globals [
  time
  color-sep              ;; amount color is changed for patches
]

breeds [ balls center-of-mass ]

to setup
  ca
  set time 0
  setup-border                        
  setup-balls
  setup-center
  set color-sep (13 - (sqrt count balls)) * .1   ;;color-sep is calculated this way to create a value
  if color-sep < 0.5                             ;;that is appropriate given the number of turtles
    [ set color-sep 2 * color-sep ]
end

to setup-border
  ask patches
    [if (pxcor < 10 - screen-edge-x)
       [set pcolor blue]
     if (pxcor > screen-edge-x - 10)
       [set pcolor blue]
     if (pycor > screen-edge-y - 10)
       [set pcolor blue]
     if (pycor < 10 - screen-edge-y)
       [set pcolor blue]
    ]
end

to setup-balls            ;;creates and distributes the green turtles
  set-default-shape balls "circle"
  create-custom-balls number
    [ set color green
      rt random-float 360
      setxy (random-float (2 * (screen-edge-x - 11) ) - (screen-edge-x - 11))
            (random-float (2 * (screen-edge-y - 11) ) - (screen-edge-y - 11)) ]
end

to setup-center
  create-center-of-mass 1
  ask center-of-mass [ set color yellow ]
end

to go
  ask balls [ bounce ]
  ask center-of-mass [ move-center ]
  if trace-center?
    [ ask center-of-mass
      [ draw-center ] ]
  set time time + 1
end

to move-center  ;; center-of-mass procedure
  setxy (sum values-from turtles [xcor] - (xcor-of turtle 0) ) / (count turtles - 1)
        (sum values-from turtles [ycor] - (ycor-of turtle 0) ) / (count turtles - 1)
end

;; increases the brightness of the trace on the current patch
to draw-center  ;; center-of-mass procedure
  ifelse (pcolor = black)
    [ stamp red - (5 - color-sep) ]
    [ if (pcolor < red + (5 - color-sep - .1))
      [ stamp (pcolor + color-sep) ] ]
end

to bounce            ;; balls procedure, balls bounce off the border
  if ( (round xcor) < (10 - screen-edge-x))
    [set heading (- heading)]
  if ( (round xcor) > (screen-edge-x - 10))
    [set heading (- heading)]
  if ( (round ycor) < (10 - screen-edge-y))
    [set heading (180 - heading)]
  if ( (round ycor) > (screen-edge-y - 10))
    [set heading (180 - heading)]
  fd 1
end


; *** NetLogo Model Copyright Notice ***
;
; This model was created as part of the project: CONNECTED MATHEMATICS:
; MAKING SENSE OF COMPLEX PHENOMENA THROUGH BUILDING OBJECT-BASED PARALLEL
; MODELS (OBPML).  The project gratefully acknowledges the support of the
; National Science Foundation (Applications of Advanced Technologies
; Program) -- grant numbers RED #9552950 and REC #9632612.
;
; Copyright 1998 by Uri Wilensky. All rights reserved.
;
; Permission to use, modify or redistribute this model is hereby granted,
; provided that both of the following requirements are followed:
; a) this copyright notice is included.
; b) this model will not be redistributed for profit without permission
;    from Uri Wilensky.
; Contact Uri Wilensky for appropriate licenses for redistribution for
; profit.
;
; This model was converted to NetLogo as part of the project:
; PARTICIPATORY SIMULATIONS: NETWORK-BASED DESIGN FOR SYSTEMS LEARNING IN
; CLASSROOMS.  The project gratefully acknowledges the support of the
; National Science Foundation (REPP program) -- grant number REC #9814682.
; Converted from StarLogoT to NetLogo, 2001.  Updated 2002.
;
; To refer to this model in academic publications, please use:
; Wilensky, U. (1998).  NetLogo Random Balls model.
; http://ccl.northwestern.edu/netlogo/models/RandomBalls.
; Center for Connected Learning and Computer-Based Modeling,
; Northwestern University, Evanston, IL.
;
; In other publications, please use:
; Copyright 1998 by Uri Wilensky.  All rights reserved.  See
; http://ccl.northwestern.edu/netlogo/models/RandomBalls
; for terms of use.
;
; *** End of NetLogo Model Copyright Notice ***
@#$#@#$#@
GRAPHICS-WINDOW
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777
535
40
40
6.0
1
10
1
1
1

CC-WINDOW
3
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Command Center

BUTTON
49
50
104
83
setup
setup
NIL
1
T
OBSERVER

SLIDER
22
107
222
140
number
number
2
1000
20
1
1
NIL

BUTTON
119
50
174
83
go
go
T
1
T
OBSERVER

SWITCH
59
182
191
215
trace-center?
trace-center?
0
1
-1000

@#$#@#$#@
WHAT IS IT?
-----------
Random Balls simulates a frictionless billiard table.  The balls are drawn in green. They move in straight lines and bounce off the walls but not off of each other.  The center of mass is drawn in yellow.  A continuous trace is optionally made of it in red, with the brightness increasing each time the center of mass is on that patch, which results in the display of its statistical behavior.

HOW TO USE IT
------------- 
Select the number of balls to be used, then push SETUP.  Push GO to run the model.

THINGS TO NOTICE
----------------
Watch how the center of mass moves for a while.  Is there a pattern?  Is there a region in the box that it stays within?  

THINGS TO TRY
--------------
Run the model with a lot of turtles, then just a few.  What happens to the motion of the center of mass?  Why?  

Let the model run for a while.  What do you notice about how much time the center of mass spends at different distances from the origin (its frequency distribution)?

Push SETUP, then in the command center, type "ask balls [set heading 60]" and press ENTER.  This points all of the turtles in the same direction.  What does the center of mass do now?  Try other headings.  

EXTENDING THE MODEL
-------------------
Presently the balls don't bounce off each other.  If they did, would it make a difference in the behavior of the center of mass?  Try it. 

CREDITS AND REFERENCES
----------------------
To refer to this model in academic publications, please use: Wilensky, U. (1998).  NetLogo Random Balls model. http://ccl.northwestern.edu/netlogo/models/RandomBalls. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

In other publications, please use: Copyright 1998 by Uri Wilensky.  All rights reserved.  See http://ccl.northwestern.edu/netlogo/models/RandomBalls for terms of use.
@#$#@#$#@
default
true
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Polygon -7566196 true true 150 5 40 250 150 205 260 250

circle
true
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Circle -7566196 true true 35 35 230

@#$#@#$#@
NetLogo 2.0alpha1
@#$#@#$#@
@#$#@#$#@
@#$#@#$#@