Suppose we take an expression in x and y, built by nesting simple primitives: product, average, sin(pi*_), and cos(pi*_). These four operations map arguments in the range -1 to 1 to results in this same range. Thus, at any point with -1 <= x,y <= 1, our expression built from these primitives will return a value between -1 and 1. By scaling the answer to a grayscale value 0-255, we can plot the function in this 2-by-2 square. (From three such expressions, we can get red, green, and blue values for each point.)

What you get is some very nifty art!

(via PLT)

**Addendum: 03/11/09**

Noel posted some PLT Scheme code for implementation here:

```
#lang scheme/gui
(define (make-plotter drawing-fn size)
(lambda (canvas dc)
(for* ((x (in-range size))
(y (in-range size)))
(let* ([intensity (inexact->exact (round (* (/ (add1
(drawing-fn x y)) 2) 255)))]
[colour (make-object color% intensity intensity intensity)])
;;(printf "~a ~a ~a\n" intensity x y)
(send dc set-pen colour 1 'solid)
(send dc draw-point x y)))))
(define (draw-grayscale size drawing-fn)
(define frame (new frame%
[label "Random Art"]
[width size]
[height size]))
(define canvas (new canvas%
[parent frame]
[paint-callback (make-plotter drawing-fn size)]))
(send frame show #t))
(define (example1 x y)
;; some random stuff
(sin (* (sin (* (cos x) y))
(cos (*
(sin (* (sin y) (cos x)))
(cos (* (cos (* y x)))))))))
(define (example2 x y)
(if (> x 200)
1
-1))
;;(draw-grayscale 400 example1)
```