71 lines
5.9 KiB
HTML
71 lines
5.9 KiB
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<html><head><title>Brusselator</title>
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<link rel='stylesheet' href='./../scdoc.css' type='text/css' />
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<body onload='fixTOC();prettyPrint()'>
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<div class='contents'>
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<div class='header'>
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<div id='label'>SuperCollider CLASSES (extension)</div>
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<div id='categories'><a href='./../Browse.html#UGens>Generators>Chaotic'>UGens>Generators>Chaotic</a></div>
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<h1>Brusselator</h1>
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<div id='summary'>Prigogine oscillator</div>
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</div>
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<div class='subheader'>
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<div id='filename'>Source: <a href='file:///Users/zzk/Library/Application Support/SuperCollider/Extensions/SLUGens/classes/SLUGens.sc'>/Users/zzk/Library/Application Support/SuperCollider/Extensions/SLUGens/classes/SLUGens.sc</a></div><div id='superclasses'>Inherits from: <a href="../Classes/MultiOutUGen.html">MultiOutUGen</a> : <a href="../Classes/UGen.html">UGen</a> : <a href="../Classes/AbstractFunction.html">AbstractFunction</a> : <a href="../Classes/Object.html">Object</a></div>
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<div id='related'>See also: <a href="./../Classes/Oregonator.html">Oregonator</a></div>
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</div>
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<div id='toc'>
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<ul class='toc'><li class='toc1'><a href='#description'>Description</a></li>
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<ul class='toc'></ul><li class='toc1'><a href='#classmethods'>Class methods</a></li>
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<ul class='toc'><li class='toc3'><a href='#*ar'>ar</a> </li>
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<li class='toc2'><a href='#Inherited%20class%20methods'>Inherited class methods</a></li>
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</ul><li class='toc1'><a href='#instancemethods'>Instance methods</a></li>
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<ul class='toc'><li class='toc2'><a href='#Inherited%20instance%20methods'>Inherited instance methods</a></li>
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</ul><li class='toc1'><a href='#examples'>Examples</a></li>
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<ul class='toc'></ul></ul></div>
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<p>//SLUGens released under the GNU GPL as extensions for SuperCollider 3, by Nick Collins, <a href="http://composerprogrammer.com/index.html">http://composerprogrammer.com/index.html</a><a class='anchor' name='kw_SLUGens'> </a><h2><a class='anchor' name='description'>Description</a></h2>
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<p>Euler ODE solver implementation of the Brusselator equations (<a href="http://en.wikipedia.org/wiki/Brusselator).">http://en.wikipedia.org/wiki/Brusselator).</a>
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<p>x' = x^2*y - (mu+1)*x + gamma
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<p>y' = -x^2*y + mu*x
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<p>All inputs can have .kr rate UGens plugged in.
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<p>Nonlinear oscillators can blow up, treat with caution. This one is relatively stable however, converging to a fixed point, or a limit cycle, in the upper positive quadrant. for some reasonable values. Just be careful if mu gets much bigger than gamma (though making it larger is necessary to get some chaotic oscillation behaviour); you can retrigger to get back to normal, and keep the rate lower to avoid Euler integration blow-ups. You may just need to scale and push down around zero to avoid a DC offset. Fixed point is at (x,y) = (gamma, mu/gamma)<h2><a class='anchor' name='classmethods'>Class Methods</a></h2>
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<h3 class='cmethodname'><span class='methprefix'>*</span><a name='*ar' href='./../Overviews/Methods.html#ar'>ar</a> (<span class='argstr'>reset: 0</span>, <span class='argstr'>rate: 0.01</span>, <span class='argstr'>mu: 1</span>, <span class='argstr'>gamma: 1</span>, <span class='argstr'>initx: 0.5</span>, <span class='argstr'>inity: 0.5</span>, <span class='argstr'>mul: 1</span>, <span class='argstr'>add: 0</span>)</h3>
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<div class='method'>
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<p><h4>Arguments:</h4>
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<table class='arguments'>
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<tr><td class='argumentname'>reset<td class='argumentdesc'>
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<p>If > 0.0, restart with new initial conditions sampled from initx, inity<tr><td class='argumentname'>rate<td class='argumentdesc'>
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<p>update rate for a sample step<tr><td class='argumentname'>mu<td class='argumentdesc'>
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<p>equation constant. Set mu > (gamma**2 + 1.0) for the more fun limit cycle regions<tr><td class='argumentname'>gamma<td class='argumentdesc'>
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<p>equation constant<tr><td class='argumentname'>initx<td class='argumentdesc'>
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<p>reset value for x<tr><td class='argumentname'>inity<td class='argumentdesc'>
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<p>reset value for y</table></div><h3><a class='anchor' name='Inherited%20class%20methods'>Inherited class methods</a></h3>
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<div id='inheritedclassmets'></div><h2><a class='anchor' name='instancemethods'>Instance Methods</a></h2>
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<h3><a class='anchor' name='Inherited%20instance%20methods'>Inherited instance methods</a></h3>
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<div id='inheritedinstmets'></div><h2><a class='anchor' name='examples'>Examples</a></h2>
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<pre class='code prettyprint lang-sc'>//listen to x and y output
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{Out.ar(0,Brusselator.ar(Impulse.kr(MouseY.kr(1,50,'exponential')),MouseX.kr(0.01,1,'exponential')))}.play
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//avoid DC offset (default gamma is 1.0, listening to x only, so take off gamma
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{Out.ar(0,Pan2.ar((Brusselator.ar(Impulse.kr(MouseY.kr(1,50,'exponential')),MouseX.kr(0.01,1,'exponential')))[0] - 1.0) )}.play
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//fun time, stable oscillation with these parameters
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{var mu = MouseY.kr(1.0,1.5); Out.ar(0,Pan2.ar(Brusselator.ar(0.0,MouseX.kr(0.01,0.1,'exponential'),mu,0.25)[0] ) )}.play
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{ Out.ar(0,Pan2.ar(Brusselator.ar(Impulse.kr(10),MouseX.kr(0.01,0.1,'exponential'),1.5,0.25,MouseY.kr(-1.0,1.0),0.0)[0]) )}.play
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{ Out.ar(0,Brusselator.ar(Impulse.kr(MouseY.kr(1,500,'exponential')),MouseX.kr(0.01,0.1,'exponential'),1.15,0.5,0.5,1.0) )}.play</pre>
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<p><div class='doclink'>helpfile source: <a href='file:///Users/zzk/Library/Application Support/SuperCollider/Extensions/SLUGens/HelpSource/Classes/Brusselator.schelp'>/Users/zzk/Library/Application Support/SuperCollider/Extensions/SLUGens/HelpSource/Classes/Brusselator.schelp</a><br>link::Classes/Brusselator::<br>sc version: 3.8.0</div></div></body></html>
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