Help/Other Topics/Randomness.html

   1 <html><head>
   2 <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
   3 <meta http-equiv="Content-Style-Type" content="text/css">
   4 <title></title>
   5 <meta name="Generator" content="Cocoa HTML Writer">
   6 <meta name="CocoaVersion" content="824.41">
   7 <style type="text/css">
   8 p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica; min-height: 14.0px}
   9 p.p2 {margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px Helvetica}
  10 p.p3 {margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica}
  11 p.p4 {margin: 0.0px 0.0px 0.0px 0.0px; font: 14.0px Helvetica}
  12 p.p5 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Monaco; color: #882917}
  13 p.p6 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Monaco; min-height: 12.0px}
  14 p.p7 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Monaco}
  15 p.p8 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Monaco; color: #ba1100}
  16 p.p9 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Monaco; color: #606060}
  17 p.p10 {margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica; color: #0027ee}
  18 p.p11 {margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica; color: #0000ff}
  19 p.p12 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Monaco; color: #0027ee}
  20 p.p13 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Monaco; color: #001fbf}
  21 span.s1 {color: #000000}
  22 span.s2 {color: #882917}
  23 span.s3 {color: #0036ad}
  24 span.s4 {color: #0042f1}
  25 span.s5 {color: #001fbf}
  26 span.s6 {color: #606060}
  27 span.s7 {color: #4f6926}
  28 span.s8 {font: 12.0px Helvetica}
  29 span.s9 {color: #ba1100}
  30 span.s10 {text-decoration: underline}
  31 span.s11 {text-decoration: underline ; color: #0000ff}
  32 span.s12 {text-decoration: underline ; color: #0027ee}
  33 span.s13 {color: #002aff}
  34 span.s14 {font: 9.0px Monaco; text-decoration: underline}
  35 span.s15 {color: #1d7008}
  36 span.Apple-tab-span {white-space:pre}
  37 </style>
  38 </head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; ">
  39 <p class="p1"><span class="Apple-style-span" style="font-size: 18px; font-weight: bold; ">Randomness in SC</span><br></p>
  40 <p class="p1"><br></p>
  41 <p class="p3">As in any computer program, there are no "truly random" number generators in SC.<span class="Apple-converted-space"> </span></p>
  42 <p class="p3">They are pseudo-random, meaning they use very complex, but deterministic<span class="Apple-converted-space"> </span></p>
  43 <p class="p3">algorithms to generate sequences of numbers that are long enough and complicated enough<span class="Apple-converted-space"> </span></p>
  44 <p class="p3">to seem "random" for human beings. (i.e. the patterns are too complex for us to detect.)</p>
  45 <p class="p1"><br></p>
  46 <p class="p3">If you start a random number generator algorithm with the same "seed" number<span class="Apple-converted-space"> </span></p>
  47 <p class="p3">several times, you get the same sequence of random numbers.<span class="Apple-converted-space"> </span></p>
  48 <p class="p3">(See example below, <i>randomSeed</i>)</p>
  49 <p class="p1"><br></p>
  50 <p class="p1"><br></p>
  51 <p class="p4"><b>Create single random numbers:</b></p>
  52 <p class="p1"><br></p>
  53 <p class="p1"><br></p>
  54 <p class="p3"><b>1. Between zero and &lt;number&gt;:</b></p>
  55 <p class="p1"><br></p>
  56 <p class="p5"><span class="s1">5.rand<span class="Apple-tab-span">      </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span></span>// evenly distributed.</p>
  57 <p class="p6"><br></p>
  58 <p class="p5"><span class="s1">1.0.linrand<span class="Apple-tab-span"> </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span></span>// probability decreases linearly from 0 to &lt;number&gt;.</p>
  59 <p class="p1"><br></p>
  60 <p class="p1"><br></p>
  61 <p class="p3"><b>2. Between -&lt;number&gt; and &lt;number&gt;:</b></p>
  62 <p class="p1"><br></p>
  63 <p class="p5"><span class="s1">5.0.rand2<span class="Apple-tab-span">   </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span></span>// evenly distributed.</p>
  64 <p class="p6"><br></p>
  65 <p class="p5"><span class="s1">10.bilinrand<span class="Apple-tab-span">        </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span></span>// probability is highest around 0,<span class="Apple-converted-space"> </span></p>
