A cubic-interpolating sound generator based on the difference equation:
x(n+2) = 1 - a * x(n+1)^2 + b * x(n)
This equation was discovered by French astronomer Michel Hénon while studying the orbits of stars in globular clusters.
for more information on chaos theory henon formulas:
"https://en.wikipedia.org/wiki/Chaos_theory"
"https://en.wikipedia.org/wiki/Hénon_map"
sclang code translation:
(var a = 1.4, b = 0.3, x0 = 0, x1 = 1, size = 64;plot(size.collect { var aux = 1 - (a * (x1 ** 2)) + (b * x0); x0 = x1; x1 = aux; aux });)| freq |
Iteration frequency in Hertz |
| a |
Equation variable |
| b |
Equation variable |
| x0 |
Initial value of x |
| x1 |
Second value of x |
// default initial params{ HenonC.ar(MouseX.kr(20, SampleRate.ir)) * 0.2 !2}.scope(s);// mouse-control of params{ HenonC.ar(SampleRate.ir/4, MouseX.kr(1,1.4), MouseY.kr(0,0.3)) * 0.2 !2}.scope(s);// randomly modulate params({ HenonC.ar(SampleRate.ir/8, LFNoise2.kr(1, 0.2, 1.2), LFNoise2.kr(1, 0.15, 0.15)) ! 2 * 0.02 }).scope(s);// as a frequency control{ SinOsc.ar(HenonC.ar(40, MouseX.kr(1,1.4), MouseY.kr(0,0.3))*800+900) * 0.04 ! 2 }.scope(s);