LatoocarfianL latoocarfian chaotic generator

LatoocarfianL.ar(freq, a, b, c, d, xi, yi, mul, add)

freq - iteration frequency in Hertz

a, b, c, d - equation variables

xi - initial value of x

yi - initial value of y

A linear-interpolating sound generator based on a function given in Clifford Pickover's 

book Chaos In Wonderland, pg 26. 

The function is:

x_n+1 = sin(by_n) + c*sin(bx_n)

y_n+1 = sin(ay_n) + d*sin(ax_n)

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.

// default initial params

{ LatoocarfianL.ar(MouseX.kr(20, SampleRate.ir)) * 0.2 }.play(s);

// randomly modulate all params

(

{ LatoocarfianL.ar(

SampleRate.ir/4,

LFNoise2.kr(2,1.5,1.5), 

LFNoise2.kr(2,1.5,1.5),

LFNoise2.kr(2,0.5,1.5),

LFNoise2.kr(2,0.5,1.5)

) * 0.2 }.play(s);

)