// Mandelbrot pictures

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

//

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

//

//

//   scala mandelbrot.sc

//

//

//

// !! UPDATE ON TIMING: On my faster Mac-M1 machine

// !! the times for the first example are ca. 4 secs for

// !! the sequential version and around 0.7 secs for the

// !! par-version.

// for parallel collections

//> using dep org.scala-lang.modules::scala-parallel-collections:1.0.4

import scala.collection.parallel.CollectionConverters.*

// for graphics

import javax.swing.{JFrame, JPanel, WindowConstants}

import java.awt.{Color, Dimension, Graphics, Graphics2D}

import java.awt.image.BufferedImage

// for implicits in comples numbers

import scala.language.implicitConversions

// complex numbers

//   represents the complex number re + im * i

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

  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 usual mathmo notation n + m * i

object i extends Complex(0, 1)

// implicit conversion from Doubles to Complex

given Conversion[Double, Complex] = Complex(_, 0)

// some customn colours for the "sliding effect" outside

// the mandelbrot set

val colours = List(

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

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

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

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

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

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

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

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

// the viewer panel with an image canvas

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

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

  override def paintComponent(g: Graphics) =

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

  override def getPreferredSize() =

    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 viewer = Viewer(width, height)

  val frame = JFrame("XYPlane")

  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 colour =

        if (iters == max) black

        else colours(iters % 16)

     pixel(x, y, colour)

    }

    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

println(s"${time_needed(mandelbrot(exa1, exa2, 1000))} secs")

// 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) * 0.01

println(s"${time_needed(

  for (n <- (0 to 25))

     mandelbrot(exc1 + delta * n,

                exc2 - delta * n, 1000))} secs")

// Larry Paulson's example

val exl1 = -0.74364990 + 0.13188170 * i

val exl2 = -0.74291189 + 0.13261971 * i

//println(s"${time_needed(mandelbrot(exl1, exl2, 1000))} secs")

// example by Jorgen Villadsen

val exj1 = 0.10284 - 0.63275 * i

val exj2 = 0.11084 - 0.64075 * i

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

// another example

val exA = 0.3439274 + 0.6516478 * i

val exB = 0.3654477 + 0.6301795 * i

//time_needed(mandelbrot(exA, exB, 1000))