#lang scribble/manual
@(require (for-label racket))

@title{(standard-l rate freq k xi yi)}

(standard-n rate freq k xi yi)

Standard map chaotic generator.

freq - iteration frequency in Hertz
k    - perturbation amount
xi   - initial value of x
yi   - initial value of y

A linear-interpolating sound generator based on the difference
equations:

	xn+1 = (xn + yn+1) % 2pi
	yn+1 = (yn + ksin(xn)) % 2pi

The standard map is an area preserving map of a cylinder discovered by
the plasma physicist Boris Chirikov.

Vary frequency


@racketblock[
(audition
 (out 0 (mul (standard-l ar (mouse-x kr 20 sample-rate 0 0.1) 1 0.5 0) 0.3)))
]

Mouse-controlled parameter.


@racketblock[
(let ((f (fdiv sample-rate 2))
      (x (mouse-x kr 0.9 4 0 0.1)))
  (audition
   (out 0 (mul (standard-l ar f x 0.5 0) 0.3))))
]

As a frequency control


@racketblock[
(let* ((x (mouse-x kr 0.9 4 0 0.1))
       (f (mul-add (standard-l ar 40 x 0.5 0) 800 900)))
  (audition
   (out 0 (mul (sin-osc ar f 0) 0.4))))
]