turtles-own
[
  ;; a number representing the group this turtle is a member of, or -1 if this
  ;; turtle is not in a group.
  my-group
]

;;; ABOUT THE PROBLEM
;;;
;;; In some cases, you have a group of turtles that you wish to divide into
;;; groups of roughly the same size.
;;;
;;; Note that if you have a fixed number of groups known in advance, there are
;;; probably better ways to do this, using breeds, for instance. The
;;; techniques here are only necessary when you need to dynamically modify the
;;; size or number of the groups.
;;;
;;; Conceptually, there are two basic ways to form groups: by desired group
;;; size, or by desired number of groups. In either case, if the target number
;;; evenly divides the total number of turtles, there's no problem. But if it
;;; doesn't, then we have to make some decisions.
;;;
;;; When creating groups of a fixed size, say k, it's most natural to form as
;;; many groups of k turtles as possible, and then consider the remainder of
;;; the turtles "extra", and create one smaller group containing only those
;;; turtles. That way, all but one of the groups will have the desired size.
;;;
;;; When creating a fixed number of groups, it's most natural to assign one
;;; turtle to each group, and continue in this way until all turtles have been
;;; assigned. This, for instance, is the strategy one would most likely adopt
;;; in trying to distribute a large number of ping-pong balls as evenly as
;;; possible among a fixed number of buckets. In this case, all the groups
;;; will have either size k or size k + 1, for some k.
;;;
;;; The following two procedures implement each of these strategies. Which is
;;; appropriate for your model depends on your requirements. Other variations
;;; on these schemes are, of course, possible.



;;; this procedure randomly assigns turtles to groups based on the desired
;;; size of the groups. all the groups will have the desired size except for
;;; at most one group, which contains the remainder of the turtles. more
;;; formally, if there are n turtles, and the desired group size is k, this
;;; procedure will produce j = floor (n / k) groups of k turtles, and if
;;; n mod k > 0, it will produce one group of n mod k turtles.
to assign-by-size

  ;; all turtles are initially ungrouped
  ask turtles [ set my-group -1 ]
  let unassigned turtles

  ;; start with group 0 and loop to build each group
  let current 0
  while [any? unassigned]
  [
    ;; place a randomly chosen set of group-size turtles into the current
    ;; group. or, if there are less than group-size turtles left, place the
    ;; rest of the turtles in the current group.
    ask n-of (min (list group-size (count unassigned))) unassigned
      [ set my-group current ]
    ;; consider the next group.
    set current current + 1
    ;; remove grouped turtles from the pool of turtles to assign
    set unassigned unassigned with [my-group = -1]
  ]
end

;;; this procedure randomly assigns turtles to groups based on the desired
;;; number of groups. all the groups will have as close as possible to the
;;; same number of turtles. more formally, if there are n turtles, and the
;;; desired number of groups is j, then let the initial group size be
;;; k = ceiling (n / j). this procedure will produce n mod j groups of size
;;; k and j - (n mod j) groups of size k - 1.
to assign-by-number
  ;; figure out the larger of the two group sizes
  let tmp-group-size ceiling (count turtles / number-of-groups)

  ;; all turtles are initially ungrouped
  ask turtles [ set my-group -1 ]
  let unassigned turtles

  ;; start with group 0 and loop to build each group
  let current 0
  while [any? unassigned]
  [
    ;; place a randomly chosen set of tmp-group-size turtles into the current group
    ask n-of tmp-group-size unassigned
      [ set my-group current ]
    ;; consider the next group. if we're done building the larger groups,
    ;; reduce the group size by 1 for the rest of the groups.
    set current current + 1
    if current = ((count turtles) mod number-of-groups)
      [ set tmp-group-size tmp-group-size - 1 ]
    ;; remove grouped turtles from the pool of turtles to assign
    set unassigned unassigned with [my-group = -1]
  ]
end

;;;
;;; the following procedures are used to implement the visualization,
;;; and really don't have anything to do with grouping.
;;; unless you're particularly interested, it's safe to ignore the rest of the
;;; code.
;;;

;;; sets up the model
to setup
  clear-all
  crt number-of-turtles
  [
    ;; we want the color to be related to the who number of the turtles, so
    ;; that it will be fairly obvious if turtles are grouped in an ordered way.
    set color scale-color green who (number-of-turtles / -4)
                                    (number-of-turtles * 1.2)
    ;; randomly place them initially
    setxy random-xcor random-ycor
    ;; turtles start out ungrouped
    set my-group -1
  ]
  reset-ticks
end

;; causes the turtles to run around, going to their group's "home" if they're
;; in a group.
to go
  ask turtles
  [
    ;; if i'm in a group, move towards "home" for my group
    if my-group != -1
      [ face get-home ]
    ;; wiggle a little and always move forward, to make sure turtles don't all
    ;; pile up
    lt random 5
    rt random 5
    fd 1
  ]
  tick
end

;; figures out the home patch for a group. this looks complicated, but the
;; idea is simple. we just want to lay the groups out in a regular grid,
;; evenly spaced throughout the world. we want the grid to be square, so in
;; some cases not all the positions are filled.
to-report get-home ;; turtle procedure
  ;; calculate the minimum length of each side of our grid
  let side ceiling (sqrt (max [my-group] of turtles + 1))

  report patch
           ;; compute the x coordinate
           (round ((world-width / side) * (my-group mod side)
             + min-pxcor + int (world-width / (side * 2))))
           ;; compute the y coordinate
           (round ((world-height / side) * int (my-group / side)
             + min-pycor + int (world-height / (side * 2))))
end


; Public Domain:
; To the extent possible under law, Uri Wilensky has waived all
; copyright and related or neighboring rights to this model.
@#$#@#$#@
GRAPHICS-WINDOW
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17
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ticks
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TEXTBOX
11
282
232
350
To group turtles into a fixed number of groups, each of similar size, select the number of groups and press assign-by-number.
11
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TEXTBOX
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220
192
To group turtles into groups of a particular size, select the size and press assign-by-size.
11
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BUTTON
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NIL
go
T
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OBSERVER
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NIL
NIL
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BUTTON
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OBSERVER
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BUTTON
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SLIDER
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1
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HORIZONTAL

@#$#@#$#@
## WHAT IS IT?

This example demonstrates two different methods for dividing an arbitrary number of turtles into groups, either by desired group size, or by desired number of groups.

Please see the Code tab for details.
@#$#@#$#@
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@#$#@#$#@
NetLogo 5.1.0
@#$#@#$#@
set number-of-groups 25
setup
assign-by-number
repeat 25 [ go ]
@#$#@#$#@
@#$#@#$#@
@#$#@#$#@
@#$#@#$#@
default
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@#$#@#$#@
0
@#$#@#$#@