.blue)
 
        override def paintComponent(gg: Graphics): Unit = {
          val g = gg.asInstanceOf[Graphics2D]
 
          def drawPoints(g: Graphics2D): Unit = {
            for (p <- stack) {
              g.setColor(colors(p.colorIndex))
              g.fillOval(p.x, p.y, 1, 1)
            }
          }
 
          super.paintComponent(gg)
          g.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON)
          drawPoints(g)
        }
 
 
        private def addPoint(): Unit = {
          val colorIndex = r.nextInt(3)
 
          def halfwayPoint(a: Point, b: Point, idx: Int) =
            new ColoredPoint((a.x + b.x) / 2, (a.y + b.y) / 2, idx)
 
          stack.push(halfwayPoint(stack.top, points(colorIndex), colorIndex))
        }
 
        class ColoredPoint(x: Int, y: Int, val colorIndex: Int) extends Point(x, y)
 
        stack.push(new ColoredPoint(-1, -1, 0))
        new Timer(100, (_: ActionEvent) => {
          if (stack.size < 50000) {
            for (i <- 0 until 1000) addPoint()
            repaint()
          }
        }).start()
        setBackground(Color.white)
        setPreferredSize(dim)
      }
 
      add(new ChaosGame, BorderLayout.CENTER)
      pack()
      setDefaultCloseOperation(WindowConstants.EXIT_ON_CLOSE)
      setLocationRelativeTo(null)
      setResizable(false)
      setVisible(true)
    }
  )
 
}