  66 <p class="p5"><span class="s1"><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span></span>// decreases linearly toward +-&lt;number&gt;.</p>
  67 <p class="p6"><br></p>
  68 <p class="p5"><span class="s1">1.0.sum3rand<span class="Apple-tab-span">        </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span></span>// quasi-gaussian, bell-shaped distribution.</p>
  69 <p class="p1"><br></p>
  70 <p class="p3"><b>3. Within a given range:</b></p>
  71 <p class="p1"><br></p>
  72 <p class="p5"><span class="s1">rrand(24, 48)<span class="Apple-tab-span">       </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span></span>// linear distribution in the given range.</p>
  73 <p class="p6"><br></p>
  74 <p class="p5"><span class="s1">exprand(0.01, 1)<span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span></span>// exponential distribution;<span class="Apple-converted-space"> </span></p>
  75 <p class="p5"><span class="s1"><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span></span>// both numbers must have the same sign.</p>
  76 <p class="p1"><br></p>
  77 <p class="p1"><br></p>
  78 <p class="p3"><b>Test them multiple times with a do loop:</b></p>
  79 <p class="p1"><br></p>
  80 <p class="p1"><br></p>
  81 <p class="p7">20.do({ 5.rand.postln; });<span class="Apple-tab-span">   </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="s2">// evenly distributed</span></p>
  82 <p class="p6"><br></p>
  83 <p class="p5"><span class="s1">20.do({ 1.0.linrand.postln; });<span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span></span>// probability decreases linearly from 0 to 1.0</p>
  84 <p class="p6"><br></p>
  85 <p class="p6"><br></p>
  86 <p class="p7">20.do({ 5.0.rand2.postln; });<span class="Apple-tab-span">        </span><span class="Apple-tab-span">    </span><span class="s2">// even</span></p>
  87 <p class="p6"><br></p>
  88 <p class="p5"><span class="s1">20.do({ 10.bilinrand.postln; });<span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span></span>// probability is highest around 0,<span class="Apple-converted-space"> </span></p>
  89 <p class="p5"><span class="s1"><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span></span>// decreases linearly toward +-&lt;number&gt;.</p>
  90 <p class="p6"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span></p>
  91 <p class="p7">20.do({ 1.0.sum3rand.postln; });<span class="Apple-tab-span">     </span><span class="s2">// quasi-gaussian, bell-shaped.</span></p>
  92 <p class="p1"><br></p>
  93 <p class="p1"><br></p>
  94 <p class="p1"><br></p>
  95 <p class="p3"><b>Collect the results in an array:</b></p>
  96 <p class="p1"><br></p>
  97 <p class="p7"><span class="s3">Array</span>.fill(10, { 1000.linrand }).postln;<span class="Apple-converted-space"> </span></p>
  98 <p class="p6"><br></p>
  99 <p class="p5">// or more compact:<span class="Apple-converted-space"> </span></p>
 100 <p class="p6"><br></p>
 101 <p class="p7">{ 1.0.sum3rand }.dup(100)<span class="Apple-converted-space"> </span></p>
 102 <p class="p6"><br></p>
 103 <p class="p5">// or:</p>
 104 <p class="p6"><br></p>
 105 <p class="p7">({ 1.0.sum3rand } ! 100)</p>
 106 <p class="p1"><br></p>
 107 <p class="p1"><br></p>
 108 <p class="p1"><br></p>
 109 <p class="p3"><b>You can seed a random generator in order to repeat<span class="Apple-converted-space"> </span></b></p>
 110 <p class="p3"><b>the same sequence of random numbers:</b></p>
 111 <p class="p1"><br></p>
 112 <p class="p7">(</p>
 113 <p class="p7">5.do({<span class="Apple-converted-space"> </span></p>
 114 <p class="p7"><span class="Apple-tab-span">     </span><span class="s3">thisThread</span>.randSeed = 4;</p>
 115 <p class="p7"><span class="Apple-tab-span">     </span><span class="s3">Array</span>.fill(10, { 1000.linrand}).postln;<span class="Apple-converted-space"> </span></p>
 116 <p class="p7">});</p>
 117 <p class="p7">)</p>
 118 <p class="p6"><br></p>
 119 <p class="p5">// Just to check, no seeding:</p>
 120 <p class="p6"><br></p>
 121 <p class="p7">(</p>
 122 <p class="p7">5.do({ <span class="s3">Array</span>.fill(10, { 1000.linrand }).postln; });</p>
 123 <p class="p7">)</p>
 124 <p class="p6"><br></p>
 125 <p class="p5">// see also <a href="../Core/Kernel/randomSeed.html"><span class="s4">randomSeed</span></a>.</p>
