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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 // under scala 2.13.XX needs to be called with |
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7 // |
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8 // scala -cp scala-parallel-collections_2.13-0.2.0.jar mandelbrot.scala |
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9 |
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10 import java.awt.Color |
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11 import java.awt.Dimension |
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12 import java.awt.Graphics |
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13 import java.awt.Graphics2D |
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14 import java.awt.image.BufferedImage |
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15 import javax.swing.JFrame |
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16 import javax.swing.JPanel |
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17 import javax.swing.WindowConstants |
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18 import scala.language.implicitConversions |
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19 import scala.collection.parallel.CollectionConverters._ |
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20 |
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21 // complex numbers |
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22 case class Complex(val re: Double, val im: Double) { |
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23 // represents the complex number re + im * i |
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24 def +(that: Complex) = Complex(this.re + that.re, this.im + that.im) |
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25 def -(that: Complex) = Complex(this.re - that.re, this.im - that.im) |
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26 def *(that: Complex) = Complex(this.re * that.re - this.im * that.im, |
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27 this.re * that.im + that.re * this.im) |
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28 def *(that: Double) = Complex(this.re * that, this.im * that) |
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29 def abs() = Math.sqrt(this.re * this.re + this.im * this.im) |
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30 } |
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31 |
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32 // to allow the notation n + m * i |
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33 object i extends Complex(0, 1) |
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34 implicit def double2complex(re: Double) = Complex(re, 0) |
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35 |
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36 |
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37 // some customn colours for the "sliding effect" |
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38 val colours = List( |
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39 new Color(66, 30, 15), new Color(25, 7, 26), |
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40 new Color(9, 1, 47), new Color(4, 4, 73), |
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41 new Color(0, 7, 100), new Color(12, 44, 138), |
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42 new Color(24, 82, 177), new Color(57, 125, 209), |
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43 new Color(134, 181, 229), new Color(211, 236, 248), |
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44 new Color(241, 233, 191), new Color(248, 201, 95), |
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45 new Color(255, 170, 0), new Color(204, 128, 0), |
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46 new Color(153, 87, 0), new Color(106, 52, 3)) |
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47 |
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48 // the viewer panel with an image canvas |
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49 class Viewer(width: Int, height: Int) extends JPanel { |
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50 val canvas = new BufferedImage(width, height, BufferedImage.TYPE_INT_ARGB) |
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51 |
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52 override def paintComponent(g: Graphics) = |
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53 g.asInstanceOf[Graphics2D].drawImage(canvas, null, null) |
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54 |
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55 override def getPreferredSize() = |
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56 new Dimension(width, height) |
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57 |
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58 def clearCanvas(color: Color) = { |
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59 for (x <- 0 to width - 1; y <- 0 to height - 1) |
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60 canvas.setRGB(x, y, color.getRGB()) |
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61 repaint() |
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62 } |
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63 } |
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64 |
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65 // initialising the viewer panel |
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66 def openViewer(width: Int, height: Int) : Viewer = { |
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67 val frame = new JFrame("XYPlane") |
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68 val viewer = new Viewer(width, height) |
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69 frame.add(viewer) |
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70 frame.pack() |
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71 frame.setVisible(true) |
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72 frame.setResizable(false) |
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73 frame.setDefaultCloseOperation(WindowConstants.EXIT_ON_CLOSE) |
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74 viewer |
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75 } |
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76 |
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77 // some hardcoded parameters |
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78 val W = 900 // width |
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79 val H = 800 // height |
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80 val black = Color.black |
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81 val viewer = openViewer(W, H) |
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82 |
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83 // draw a pixel on the canvas |
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84 def pixel(x: Int, y: Int, color: Color) = |
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85 viewer.canvas.setRGB(x, y, color.getRGB()) |
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86 |
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87 |
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88 // calculates the number of iterations using lazy lists (streams) |
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89 // the iteration goes on for a maximum of max steps, |
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90 // but might leave early when the pred is satisfied |
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91 def iterations(c: Complex, max: Int) : Int = { |
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92 def next(z: Complex) = z * z + c |
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93 def pred(z: Complex) = z.abs() < 2 // exit condition |
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94 LazyList.iterate(0.0 * i, max)(next).takeWhile(pred).size |
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95 } |
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96 |
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97 // main function |
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98 // start and end are the upper-left and lower-right corners, |
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99 // max is the number of maximum iterations |
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100 def mandelbrot(start: Complex, end: Complex, max: Int) : Unit = { |
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101 viewer.clearCanvas(black) |
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102 |
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103 // deltas for each grid step |
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104 val d_x = (end.re - start.re) / W |
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105 val d_y = (end.im - start.im) / H |
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106 |
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107 for (y <- (0 until H).par) { |
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108 for (x <- (0 until W).par) { |
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109 |
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110 val c = start + |
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111 (x * d_x + y * d_y * i) |
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112 val iters = iterations(c, max) |
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113 val col = |
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114 if (iters == max) black |
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115 else colours(iters % 16) |
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116 |
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117 pixel(x, y, col) |
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118 } |
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119 viewer.updateUI() |
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120 } |
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121 } |
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122 |
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123 |
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124 // Examples |
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125 //========== |
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126 |
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127 //for measuring time |
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128 def time_needed[T](code: => T) = { |
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129 val start = System.nanoTime() |
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130 code |
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131 val end = System.nanoTime() |
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132 (end - start) / 1.0e9 |
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133 } |
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134 |
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135 |
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136 |
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137 // example 1 |
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138 val exa1 = -2.0 + -1.5 * i |
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139 val exa2 = 1.0 + 1.5 * i |
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140 |
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141 println(s"${time_needed(mandelbrot(exa1, exa2, 1000))} secs") |
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142 |
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143 // example 2 |
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144 val exb1 = -0.37465401 + 0.659227668 * i |
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145 val exb2 = -0.37332410 + 0.66020767 * i |
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146 |
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147 //time_needed(mandelbrot(exb1, exb2, 1000)) |
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148 |
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149 // example 3 |
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150 val exc1 = 0.435396403 + 0.367981352 * i |
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151 val exc2 = 0.451687191 + 0.380210061 * i |
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152 |
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153 //time_needed(mandelbrot(exc1, exc2, 1000)) |
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154 |
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155 |
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156 |
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157 // some more computations with example 3 |
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158 |
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159 val delta = (exc2 - exc1) * 0.0333 |
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160 |
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161 //println(s"${time_needed( |
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162 // for (n <- (0 to 12)) |
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163 // mandelbrot(exc1 + delta * n, |
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164 // exc2 - delta * n, 100))} secs") |
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165 |
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166 |
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167 |
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168 // Larry Paulson's example |
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169 val exl1 = -0.74364990 + 0.13188170 * i |
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170 val exl2 = -0.74291189 + 0.13261971 * i |
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171 |
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172 //println(s"${time_needed(mandelbrot(exl1, exl2, 1000))} secs") |
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173 |
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174 |
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175 // example by Jorgen Villadsen |
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176 val exj1 = 0.10284 - 0.63275 * i |
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177 val exj2 = 0.11084 - 0.64075 * i |
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178 |
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179 //time_needed(mandelbrot(exj1, exj2, 1000)) |
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180 |
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181 |
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182 // another example |
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183 val exA = 0.3439274 + 0.6516478 * i |
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184 val exB = 0.3654477 + 0.6301795 * i |
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185 |
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186 //time_needed(mandelbrot(exA, exB, 1000)) |