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<body><b><font size="5"><font color="#000000">FincoSprottM<!--invalid font number 1-->
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<b> Yet another chaotic system UGen<br>
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<span style="font-size:9pt"><font color="#000000"># x,y,z = <font color="#0000bf">FincoSprottM<font color="#000000">.ar(freq=22050, a= -7, b=4, h=0.05, xi=0, yi=0, zi=0, mul=1.0, add=0.0)<br>
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<font color="#000000">The "system M" described by Lucas Finco and Clint Sprott:<br>
http://sprott.physics.wisc.edu/chaos/finco/abs.html<br>
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The system is defined by:<br>
<br>
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<b><span style="font-size:16pt"><font color="#000000"><center>d<!--invalid font number 4-->
<i>x<!--invalid font number 3-->
</i>/d<!--invalid font number 4-->
<i>t<!--invalid font number 3-->
</i> = -<!--invalid font number 4-->
<i>z<!--invalid font number 5-->
</i></font></span></b><span style="font-size:16pt"><font color="#000000"> <br>
<!--invalid font number 3-->
<b>d<!--invalid font number 4-->
<i>y<!--invalid font number 3-->
</i>/d<!--invalid font number 4-->
<i>t<!--invalid font number 3-->
</i> =<!--invalid font number 4-->
<i>a<!--invalid font number 3-->
</i>|<!--invalid font number 4-->
<i>x<!--invalid font number 3-->
</i>| -<!--invalid font number 4-->
<i>y<!--invalid font number 5-->
</i></b> <br>
<!--invalid font number 3-->
<b>d<!--invalid font number 4-->
<i>z<!--invalid font number 3-->
</i>/d<!--invalid font number 4-->
<i>t<!--invalid font number 3-->
</i> = 1 +<!--invalid font number 4-->
<i>bx<!--invalid font number 3-->
</i>+<!--invalid font number 4-->
<i>y<!--invalid font number 2-->
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(NB: The parameter "a" should be negative. Its sign has been reversed compared to the formulation presented by Finco and Sprott.)<br>
<br>
See also <u>[FincoSprottL]</u> and <u>[FincoSprottS]</u><br>
</font><span style="font-size:9pt"><font color="#bf0000"><br>
</font></span><font size="3"><font color="#000000">An example using just the x value:<span style="font-size:9pt"><font color="#bf0000"><br>
<br>
</font></span></font></font><font color="#000000">{ <font color="#0000bf">FincoSprottM<font color="#000000">.ar(<font color="#0000bf">MouseX<font color="#000000">.kr(20, <font color="#0000bf">SampleRate<font color="#000000">.ir)) * 0.3 }.play(s);<br>
<br>
<br>
</font></font></font></font></font></font></font><font size="3"><font color="#000000">An example utilising the three different outputs as pitch, PWM and pan values (respectively):<br>
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<span style="font-size:9pt"><font color="#000000">(<br>
{<br>
# x,y,z = <font color="#0000bf">FincoSprottM<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 + 0.5)<br>
}.play(s)<br>
)<br>
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