(defclass quadtree ()
  ((nw
    :initarg :nw
    :initform nil)
   (ne
    :initarg :ne
    :initform nil)
   (sw
    :initarg :sw
    :initform nil)
   (se
    :initarg :se
    :initform nil)
   (tl
    :initarg :tl
    :initform nil)
   (br
    :initarg :br
    :initform nil)
   (conts
    :initarg :conts
    :initform nil)))

(defmethod subdivide ((tree quadtree))
  (with-slots (tl br ne nw se sw) tree
    (setf ne
          (make-instance 'quadtree :tl tl :br (mapcar #'* '(1/2 1/2) br)))
    (setf nw
          (make-instance 'quadtree :tl (mapcar #'* '(1/2 05) br) :br (mapcar #'* '(1/2 0) br)))
    (setf se
          (make-instance 'quadtree :tl (mapcar #'* '(0 1/2) br) :br (mapcar #'* '(1/2 1) br)))
    (setf sw
          (make-instance 'quadtree :tl (mapcar #'* '(1/2 1/2) br) :br br))))

(defmethod subdivide-n ((tree quadtree) times)
  (unless (= times 0)
    (subdivide tree)
    (with-slots (ne nw se sw) tree
      (subdivide-n ne (- times 1))
      (subdivide-n nw (- times 1))\
      (subdivide-n se (- times 1))
      (subdivide-n sw (- times 1)))))