 126 <p class="p6"><br></p>
 127 <p class="p1"><br></p>
 128 <p class="p1"><br></p>
 129 <p class="p3"><b>Demonstrate the various statistical distributions visually, with histograms:</b></p>
 130 <p class="p1"><br></p>
 131 <p class="p3">[plot may not work in non-Mac SC3 versions.]</p>
 132 <p class="p1"><br></p>
 133 <p class="p7"><span class="s5">Array</span>.fill(500, {<span class="Apple-converted-space">  </span>1.0.rand }).plot(<span class="s6">"Sequence of 500x 1.0.rand"</span>);</p>
 134 <p class="p6"><br></p>
 135 <p class="p7"><span class="s5">Array</span>.fill(500, {<span class="Apple-converted-space">  </span>1.0.linrand }).plot(<span class="s6">"Sequence of 500x 1.0.linrand"</span>);</p>
 136 <p class="p6"><br></p>
 137 <p class="p7"><span class="s5">Array</span>.fill(500, {<span class="Apple-converted-space">  </span>1.0.sum3rand }).plot(<span class="s6">"Sequence of 500x 1.0.sum3rand"</span>);</p>
 138 <p class="p6"><br></p>
 139 <p class="p8">// Use a histogram to display how often each (integer)<span class="Apple-converted-space"> </span></p>
 140 <p class="p8">// occurs in a collection of random numbers, :</p>
 141 <p class="p7">(</p>
 142 <p class="p7"><span class="s5">var</span> randomNumbers, histogram, maxValue = 500, numVals = 10000, numBins = 500;</p>
 143 <p class="p6"><br></p>
 144 <p class="p7">randomNumbers = <span class="s5">Array</span>.fill(numVals, { maxValue.rand; });</p>
 145 <p class="p7">histogram = randomNumbers.histo(numBins, 0, maxValue);</p>
 146 <p class="p7">histogram.plot(<span class="s6">"histogram for rand 0 - "</span> ++ maxValue);</p>
 147 <p class="p7">)</p>
 148 <p class="p6"><br></p>
 149 <p class="p1"><br></p>
 150 <p class="p1"><br></p>
 151 <p class="p3"><b>A histogram for linrand:</b></p>
 152 <p class="p1"><br></p>
 153 <p class="p7">(</p>
 154 <p class="p7"><span class="s5">var</span> randomNumbers, histogram, maxValue = 500.0, numVals = 10000, numBins = 500;</p>
 155 <p class="p6"><br></p>
 156 <p class="p7">randomNumbers = <span class="s5">Array</span>.fill(numVals, { maxValue.linrand; });</p>
 157 <p class="p7">histogram = randomNumbers.histo(numBins, 0, maxValue);</p>
 158 <p class="p7">histogram.plot(<span class="s6">"histogram for linrand 0 - "</span> ++ maxValue);</p>
 159 <p class="p7">)</p>
 160 <p class="p1"><br></p>
 161 <p class="p3"><b>A histogram for bilinrand:</b></p>
 162 <p class="p1"><br></p>
 163 <p class="p7">(</p>
 164 <p class="p7"><span class="s5">var</span> randomNumbers, histogram, minValue = -250, maxValue = 250, numVals = 10000, numBins = 500;</p>
 165 <p class="p6"><br></p>
 166 <p class="p7">randomNumbers = <span class="s5">Array</span>.fill(numVals, { maxValue.bilinrand; });</p>
 167 <p class="p7">histogram = randomNumbers.histo(numBins, minValue, maxValue);</p>
 168 <p class="p7">histogram.plot(<span class="s6">"histogram for bilinrand"</span> + minValue + <span class="s6">"to"</span> + maxValue);</p>
 169 <p class="p7">)</p>
 170 <p class="p1"><br></p>
 171 <p class="p1"><br></p>
 172 <p class="p1"><br></p>
 173 <p class="p3"><b>A histogram for exprand:</b></p>
 174 <p class="p1"><br></p>
 175 <p class="p7">(</p>
 176 <p class="p7"><span class="s5">var</span> randomNumbers, histogram, minValue = 5.0, maxValue = 500, numVals = 10000, numBins = 500;</p>
 177 <p class="p6"><br></p>
 178 <p class="p7">randomNumbers = <span class="s5">Array</span>.fill(numVals, { exprand(minValue, maxValue); });</p>
 179 <p class="p7">histogram = randomNumbers.histo(numBins, minValue, maxValue);</p>
 180 <p class="p7">histogram.plot(<span class="s6">"histogram for exprand: "</span> ++ minValue ++ <span class="s6">" to "</span> ++ maxValue);</p>
 181 <p class="p7">)</p>
 182 <p class="p1"><br></p>
 183 <p class="p1"><br></p>
 184 <p class="p3"><b>And for sum3rand (cheap quasi-gaussian):</b></p>
 185 <p class="p1"><br></p>
 186 <p class="p1"><br></p>
 187 <p class="p7">(</p>
 188 <p class="p7"><span class="s5">var</span> randomNumbers, histogram, minValue = -250, maxValue = 250, numVals = 10000, numBins = 500;</p>
 189 <p class="p6"><br></p>
 190 <p class="p7">randomNumbers = <span class="s5">Array</span>.fill(numVals, { maxValue.sum3rand; });</p>
 191 <p class="p7">histogram = randomNumbers.histo(numBins, minValue, maxValue);</p>
