1 // Mandelbrot pictures |
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2 //===================== |
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3 // |
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4 // see https://en.wikipedia.org/wiki/Mandelbrot_set |
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5 // |
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6 // needs to be called with |
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7 // |
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8 // scala-cli --extra-jars scala-parallel-collections_3-1.0.4.jar |
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9 // |
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10 // the jar-file is uploaded to KEATS |
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11 // |
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12 // |
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13 // !! UPDATE ON TIMING: On my faster Mac-M1 machine |
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14 // !! the times for the first example are ca. 4 secs for |
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15 // !! the sequential version and around 0.7 secs for the |
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16 // !! par-version. |
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17 |
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18 |
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19 import javax.swing.{JFrame, JPanel, WindowConstants} |
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20 import java.awt.{Color, Dimension, Graphics, Graphics2D} |
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21 import java.awt.image.BufferedImage |
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22 |
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23 import scala.language.implicitConversions |
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24 import scala.collection.parallel.CollectionConverters.* |
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25 |
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26 // complex numbers |
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27 // represents the complex number re + im * i |
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28 case class Complex(val re: Double, val im: Double) { |
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29 |
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30 def +(that: Complex) = Complex(this.re + that.re, this.im + that.im) |
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31 def -(that: Complex) = Complex(this.re - that.re, this.im - that.im) |
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32 def *(that: Complex) = Complex(this.re * that.re - this.im * that.im, |
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33 this.re * that.im + that.re * this.im) |
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34 def *(that: Double) = Complex(this.re * that, this.im * that) |
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35 def abs() = Math.sqrt(this.re * this.re + this.im * this.im) |
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36 } |
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37 |
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38 // to allow the usual mathmo notation n + m * i |
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39 object i extends Complex(0, 1) |
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40 |
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41 // implicit conversion from Doubles to Complex |
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42 given Conversion[Double, Complex] = Complex(_, 0) |
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43 |
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44 // some customn colours for the "sliding effect" |
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45 val colours = List( |
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46 Color(66, 30, 15), Color(25, 7, 26), |
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47 Color(9, 1, 47), Color(4, 4, 73), |
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48 Color(0, 7, 100), Color(12, 44, 138), |
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49 Color(24, 82, 177), Color(57, 125, 209), |
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50 Color(134, 181, 229), Color(211, 236, 248), |
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51 Color(241, 233, 191), Color(248, 201, 95), |
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52 Color(255, 170, 0), Color(204, 128, 0), |
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53 Color(153, 87, 0), Color(106, 52, 3)) |
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54 |
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55 // the viewer panel with an image canvas |
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56 class Viewer(width: Int, height: Int) extends JPanel { |
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57 val canvas = BufferedImage(width, height, BufferedImage.TYPE_INT_ARGB) |
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58 |
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59 override def paintComponent(g: Graphics) = |
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60 g.asInstanceOf[Graphics2D].drawImage(canvas, null, null) |
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61 |
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62 override def getPreferredSize() = |
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63 Dimension(width, height) |
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64 |
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65 def clearCanvas(color: Color) = { |
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66 for (x <- 0 to width - 1; y <- 0 to height - 1) |
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67 canvas.setRGB(x, y, color.getRGB()) |
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68 repaint() |
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69 } |
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70 } |
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71 |
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72 // initialising the viewer panel |
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73 def openViewer(width: Int, height: Int) : Viewer = { |
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74 val frame = JFrame("XYPlane") |
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75 val viewer = Viewer(width, height) |
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76 frame.add(viewer) |
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77 frame.pack() |
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78 frame.setVisible(true) |
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79 frame.setResizable(false) |
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80 frame.setDefaultCloseOperation(WindowConstants.EXIT_ON_CLOSE) |
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81 viewer |
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82 } |
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83 |
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84 // some hardcoded parameters |
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85 val W = 900 // width |
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86 val H = 800 // height |
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87 val black = Color.black |
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88 val viewer = openViewer(W, H) |
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89 |
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90 // draw a pixel on the canvas |
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91 def pixel(x: Int, y: Int, color: Color) = |
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92 viewer.canvas.setRGB(x, y, color.getRGB()) |
