Latoocarfian chaotic function

Latoocarfian.ar(a, b, c, d, mul, add)

This is a function given inClifford Pickover's book Chaos In Wonderland, pg 26. 

The function has four parameters a, b, c, and d.

The function is:

xnew = sin(y * b) + c * sin(x * b);

ynew = sin(x * a) + d * sin(y * a);

x = xnew;

y = ynew;

output = x;

According to Pickover, parameters a and b should be in the range from -3 to +3,

and parameters c and d should be in the range from 0.5 to 1.5.

The function can, depending on the parameters given, give continuous chaotic

output, converge to a single value (silence)  or oscillate in a cycle (tone).

This UGen is experimental and not optimized currently, so is rather hoggish of CPU.

//not installed yet!

(

SynthDef("help-Latoocarfian", { arg out=0, a=1.0, b=1.0, c=0.7, d=0.7;

var env, a, b, c, d;

env = EnvGen.kr(Env.linen(0.1, 1, 0.1), doneAction:2);

Out.ar(out, 

Latoocarfian.ar(a, b, c, d, 0.05)

)

}).send(s);

)

{

Synth.new("help-Latoocarfian", [

\a, 3.0.rand, \b, 3.0.rand, 

\c, 0.5 + 1.5.rand, \d, 0.5 + 1.5.rand]

);

1.0.wait;

}.play;

//todo:

(

// GUI version:

w = GUIWindow.new("Latoocarfian", Rect.newBy(40,40,200,300));

SliderView.new(w, Rect.newBy(8,8,20,280), nil, 0, -3, 3);

SliderView.new(w, Rect.newBy(32,8,20,280), nil, 0, -3, 3);

SliderView.new(w, Rect.newBy(56,8,20,280), nil, 1, 0.5, 1.5);

SliderView.new(w, Rect.newBy(80,8,20,280), nil, 1, 0.5, 1.5);

{ XFadeTexture.ar({

w.views.at(0).value = 3.0.rand2;

w.views.at(1).value = 3.0.rand2;

w.views.at(2).value = 0.5 + 1.0.rand;

w.views.at(3).value = 0.5 + 1.0.rand;

//[a, b, c, d].postln;

Latoocarfian.ar(w.views.at(0).value, w.views.at(1).value, 

w.views.at(2).value, w.views.at(3).value, 0.05)

},  1, 0.1, 1) }.play;

)