 192 <p class="p7">histogram.plot(<span class="s6">"histogram for sum3rand "</span> ++ minValue ++ <span class="s6">" to "</span> ++ maxValue);</p>
 193 <p class="p7">)</p>
 194 <p class="p1"><br></p>
 195 <p class="p1"><br></p>
 196 <p class="p1"><br></p>
 197 <p class="p3">All of the single-number methods also work for (Sequenceable)Collections,<span class="Apple-converted-space"> </span></p>
 198 <p class="p3">simply by applying the given random message to each element of the collection:</p>
 199 <p class="p1"><br></p>
 200 <p class="p5"><span class="s1">[ 1.0, 10, 100.0, </span><span class="s7">\aSymbol</span><span class="s1"> ].rand.postln;<span class="Apple-tab-span">   </span><span class="Apple-tab-span">    </span></span>// note: Symbols are left as they are.</p>
 201 <p class="p7"><span class="s3">List</span>[ 10, -3.0, <span class="s7">\aSymbol</span> ].sum3rand.postln;</p>
 202 <p class="p6"><br></p>
 203 <p class="p1"><br></p>
 204 <p class="p1"><br></p>
 205 <p class="p1"><br></p>
 206 <p class="p3"><b>Arbitrary random distributions</b></p>
 207 <p class="p1"><br></p>
 208 <p class="p3">An <i>integral table</i> can be used to create an arbitrary random distribution quite efficiently. The table</p>
 209 <p class="p3">building is expensive though. The more points there are in the random table, the more accurate the</p>
 210 <p class="p3">distribution.</p>
 211 <p class="p1"><br></p>
 212 <p class="p7">(</p>
 213 <p class="p7"><span class="s5">var</span> randomNumbers, histogram, distribution, randomTable, randTableSize=200;</p>
 214 <p class="p7"><span class="s5">var</span> minValue = -250, maxValue = 250, numVals = 10000, numBins = 500;</p>
 215 <p class="p6"><br></p>
 216 <p class="p8">// create some random distribution with values between 0 and 1</p>
 217 <p class="p7">distribution = <span class="s5">Array</span>.fill(randTableSize,<span class="Apple-converted-space"> </span></p>
 218 <p class="p7"><span class="Apple-tab-span">     </span>{ <span class="s5">arg</span> i; (i/ randTableSize * 35).sin.max(0) * (i / randTableSize) }</p>
 219 <p class="p7">);</p>
 220 <p class="p6"><br></p>
 221 <p class="p8">// render a randomTable</p>
 222 <p class="p7">randomTable = distribution.asRandomTable;<span class="Apple-converted-space"> </span></p>
 223 <p class="p6"><br></p>
 224 <p class="p8">// get random numbers, scale them</p>
 225 <p class="p6"><br></p>
 226 <p class="p7">randomNumbers = <span class="s5">Array</span>.fill(numVals, { randomTable.tableRand * (maxValue - minValue) + minValue; });<span class="Apple-converted-space"> </span></p>
 227 <p class="p7">histogram = randomNumbers.histo(numBins, minValue, maxValue);</p>
 228 <p class="p6"><br></p>
 229 <p class="p6"><br></p>
 230 <p class="p9"><span class="s1">histogram.plot(</span>"this is the histogram we got"<span class="s1">);</span></p>
 231 <p class="p9"><span class="s1">distribution.plot(</span>"this was the histogram we wanted"<span class="s1">);</span></p>
 232 <p class="p7">)</p>
 233 <p class="p1"><br></p>
 234 <p class="p1"><br></p>
 235 <p class="p1"><br></p>
 236 <p class="p1"><br></p>
 237 <p class="p1"><br></p>
 238 <p class="p1"><br></p>
 239 <p class="p4"><b>Random decisions:</b></p>
 240 <p class="p1"><br></p>
 241 <p class="p1"><br></p>
 242 <p class="p3"><b>coin</b> <span class="Apple-tab-span"> </span>simulates a coin toss and results in true or false.<span class="Apple-converted-space"> </span></p>
 243 <p class="p3"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span>1.0 is always true, 0.0 is always false, 0.5 is 50:50 chance.</p>
 244 <p class="p1"><br></p>
 245 <p class="p7">20.do({ 0.5.coin.postln });</p>
 246 <p class="p1"><br></p>
 247 <p class="p3">biased random decision can be simulated bygenerating a single value<span class="Apple-converted-space"> </span></p>
 248 <p class="p3">and check against a threshhold:</p>
 249 <p class="p1"><br></p>
 250 <p class="p7">20.do({ (1.0.linrand &gt; 0.5).postln });</p>
 251 <p class="p7">20.do({ (exprand(0.05, 1.0) &gt; 0.5).postln });</p>
 252 <p class="p1"><br></p>
 253 <p class="p4"><b>Generating Collections of random numbers:</b></p>
 254 <p class="p1"><br></p>
 255 <p class="p8"><span class="s1"><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span></span>// size, minVal, maxVal<span class="Apple-converted-space"> </span></p>