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93 |
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94 |
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95 // calculates the number of iterations using lazy lists (streams) |
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96 // the iteration goes on for a maximum of max steps, |
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97 // but might leave early when the pred is satisfied |
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98 def iterations(c: Complex, max: Int) : Int = { |
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99 def next(z: Complex) = z * z + c |
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100 def pred(z: Complex) = z.abs() < 2 // exit condition |
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101 LazyList.iterate(0.0 * i, max)(next).takeWhile(pred).size |
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102 } |
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103 |
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104 // main function |
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105 // start and end are the upper-left and lower-right corners, |
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106 // max is the number of maximum iterations |
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107 def mandelbrot(start: Complex, end: Complex, max: Int) : Unit = { |
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108 viewer.clearCanvas(black) |
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109 |
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110 // deltas for each grid step |
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111 val d_x = (end.re - start.re) / W |
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112 val d_y = (end.im - start.im) / H |
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113 |
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114 for (y <- (0 until H).par) { |
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115 for (x <- (0 until W).par) { |
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116 |
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117 val c = start + x * d_x + y * d_y * i |
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118 val iters = iterations(c, max) |
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119 val colour = |
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120 if (iters == max) black |
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121 else colours(iters % 16) |
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122 |
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123 pixel(x, y, colour) |
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124 } |
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125 viewer.updateUI() |
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126 } |
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127 } |
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128 |
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129 |
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130 // Examples |
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131 //========== |
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132 |
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133 //for measuring time |
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134 def time_needed[T](code: => T) = { |
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135 val start = System.nanoTime() |
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136 code |
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137 val end = System.nanoTime() |
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138 (end - start) / 1.0e9 |
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139 } |
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140 |
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141 |
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142 |
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143 // example 1 |
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144 val exa1 = -2.0 + -1.5 * i |
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145 val exa2 = 1.0 + 1.5 * i |
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146 |
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147 println(s"${time_needed(mandelbrot(exa1, exa2, 1000))} secs") |
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148 |
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149 // example 2 |
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150 val exb1 = -0.37465401 + 0.659227668 * i |
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151 val exb2 = -0.37332410 + 0.66020767 * i |
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152 |
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153 //time_needed(mandelbrot(exb1, exb2, 1000)) |
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154 |
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155 // example 3 |
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156 val exc1 = 0.435396403 + 0.367981352 * i |
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157 val exc2 = 0.451687191 + 0.380210061 * i |
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158 |
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159 //time_needed(mandelbrot(exc1, exc2, 1000)) |
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160 |
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161 |
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162 |
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163 // some more computations with example 3 |
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164 |
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165 val delta = (exc2 - exc1) * 0.0333 |
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166 |
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167 println(s"${time_needed( |
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168 for (n <- (0 to 25)) |
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169 mandelbrot(exc1 + delta * n, |
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170 exc2 - delta * n, 1000))} secs") |
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171 |
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172 |
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173 |
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174 // Larry Paulson's example |
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175 val exl1 = -0.74364990 + 0.13188170 * i |
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176 val exl2 = -0.74291189 + 0.13261971 * i |
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177 |
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178 //println(s"${time_needed(mandelbrot(exl1, exl2, 1000))} secs") |
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179 |
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180 |
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181 // example by Jorgen Villadsen |
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182 val exj1 = 0.10284 - 0.63275 * i |
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183 val exj2 = 0.11084 - 0.64075 * i |
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184 |
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185 //time_needed(mandelbrot(exj1, exj2, 1000)) |
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186 |
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187 |
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188 // another example |
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189 val exA = 0.3439274 + 0.6516478 * i |
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190 val exB = 0.3654477 + 0.6301795 * i |
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191 |
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192 //time_needed(mandelbrot(exA, exB, 1000)) |
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