En général, Space Filling Fractals vous donnera quelques-uns des meilleurs résultats à les coûts les plus bas. En particulier, je recommanderais Sierpiński curve.
Voici une exemple d'implémentation qui l'utilise:
(defvar *grid-width* 100000)
(defvar *grid-heigth* 100000)
(defvar *max-number-of-points* 1000)
(defvar *search-area-width* (* 2 *grid-width*))
(defvar *search-area-heigth* (* 2 *grid-heigth*))
(defun make-random-point (max-x max-y)
"makes a point in a random position of the grid"
(complex
(/ (random (* max-x 1000)) 1000)
(/ (random (* max-y 1000)) 1000)))
(defun make-random-point-list (max-len)
"makes a list of random points up to max-len length"
(let ((value())) ; Make a set of random points
(dotimes (n (random max-len) value)
(setq value
(cons (make-random-point *grid-width* *grid-heigth*) value)))))
(defun get-printable-point-position (point)
"Gets a rounded-off point that can be used to make a dot on a visual grid"
(complex
(round (realpart point))
(round (imagpart point))))
(defun euclid (point-a point-b)
"calculates the euclidean distance in between two points"
(let* ((p (- point-a point-b)))
(sqrt
(+ (expt (realpart p) 2)
(expt (imagpart p) 2)))))
(defstruct triangle
"A triangle consists of 3 points.
Complex numbers are used to construct the points,
the real part signifying the X axis,
and the imaginary part signifying the Y axis."
a b c)
(defun avg (&rest numbers)
"Gets the average of the numbers provided"
(if
(null numbers)
1 ; prevents divide by 0
(/ (apply #'+ numbers) (length numbers)))) ;/
(defun get-triangle-centre (triangle)
"Gets the centre of a triangle"
(avg (triangle-a triangle)
(triangle-b triangle)
(triangle-c triangle)))
(defstruct (triangle-list
(:include triangle))
point-list)
(defun triangle-split (triangle)
"Splits a triangle in two according to the rule:
{ a0->c1; b0->a1,c2; c0->a2; avg(c0,a0)->b1,b2 }"
(let* ((old-a-point (triangle-a triangle))
(old-b-point (triangle-b triangle))
(old-c-point (triangle-c triangle))
(new-b-point (avg old-a-point old-c-point)))
(list
(make-triangle-list :a old-b-point :b new-b-point :c old-a-point)
(make-triangle-list :a old-c-point :b new-b-point :c old-b-point))))
(defun triangle-list-split (triangle-list)
"Split a triangle list and acomodate all the points in their right places"
(let* ((triangles (triangle-split triangle-list))
(triangle-a (car triangles))
(triangle-b (cadr triangles))
(centre-a (get-triangle-centre triangle-a))
(centre-b (get-triangle-centre triangle-b)))
(dolist (point (triangle-list-point-list triangle-list))
(if (< (euclid point centre-a) (euclid point centre-b))
(setf (triangle-list-point-list triangle-a)
(cons point (triangle-list-point-list triangle-a)))
(setf (triangle-list-point-list triangle-b)
(cons point (triangle-list-point-list triangle-b)))))
(let ((list-a (triangle-list-point-list triangle-a))
(list-b (triangle-list-point-list triangle-b)))
(if (= 1 (length list-a))
(setf (triangle-list-point-list triangle-a) (car list-a)))
(if (= 1 (length list-b))
(setf (triangle-list-point-list triangle-b) (car list-b))))
(list triangle-a triangle-b)))
(defun print-point (out point &rest args)
"Utility function - Pretty-prints a point"
(format out "(X:~F, Y:~F)"
(realpart point)
(imagpart point))
args)
(defun pprint-triangle-list (out triangle-list &rest args)
"Utility function - Pretty-prints a triangle-list object"
(format out " TRIANGLE{
A:~/print-point/
B:~/print-point/
C:~/print-point/
CENTRE:~/print-point/
POINTS:{~{~/print-point/~^,~% ~}}~& }"
(triangle-a triangle-list)
(triangle-b triangle-list)
(triangle-c triangle-list)
(get-triangle-centre triangle-list)
(let ((points (triangle-list-point-list triangle-list)))
(cond
((null points) ())
((listp points) points)
(t (list points)))))
args)
(defun print-list-of-triangle-list (lst)
"Pretty-prints a list of triangle-list objects"
(format t "(~{~/pprint-triangle-list/~^,~% ~}~&)" lst))
(defun explode (lst)
"explodes a triangle-list list and gets all
the points in the order they should be"
(let ((l (flatten lst)))
(cond
((null l)())
((triangle-list-p l) (explode (triangle-list-split l)))
((null (triangle-list-point-list (car l)))
(explode (cdr l)))
((atom (triangle-list-point-list (car l)))
(cons (car l) (explode (cdr l))))
(t (explode (append (triangle-list-split (car l)) (cdr l)))))))
(defun flatten (lst)
"Flattens a list (removes nesting and nulls)"
(cond
((atom lst) lst)
((listp (car lst))
(append (flatten (car lst)) (flatten (cdr lst))))
(t (append (list (car lst)) (flatten (cdr lst))))))
(let ((triangle (make-triangle-list
:a (complex 0 *search-area-heigth*)
:b 0
:c *search-area-width*
:point-list (make-random-point-list *max-number-of-points*))))
(print-list-of-triangle-list (explode triangle)))
J'avais aussi une version à l'aide d'un GA (que l'on en C), mais il vit dans un disque dur mort.