 256 <p class="p7"><span class="s5">Array</span>.rand(7, 0.0, 1.0).postln;<span class="Apple-tab-span">      </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span></p>
 257 <p class="p6"><br></p>
 258 <p class="p8">// is short for:</p>
 259 <p class="p6"><br></p>
 260 <p class="p7"><span class="s5">Array</span>.fill(7, { rrand(0.0, 1.0) }).postln;<span class="Apple-tab-span">   </span></p>
 261 <p class="p6"><br></p>
 262 <p class="p6"><br></p>
 263 <p class="p8"><span class="s1"><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span></span>// size, minVal, maxVal<span class="Apple-converted-space"> </span></p>
 264 <p class="p7"><span class="s5">List</span>.linrand(7, 10.0, 15.0).postln;<span class="Apple-tab-span">  </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span></p>
 265 <p class="p6"><br></p>
 266 <p class="p8">// is short for:</p>
 267 <p class="p6"><br></p>
 268 <p class="p7"><span class="s5">List</span>.fill(7, { 10 + 5.0.linrand }).postln;<span class="Apple-tab-span">   </span></p>
 269 <p class="p6"><br></p>
 270 <p class="p7"><span class="s5">Signal</span>.exprand(10, 0.1, 1);</p>
 271 <p class="p6"><br></p>
 272 <p class="p7"><span class="s5">Signal</span>.rand2(10, 1.0);</p>
 273 <p class="p6"><br></p>
 274 <p class="p1"><br></p>
 275 <p class="p1"><br></p>
 276 <p class="p4"><b>Random choice from Collections</b></p>
 277 <p class="p1"><span class="Apple-tab-span">     </span></p>
 278 <p class="p3"><b>choose </b><span class="Apple-tab-span">       </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span>equal chance for each element.</p>
 279 <p class="p1"><br></p>
 280 <p class="p7">10.do({ [ 1, 2, 3 ].choose.postln });<span class="s8"><span class="Apple-tab-span">       </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span></span></p>
 281 <p class="p1"><br></p>
 282 <p class="p1"><br></p>
 283 <p class="p3"><b>Weighted choice:</b></p>
 284 <p class="p1"><br></p>
 285 <p class="p3"><b>wchoose(weights)</b><span class="Apple-tab-span">      </span>An array of weights sets the chance for each element.</p>
 286 <p class="p1"><br></p>
 287 <p class="p7">10.do({ [ 1, 2, 3 ].wchoose([0.1, 0.2, 0.7]).postln });<span class="Apple-tab-span">      </span></p>
 288 <p class="p1"><br></p>
 289 <p class="p1"><br></p>
 290 <p class="p1"><br></p>
 291 <p class="p4"><b>Randomize the order of a Collection:<span class="Apple-converted-space"> </span></b><span class="s8"><span class="Apple-tab-span">    </span></span></p>
 292 <p class="p1"><br></p>
 293 <p class="p3"><b>scramble</b></p>
 294 <p class="p1"><br></p>
 295 <p class="p7"><span class="s5">List</span>[ 1, 2, 3, 4, 5 ].scramble.postln;</p>
 296 <p class="p1"><br></p>
 297 <p class="p1"><br></p>
 298 <p class="p4"><b>Generate random numbers without duplicates:<span class="Apple-converted-space"> </span></b><span class="s8"><span class="Apple-tab-span">     </span></span></p>
 299 <p class="p1"><br></p>
 300 <p class="p7">f = { <span class="s5">|n=8, min=0, max=7|</span> (min..max).scramble.keep(n) };</p>
 301 <p class="p7">f.value(8, 0, 7)</p>
 302 <p class="p6"><br></p>
 303 <p class="p1"><br></p>
 304 <p class="p1"><br></p>
 305 <p class="p4"><b>Randomly group a Collection:<span class="Apple-tab-span">      </span></b></p>
 306 <p class="p1"><br></p>
 307 <p class="p3"><b>curdle(probability)</b></p>
 308 <p class="p1"><br></p>
 309 <p class="p3">The probability argument sets the chance that two adjacent elements will be separated.</p>
 310 <p class="p1"><br></p>
 311 <p class="p7">[ 1, 2, 3, 4, 5, 6, 7, 8 ].curdle(0.2).postln;<span class="Apple-tab-span">       </span><span class="s9">// big groups</span></p>
 312 <p class="p6"><br></p>
 313 <p class="p7">[ 1, 2, 3, 4, 5, 6, 7, 8 ].curdle(0.75).postln;<span class="Apple-tab-span">      </span><span class="s9">// small groups</span></p>
 314 <p class="p1"><br></p>
 315 <p class="p1"><br></p>
 316 <p class="p1"><br></p>
 317 <p class="p1"><br></p>
 318 <p class="p1"><br></p>
 319 <p class="p1"><br></p>
 320 <p class="p4"><b>Random signal generators, i.e. UGens:</b></p>
 321 <p class="p1"><br></p>
 322 <p class="p10"><span class="s10"><a href="../UGens/Noise/PinkNoise.html">PinkNoise</a></span></p>
 323 <p class="p10"><span class="s10"><a href="../UGens/Noise/WhiteNoise.html">WhiteNoise</a></span></p>
 324 <p class="p10"><span class="s10"><a href="../UGens/Noise/GrayNoise.html">GrayNoise</a></span></p>
