// Mandelbrot pictures

//

//   see https://en.wikipedia.org/wiki/Mandelbrot_set

// 

// under scala 2.13 needs to be called with 

// scala -cp `coursier fetch -p org.scala-lang.modules:scala-parallel-collections_2.13:0.2.0` mandelbrot.scala

import java.awt.Color

import java.awt.Dimension

import java.awt.Graphics

import java.awt.Graphics2D

import java.awt.image.BufferedImage

import javax.swing.JFrame

import javax.swing.JPanel

import javax.swing.WindowConstants

import scala.language.implicitConversions    

import scala.collection.parallel.CollectionConverters._

// complex numbers

case class Complex(val re: Double, val im: Double) { 

  // represents the complex number re + im * i

  def +(that: Complex) = Complex(this.re + that.re, this.im + that.im)

  def -(that: Complex) = Complex(this.re - that.re, this.im - that.im)

  def *(that: Complex) = Complex(this.re * that.re - this.im * that.im,

                                 this.re * that.im + that.re * this.im)

  def *(that: Double) = Complex(this.re * that, this.im * that)

  def abs() = Math.sqrt(this.re * this.re + this.im * this.im)

}

// to allow the notation n + m * i

object i extends Complex(0, 1)

implicit def double2complex(re: Double) = Complex(re, 0)

// some customn colours for the "sliding effect"

val colours = List(

  new Color(66, 30, 15),    new Color(25, 7, 26),

  new Color(9, 1, 47),      new Color(4, 4, 73),

  new Color(0, 7, 100),     new Color(12, 44, 138),

  new Color(24, 82, 177),   new Color(57, 125, 209),

  new Color(134, 181, 229), new Color(211, 236, 248),

  new Color(241, 233, 191), new Color(248, 201, 95),

  new Color(255, 170, 0),   new Color(204, 128, 0),

  new Color(153, 87, 0),    new Color(106, 52, 3))

// the viewer panel with an image canvas

class Viewer(width: Int, height: Int) extends JPanel {

  val canvas = new BufferedImage(width, height, BufferedImage.TYPE_INT_ARGB)

  override def paintComponent(g: Graphics) = 

    g.asInstanceOf[Graphics2D].drawImage(canvas, null, null)

  override def getPreferredSize() = 

    new Dimension(width, height)

  def clearCanvas(color: Color) = {

    for (x <- 0 to width - 1; y <- 0 to height - 1) 

      canvas.setRGB(x, y, color.getRGB())

    repaint()

  }  

}

// initialising the viewer panel

def openViewer(width: Int, height: Int) : Viewer = {

  val frame = new JFrame("XYPlane")

  val viewer = new Viewer(width, height)

  frame.add(viewer)

  frame.pack()

  frame.setVisible(true)

  frame.setResizable(false)

  frame.setDefaultCloseOperation(WindowConstants.EXIT_ON_CLOSE)

  viewer

}

// some hardcoded parameters

val W = 900   // width

val H = 800   // height

val black = Color.black

val viewer = openViewer(W, H)

// draw a pixel on the canvas

def pixel(x: Int, y: Int, color: Color) = 

  viewer.canvas.setRGB(x, y, color.getRGB())

// calculates the number of iterations using lazy lists (streams)

//   the iteration goes on for a maximum of max steps,

//   but might leave early when the pred is satisfied

def iterations(c: Complex, max: Int) : Int = {

  def next(z: Complex) = z * z + c    

  def pred(z: Complex) = z.abs < 2    // exit condition

  LazyList.iterate(0.0 * i, max)(next).takeWhile(pred).size

}

// main function 

//    start and end are the upper-left and lower-right corners, 

//    max is the number of maximum iterations

def mandelbrot(start: Complex, end: Complex, max: Int) : Unit = {

  viewer.clearCanvas(black)

  // deltas for each grid step 

  val d_x = (end.re - start.re) / W

  val d_y = (end.im - start.im) / H

  for (y <- (0 until H).par) {

    for (x <- (0 until W).par) {

     val c = start + 

      (x * d_x + y * d_y * i)

     val iters = iterations(c, max) 

     val col = 

       if (iters == max) black 

       else colours(iters % 16)

     pixel(x, y, col)

    }

    viewer.updateUI()

  }   

}

// Examples

//==========

//for measuring time

def time_needed[T](code: => T) = {

  val start = System.nanoTime()

  code

  val end = System.nanoTime()

  (end - start) / 1.0e9

}

// example 1

val exa1 = -2.0 + -1.5 * i

val exa2 =  1.0 +  1.5 * i

time_needed(mandelbrot(exa1, exa2, 1000))

// example 2

val exb1 = -0.37465401 + 0.659227668 * i

val exb2 = -0.37332410 + 0.66020767 * i

//time_needed(mandelbrot(exb1, exb2, 1000))

// example 3

val exc1 = 0.435396403 + 0.367981352 * i

val exc2 = 0.451687191 + 0.380210061 * i

//time_needed(mandelbrot(exc1, exc2, 1000))

// some more computations with example 3

val delta = (exc2 - exc1) * 0.0333

/*

time_needed(

  for (n <- (0 to 12)) 

     mandelbrot(exc1 + delta * n, 

                exc2 - delta * n, 100)) 

*/

/*

time_needed(

  for (n <- (0 to 12)) 

     mandelbrot(exc1 + delta * n, 

                exc2 - delta * n, 1000))

*/

// Larry Paulson's example

val exl1 = -0.74364990 + 0.13188170 * i

val exl2 = -0.74291189 + 0.13261971 * i

//time_needed(mandelbrot(exl1, exl2, 1000))

// example by Jorgen Villadsen

val exj1 = 0.10284 - 0.63275 * i

val exj2 = 0.11084 - 0.64075 * i

//time_needed(mandelbrot(exj1, exj2, 1000))