File: RosslerL.html

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<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<html>
<head>
<meta http-equiv="content-type" content="text/html; charset=utf-8">
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<body><b><font size="5"><font color="#000000">RosslerL Rossler chaotic generator<br>
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</font></font></b><font size="5"><font color="#000000"><font size="3"><br>
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<b># x, y, z = RosslerL.ar(freq, a, b, c, h, xi, yi, zi, mul, add)<br>
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</b><br>
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<b>freq<!--invalid font number 1-->
</b> - iteration frequency in Hertz<br>
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<b>a, b, c<!--invalid font number 1-->
</b>- equation variables<br>
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<b>h<!--invalid font number 1-->
</b> - integration time step<br>
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<b>xi<!--invalid font number 1-->
</b> - initial value of x<br>
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<b>yi<!--invalid font number 1-->
</b> - initial value of y<br>
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<b>zi<!--invalid font number 1-->
</b> - initial value of z<br>
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<span style="font-size:9pt"><font color="#000000"><br>
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<font size="3"><font color="#000000">A strange attractor discovered by Otto Rossler based on work in chemical kinetics.<!--invalid font number 2-->
<span style="font-size:9pt"><br>
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<font size="3">The system is composed of three ordinary differential equations:<br>
 <br>
 x' = - y - z<br>
 y' = x + ay<br>
 z' = b + z(x - c)<!--invalid font number 2-->
<span style="font-size:9pt"><br>
<br>
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<font size="3">The time step amount<!--invalid font number 0-->
<b>h<!--invalid font number 1-->
</b>determines the rate at which the ODE is evaluated. Higher values will increase the<br>
rate, but cause more instability. A safe choice is the default amount of 0.05.<br>
<br>
The following examples treat RosslerL as a single-output UGen (i.e. using x only):<br>
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<font color="#bf0000">// vary frequency - these parameters are for &quot;one-pulse&quot; orbit<font color="#000000"><br>
{ <font color="#0000bf">RosslerL<font color="#000000">.ar(<font color="#0000bf">MouseX<font color="#000000">.kr(20, <font color="#0000bf">SampleRate<font color="#000000">.ir), 0.36, 0.35, 4.5) * 0.3 }.play(s);<br>
<br>
<font color="#bf0000">// randomly modulate params<font color="#000000"><br>
(<br>
{ <font color="#0000bf">RosslerL<font color="#000000">.ar(<br>
 <font color="#0000bf">SampleRate<font color="#000000">.ir, <br>
 0.2, <font color="#bf0000">// First variable tends to lead to NaN if modulated in this example<font color="#000000"><br>
 <font color="#0000bf">LFNoise0<font color="#000000">.kr(1, 0.01, 0.2),<br>
 <font color="#0000bf">LFNoise0<font color="#000000">.kr(1, 0.2, 0.7)<br>
) * 0.2 }.play(s);<br>
)<br>
<br>
<font color="#bf0000">// as a frequency control<font color="#000000"><br>
{ <font color="#0000bf">SinOsc<font color="#000000">.ar(<font color="#0000bf">Lag<font color="#000000">.ar(<font color="#0000bf">RosslerL<font color="#000000">.ar(<font color="#0000bf">MouseX<font color="#000000">.kr(1, 200)))*800+900)*0.4 }.play(s);<br>
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<br>
An example utilising the three different outputs as pitch, PWM and pan values (respectively):<br>
<br>
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<span style="font-size:9pt"><font color="#000000">(<br>
{<br>
# x,y,z = <font color="#0000bf">RosslerL<font color="#000000">.ar(<font color="#0000bf">MouseX<font color="#000000">.kr(1, 200));<br>
<font color="#0000bf">Pan2<font color="#000000">.ar(<font color="#0000bf">Pulse<font color="#000000">.ar(x.range(100,1000), y.range(0,1), 0.3), z)<br>
}.play(s)<br>
)<br>
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<font size="3"><font color="#000000"><br>
</font></font></body>
</html>