 325 <p class="p10"><span class="s10"><a href="../UGens/Noise/BrownNoise.html">BrownNoise</a></span></p>
 326 <p class="p10"><span class="s10"><a href="../UGens/Noise/PinkerNoise.html">PinkerNoise</a></span></p>
 327 <p class="p10"><span class="s10"><a href="../UGens/Noise/ClipNoise.html">ClipNoise</a></span></p>
 328 <p class="p10"><span class="s10"><a href="../UGens/Noise/LFNoise0.html">LFNoise0</a></span></p>
 329 <p class="p10"><span class="s10"><a href="../UGens/Noise/LFNoise1.html">LFNoise1</a></span></p>
 330 <p class="p10"><span class="s10"><a href="../UGens/Noise/LFNoise2.html">LFNoise2</a></span></p>
 331 <p class="p10"><span class="s10"><a href="../UGens/Noise/LFClipNoise.html">LFClipNoise</a></span></p>
 332 <p class="p10"><span class="s10"><a href="../UGens/Noise/LFDNoise0.html">LFDNoise0</a></span></p>
 333 <p class="p10"><span class="s10"><a href="../UGens/Noise/LFDNoise1.html">LFDNoise1</a></span></p>
 334 <p class="p10"><span class="s10"><a href="../UGens/Noise/LFDNoise3.html">LFDNoise3</a></span></p>
 335 <p class="p10"><span class="s10"><a href="../UGens/Noise/LFDClipNoise.html">LFDClipNoise</a></span></p>
 336 <p class="p10"><span class="s10"><a href="../UGens/Noise/Dust.html">Dust</a></span></p>
 337 <p class="p10"><span class="s10"><a href="../UGens/Noise/Dust2.html">Dust2</a></span></p>
 338 <p class="p10"><span class="s10"><a href="../UGens/Noise/Crackle.html">Crackle</a></span></p>
 339 <p class="p11"><span class="s10"><a href="../UGens/Triggers/TWChoose.html">TWChoose<span class="s11"></span></a></span></p>
 340 <p class="p1"><br></p>
 341 <p class="p1"><br></p>
 342 <p class="p1"><br></p>
 343 <p class="p1"><br></p>
 344 <p class="p3"><b>UGens that generate random numbers once, or on trigger:</b></p>
 345 <p class="p1"><br></p>
 346 <p class="p3"><span class="s12"><a href="../UGens/Random/Rand.html">Rand</a></span><span class="Apple-tab-span">        </span><span class="Apple-tab-span">    </span>uniform distribution of float between (lo, hi), as for numbers.</p>
 347 <p class="p3"><span class="s12"><a href="../UGens/Random/IRand.html">IRand</a></span><span class="Apple-tab-span">      </span><span class="Apple-tab-span">    </span>uniform distribution of integer numbers.</p>
 348 <p class="p3"><span class="s12"><a href="../UGens/Random/TRand.html">TRand</a></span><span class="Apple-tab-span">      </span><span class="Apple-tab-span">    </span>uniform distribution of float numbers, triggered</p>
 349 <p class="p3"><span class="s12"><a href="../UGens/Random/TIRand.html">TIRand</a></span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span>uniform distribution of integer numbers, triggered</p>
 350 <p class="p3"><span class="s12"><a href="../UGens/Random/LinRand.html">LinRand</a></span><span class="Apple-tab-span">  </span><span class="Apple-tab-span">    </span>skewed distribution of float numbers, triggered</p>
 351 <p class="p3"><span class="s12"><a href="../UGens/Random/NRand.html">NRand</a></span> <span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span>sum of n uniform distributions, approximates gaussian distr. with higher n.</p>
 352 <p class="p3"><span class="s12"><a href="../UGens/Random/ExpRand.html">ExpRand</a></span> <span class="Apple-tab-span"> </span><span class="Apple-tab-span">    </span>exponential distribution</p>
 353 <p class="p3"><span class="s12"><a href="../UGens/Random/TExpRand.html">TExpRand</a></span><span class="Apple-tab-span">        </span>exponential distribution, triggered</p>
 354 <p class="p3"><span class="s12"><a href="../UGens/Random/CoinGate.html">CoinGate</a></span><span class="Apple-tab-span">        </span><span class="Apple-tab-span">    </span>statistical gate for a trigger</p>
 355 <p class="p3"><span class="s12"><a href="../UGens/Triggers/TWindex.html">TWindex</a></span><span class="Apple-tab-span">        </span><span class="Apple-tab-span">    </span>triggered weighted choice between a list</p>
 356 <p class="p1"><br></p>
 357 <p class="p3"><span class="Apple-tab-span">     </span>Like using randSeed to set the random generatorsfor each thread in sclang, <span class="Apple-converted-space"> </span></p>
 358 <p class="p3"><span class="Apple-tab-span">     </span>you can choose which of several random generators on the server to use,</p>
 359 <p class="p3"><span class="Apple-tab-span">     </span>and you can reset (seed) these random generators:<span class="Apple-converted-space"> </span></p>
