'' Some "Strange Attractor" math Per Bloland copied from a web page:

(setf a1 1.0) ;;a bunch of coefficients, which i left alone for the assn
(setf a2 .1)  ;;if i follow my plan to write variations on this, 
(setf a3 -1.0);;i will play with these.
(setf a4 .6)
(setf a5 -.1)
(setf a6 -.7)
(setf a7 -.1)
(setf a8 -.6)
(setf a9 -.4)
(setf a10 -.5)
(setf a11 -.6)
(setf a12 -.1)


(defun quadraticx (x y) ;;1st half of the formulataken from mathworld.wolfram.com
  (+ a1 (* a2 x) (* a3 x x) (* a4 x y) (* a5 y) (* a6 y y)))

(defun quadraticy (x y)
  (+ a7 (* a8 x) (* a9 x x) (* a10 x y) (* a11 y) (* a12 y y)))


(defun run-quads (x y &key (times 20));;run those suckers!
  (loop repeat times
       collect (setf xtemp (quadraticx x y))
       collect (setf y (quadraticy x y))
       do (setf x xtemp) ))

;; A procedure to make random values for all the coefficients:

(defun randomize-coefficients ()
  (setf a1 (between -1.0 1.0))
  (setf a2 (between -1.0 1.0))
  (setf a3 (between -1.0 1.0))
  (setf a4 (between -1.0 1.0))
  (setf a5 (between -1.0 1.0))
  (setf a6 (between -1.0 1.0))
  (setf a7 (between -1.0 1.0))
  (setf a8 (between -1.0 1.0))
  (setf a9 (between -1.0 1.0))
  (setf a10 (between -1.0 1.0))
  (setf a11 (between -1.0 1.0))
  (setf a12 (between -1.0 1.0)))


;; A procedure that randomizes the coefficients and tries to
;; get a list of 10 x, y values in the range [-2,2].  If a number
;; is out of range, it re-randomizes the coefficients and starts over.

(defun safe-run (x y &key (times 20));;run those suckers!
  (let ((original-x x) (original-y y))
    (randomize-coefficients)
    (let ((possible-result
	   (loop repeat times
		 for oldx = x
		 for oldy = y
		 with ok = T
		 while ok
		 collect (setf x (quadraticx oldx oldy))
		 collect (setf y (quadraticy oldx oldy))
		 do 
		 (print (list 'x x 'y y 'ok ok))
		 (if (or (> (abs x) 2) (> (abs y) 2))
		     (progn 
		       (print '(this is not OK!))
		       (setf ok nil)
		       (print (list 'ok 'is 'now ok)))))))
      (if (= (* 2 times) (length possible-result))
	  possible-result
	  (safe-run original-x original-y :times times)))))