class:: CuspN
summary:: Cusp map chaotic generator
categories:: UGens>Generators>Chaotic
related:: Classes/CuspL

description::
A non-interpolating sound generator based on the difference equation:

teletype::
	x(n+1) = a - b * sqrt(|x(n)|)
::

sclang code translation:

code::
(
var a = 1.0, b = 1.9, xi = 0, size = 64;
plot(size.collect { xi = a - (b * sqrt(abs(xi))) });
)
::

classmethods::

method:: ar
argument::freq
Iteration frequency in Hertz
argument::a
Equation variable
argument::b
Equation variable
argument::xi
Initial value of x
argument::mul
argument::add

examples::
code::
// vary frequency
{ CuspN.ar(MouseX.kr(20, SampleRate.ir), 1.0, 1.99) * 0.3 }.play(s);

// mouse-controlled params
{ CuspN.ar(SampleRate.ir/4, MouseX.kr(0.9,1.1,1), MouseY.kr(1.8,2,1)) * 0.3 }.play(s);

// as a frequency control
{ SinOsc.ar(CuspN.ar(40, MouseX.kr(0.9,1.1,1), MouseY.kr(1.8,2,1))*800+900)*0.4 }.play(s);
::