 360 <p class="p10"><span class="s10"><a href="../UGens/Random/RandID.html">RandID</a></span></p>
 361 <p class="p10"><span class="s10"><a href="../UGens/Random/RandSeed.html">RandSeed</a></span></p>
 362 <p class="p1"><br></p>
 363 <p class="p1"><br></p>
 364 <p class="p3"><b>UGens that generate random numbers on demand ("Demand UGens"):</b></p>
 365 <p class="p1"><br></p>
 366 <p class="p10"><span class="s10"><a href="../UGens/Synth control/Demand Rate/Dwhite.html">Dwhite</a></span></p>
 367 <p class="p10"><span class="s10"><a href="../UGens/Synth control/Demand Rate/Dbrown.html">Dbrown</a></span></p>
 368 <p class="p3">Diwhite</p>
 369 <p class="p3">Dibrown</p>
 370 <p class="p10"><span class="s10"><a href="../UGens/Synth control/Demand Rate/Drand.html">Drand</a></span></p>
 371 <p class="p3">Dxrand</p>
 372 <p class="p1"><br></p>
 373 <p class="p3">see random patterns with analogous names</p>
 374 <p class="p1"><br></p>
 375 <p class="p1"><br></p>
 376 <p class="p1"><br></p>
 377 <p class="p4"><b>Random Patterns:<span class="Apple-converted-space"> </span></b></p>
 378 <p class="p1"><br></p>
 379 <p class="p1"><br></p>
 380 <p class="p8"><span class="s12"><a href="../Streams-Patterns-Events/Patterns/Prand.html">Prand</a></span><span class="s1">([ 1, 2, 3 ], </span><span class="s5">inf</span><span class="s1">);<span class="Apple-tab-span">      </span><span class="Apple-tab-span">    </span></span>// choose randomly one from a list ( list, numRepeats)</p>
 381 <p class="p8"><span class="s12"><a href="../Streams-Patterns-Events/Patterns/Pxrand.html">Pxrand</a></span><span class="s1">([ 1, 2, 3 ]);<span class="Apple-tab-span"> </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span></span>// choose one element from a list, no repeat of previous choice</p>
 382 <p class="p8"><span class="s12"><a href="../Streams-Patterns-Events/Patterns/Pwhite.html">Pwhite</a></span><span class="s1">(24, 72);<span class="Apple-tab-span">      </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span></span>// within range [&lt;hi&gt;, &lt;lo&gt;], choose a random value.</p>
 383 <p class="p8"><span class="s12"><a href="../Streams-Patterns-Events/Patterns/Pbrown.html">Pbrown</a></span><span class="s1">(24, 72, 5)<span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span></span>// within range [&lt;hi&gt;, &lt;lo&gt;], do a random walk</p>
 384 <p class="p8"><span class="s1"><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span></span>// with a maximum &lt;step&gt; to the next value.</p>
 385 <p class="p8"><span class="s5">Pgbrown</span><span class="s1">(24, 72, 1.4)<span class="Apple-tab-span">        </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span></span>// geometric brownian motion</p>
 386 <p class="p6"><br></p>
 387 <p class="p12"><span class="s10"><a href="../Streams-Patterns-Events/Patterns/Plprand.html">Plprand</a></span><span class="s13"><span class="Apple-tab-span">   </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-converted-space"> </span></span></p>
 388 <p class="p12"><span class="s10"><a href="../Streams-Patterns-Events/Patterns/Phprand.html">Phprand<span class="s14"></span></a></span></p>
 389 <p class="p12"><span class="s10"><a href="../Streams-Patterns-Events/Patterns/Pmeanrand.html">Pmeanrand<span class="s14"></span></a></span></p>
 390 <p class="p12"><span class="s10"><a href="../Streams-Patterns-Events/Patterns/Pbeta.html">Pbeta<span class="s14"></span></a></span></p>
 391 <p class="p12"><span class="s10"><a href="../Streams-Patterns-Events/Patterns/Pcauchy.html">Pcauchy<span class="s14"></span></a></span></p>
 392 <p class="p12"><span class="s10"><a href="../Streams-Patterns-Events/Patterns/Pgauss.html">Pgauss<span class="s14"></span></a></span></p>
 393 <p class="p12"><span class="s10"><a href="../Streams-Patterns-Events/Patterns/Ppoisson.html">Ppoisson<span class="s14"></span></a></span></p>
 394 <p class="p12"><span class="s10"><a href="../Streams-Patterns-Events/Patterns/Pexprand.html">Pexprand<span class="s14"></span></a></span></p>
 395 <p class="p6"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span></p>
 396 <p class="p8"><span class="s12"><a href="../Streams-Patterns-Events/Patterns/Pwrand.html">Pwrand</a></span><span class="s1">([ 1, 2, 3 ], [0.1, 0.3, 0.6], 20);<span class="Apple-tab-span">    </span></span>// choose from a list, probabilities by weights</p>
