FincoSprottM Yet another chaotic system UGen
# x,y,z = FincoSprottM.ar(freq=22050, a= -7, b=4, h=0.05, xi=0, yi=0, zi=0, mul=1.0, add=0.0)
The "system M" described by Lucas Finco and Clint Sprott:
http://sprott.physics.wisc.edu/chaos/finco/abs.html
The system is defined by:
d x /d t = - z
d y /d t = a | x | - y
d z /d t = 1 + bx + y
(NB: The parameter "a" should be negative. Its sign has been reversed compared to the formulation presented by Finco and Sprott.)
See also [FincoSprottL] and [FincoSprottS]
An example using just the x value:
{ FincoSprottM.ar(MouseX.kr(20, SampleRate.ir)) * 0.3 }.play(s);
An example utilising the three different outputs as pitch, PWM and pan values (respectively):
(
{
# x,y,z = FincoSprottM.ar(MouseX.kr(1, 200));
Pan2.ar(Pulse.ar(x.range(100,1000), y.range(0,1), 0.3), z + 0.5)
}.play(s)
)