--- a/progs/mandelbrot.scala Thu Jun 06 22:18:15 2024 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,192 +0,0 @@
-// Mandelbrot pictures
-//=====================
-//
-// see https://en.wikipedia.org/wiki/Mandelbrot_set
-//
-// needs to be called with
-//
-// scala-cli --extra-jars scala-parallel-collections_3-1.0.4.jar
-//
-// the jar-file is uploaded to KEATS
-//
-//
-// !! 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.
-
-
-import javax.swing.{JFrame, JPanel, WindowConstants}
-import java.awt.{Color, Dimension, Graphics, Graphics2D}
-import java.awt.image.BufferedImage
-
-import scala.language.implicitConversions
-import scala.collection.parallel.CollectionConverters.*
-
-// 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"
-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 frame = JFrame("XYPlane")
- val viewer = 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 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"${time_needed(mandelbrot(exa1, exa2, 1000))} secs")
-
-// example 2
-val exb1 = -0.37465401 + 0.659227668 * i
-val exb2 = -0.37332410 + 0.66020767 * i
-
-//time_needed(mandelbrot(exb1, exb2, 1000))
-
-// example 3
-val exc1 = 0.435396403 + 0.367981352 * i
-val exc2 = 0.451687191 + 0.380210061 * i
-
-//time_needed(mandelbrot(exc1, exc2, 1000))
-
-
-
-// some more computations with example 3
-
-val delta = (exc2 - exc1) * 0.0333
-
-println(s"${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))