 397 <p class="p6"><br></p>
 398 <p class="p8"><span class="s12"><a href="../Streams-Patterns-Events/Patterns/Pshuf.html">Pshuf</a></span><span class="s1">([ 1, 2, 3, 4 ], 2);<span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span></span>// scramble the list, then repeat that order &lt;repeats&gt; times.</p>
 399 <p class="p6"><br></p>
 400 <p class="p7"><span class="s12"><a href="../Streams-Patterns-Events/Patterns/Pwalk.html">Pwalk</a></span>( (0 .. 10), <span class="s5">Prand</span>([ -2,-1, 1, 2], <span class="s5">inf</span>));<span class="Apple-tab-span"> </span><span class="Apple-tab-span">    </span><span class="s9">// random walk.<span class="Apple-converted-space"> </span></span></p>
 401 <p class="p6"><br></p>
 402 <p class="p8"><span class="s12"><a href="../Streams-Patterns-Events/Patterns/Pfsm.html">Pfsm</a></span><span class="s1"> <span class="Apple-tab-span">  </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span></span>// random finite state machine pattern, see its help file.<span class="Apple-converted-space"> </span></p>
 403 <p class="p8"><span class="s1"><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span></span>// see also MarkovSet in MathLib quark</p>
 404 <p class="p6"><br></p>
 405 <p class="p8"><span class="s12"><a href="../Streams-Patterns-Events/Patterns/Pseed.html">Pseed</a></span><span class="s1">(seed, pattern)<span class="Apple-tab-span">  </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span></span>// sets the random seed for that stream.</p>
 406 <p class="p6"><br></p>
 407 <p class="p6"><br></p>
 408 <p class="p8">// some basic examples</p>
 409 <p class="p6"><br></p>
 410 <p class="p7">(</p>
 411 <p class="p7"><span class="s5">Pbind</span>(<span class="s15">\note</span>, <span class="s5">Prand</span>([ 0, 2, 4 ], <span class="s5">inf</span>),<span class="Apple-converted-space"> </span></p>
 412 <p class="p7"><span class="Apple-tab-span">     </span><span class="s15">\dur</span>, 0.2</p>
 413 <p class="p7">).play;</p>
 414 <p class="p7">)</p>
 415 <p class="p6"><br></p>
 416 <p class="p7">(</p>
 417 <p class="p13">Pbind<span class="s1">(</span></p>
 418 <p class="p7"><span class="Apple-tab-span">     </span><span class="s15">\note</span>, <span class="s5">Pxrand</span>([ 0, 2, 4 ], <span class="s5">inf</span>),</p>
 419 <p class="p7"><span class="Apple-tab-span">     </span><span class="s15">\dur</span>, 0.2</p>
 420 <p class="p7">).play;</p>
 421 <p class="p7">)</p>
 422 <p class="p6"><br></p>
 423 <p class="p7">(</p>
 424 <p class="p13">Pbind<span class="s1">(</span></p>
 425 <p class="p7"><span class="Apple-tab-span">     </span><span class="s15">\note</span>, <span class="s5">Pwrand</span>([ 0, 2, 4 ], [0.1, 0.3, 0.6], <span class="s5">inf</span>),</p>
 426 <p class="p7"><span class="Apple-tab-span">     </span><span class="s15">\dur</span>, 0.2</p>
 427 <p class="p7">).play;</p>
 428 <p class="p7">)</p>
 429 <p class="p6"><br></p>
 430 <p class="p7">(</p>
 431 <p class="p13">Pbind<span class="s1">(</span></p>
 432 <p class="p7"><span class="Apple-tab-span">     </span><span class="s15">\midinote</span>, <span class="s5">Pwhite</span>(48, 72, <span class="s5">inf</span>),</p>
 433 <p class="p7"><span class="Apple-tab-span">     </span><span class="s15">\dur</span>, 0.2</p>
 434 <p class="p7">).play;</p>
 435 <p class="p7">)</p>
 436 <p class="p6"><br></p>
 437 <p class="p7">(</p>
 438 <p class="p13">Pbind<span class="s1">(</span></p>
 439 <p class="p7"><span class="Apple-tab-span">     </span><span class="s15">\midinote</span>, <span class="s5">Pbrown</span>(48, 72, 5, <span class="s5">inf</span>),</p>
 440 <p class="p7"><span class="Apple-tab-span">     </span><span class="s15">\dur</span>, 0.2</p>
 441 <p class="p7">).play;</p>
 442 <p class="p7">)</p>
 443 <p class="p6"><br></p>
 444 <p class="p7">(</p>
 445 <p class="p13">Pbind<span class="s1">(</span></p>
 446 <p class="p7"><span class="Apple-tab-span">     </span><span class="s15">\midinote</span>, <span class="s5">Pgbrown</span>(48, 72, 0.5, <span class="s5">inf</span>).round,</p>
 447 <p class="p7"><span class="Apple-tab-span">     </span><span class="s15">\dur</span>, 0.2</p>
 448 <p class="p7">).play;</p>
 449 <p class="p7">)</p>
 450 <p class="p6"><br></p>
 451
 452
 453 </body></html>