57 lines
1.4 KiB
Text
57 lines
1.4 KiB
Text
|
class:: HenonC
|
||
|
|
summary:: Henon map chaotic generator
|
||
|
|
categories:: UGens>Generators>Chaotic
|
||
|
|
related:: Classes/HenonN, Classes/HenonL
|
||
|
|
|
||
|
|
description::
|
||
|
|
A cubic-interpolating sound generator based on the difference equation:
|
||
|
|
|
||
|
|
teletype::
|
||
|
|
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:
|
||
|
|
|
||
|
|
code::
|
||
|
|
(
|
||
|
|
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 });
|
||
|
|
)
|
||
|
|
::
|
||
|
|
|
||
|
|
classmethods::
|
||
|
|
method:: ar
|
||
|
|
argument:: freq
|
||
|
|
Iteration frequency in Hertz
|
||
|
|
argument:: a
|
||
|
|
Equation variable
|
||
|
|
argument:: b
|
||
|
|
Equation variable
|
||
|
|
argument:: x0
|
||
|
|
Initial value of x
|
||
|
|
argument:: x1
|
||
|
|
Second value of x
|
||
|
|
|
||
|
|
examples::
|
||
|
|
code::
|
||
|
|
// 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);
|
||
|
|
::
|