turtles-own [ dist ]

to setup
  setup-circle radius number 
  setup-plot 
end

to setup-circle [ r n ]
  ca 
  set-default-shape turtles "turtle"
  cct n [
    set size 3
    fd r 
    set heading atan ycor (- xcor)
  ]
end

to setup-plot
  set-current-plot "Distance from the origin"
  set-plot-y-range 0 screen-edge-x
end

to all-circle
  circle radius
end

to circle [ r ]
  ask turtles [
    fd ( pi * r / 180 ) * ( speed / 50 )
    rt speed / 50
    set dist distancexy 0 0 ]
  if plot?
    [ plot-distance 0 ]
end

to move-along-circle [ r ]
  fd ( pi * r / 180 ) * ( speed / 50 )
  wait .1
  rt speed / 50
  set dist distancexy 0 0
end

to zero-circle
  ask turtle 0
    [ pd 
      move-along-circle radius ] 
end

to patch-circle [ r ]
  if ( ( distancexy 0 0 ) < ( r + .5 ) ) and
     ( ( distancexy 0 0 ) > ( r - .5 ) )
  [ set pcolor white ]
end

to plot-distance [ id ]
  plot dist-of turtle id
end

to draw-circle
  patch-circle draw-rad 
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 1997 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. (1997).  NetLogo Turtles Circling model.
; http://ccl.northwestern.edu/netlogo/models/TurtlesCircling.
; 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/TurtlesCircling
; for terms of use.
;
; *** End of NetLogo Model Copyright Notice ***
@#$#@#$#@
GRAPHICS-WINDOW
266
10
639
404
60
60
3.0
1
10
1
1
1

CC-WINDOW
266
409
633
526
Command Center

BUTTON
3
79
95
112
all-circle
all-circle
T
1
T
OBSERVER
T

SLIDER
97
117
260
150
radius
radius
0.0
50.0
20.0
1.0
1
NIL

SLIDER
97
79
260
112
speed
speed
0.0
100.0
25.0
1.0
1
NIL

SLIDER
97
42
260
75
number
number
1
300
100
1
1
NIL

BUTTON
2
42
95
75
setup
setup
NIL
1
T
OBSERVER
T

BUTTON
4
154
95
187
draw-circle
draw-circle
NIL
1
T
PATCH
T

SLIDER
97
154
261
187
draw-rad
draw-rad
0.0
50.0
20.0
1.0
1
NIL

SWITCH
84
388
184
421
plot?
plot?
1
1
-1000

BUTTON
4
117
95
150
zero-circle
zero-circle
T
1
T
OBSERVER
T

PLOT
9
194
260
386
Distance from the origin
time
dist
0.0
1440.0
0.0
30.0
true
false
PENS
"distance" 1.0 0 -11352576 true

@#$#@#$#@
WHAT IS IT?
-----------
This is a new kind of mathematical investigation -- we are investigating the emergent shape created by the movement of many turtles moving independently in simple ways. Each turtle is moving so as to create a circle of a fixed radius (set by the RADIUS slider). They create their circles by moving forward a little and turning right a little so as to end up with a circle of the specified radius. We start all the turtles on a circle of that radius so they move around the circle. What happens if the radius they are all circling at is changed in mid-action? Guess before you try it.


HOW TO USE IT
-------------
The NUMBER slider determines the number of turtles circling.

The RADIUS slider determines the size of the circle each turtle moves on.

The SPEED slider determines how large a step each turtle take at each clock tick -- it determines the speed of circling.

The SETUP button creates NUMBER turtles on a circle of radius RADIUS centered at the point (0 0). The turtles are all headed so as to move around the circle.

The ALL-CIRCLE button starts the turtles circling. They are each drawing their own circle of radius RADIUS.

Change the value of the RADIUS slider while the turtles are circling.  BEFORE you do it, what is your guess as to what will happen when you change the RADIUS?


THINGS TO NOTICE
----------------
What is happening to the shape described by the turtles?

How far out do the turtles go?

How far in do they come?


THINGS TO TRY
-------------
Try different values of both starting radius and changed radius.

You can also do further investigations with the following controls:

The ZERO-CIRCLE button lets you just focus on turtle zero's movement -- all the rest are stopped.

The DRAW-CIRCLE button lets you draw a circle on the patches with a radius equal to DRAW-RAD. This way you can strack the movement of the turtles.

If the PLOT? switch is on, the plot will show a plot of turtle zero's distance from the origin as the turtles circle. 

Try the command  LT 50  while the turtles are circling. Is this the same behavior as you observed when changing the radius?

In the Command Center, get a single (or several) turtles to trace their path using the command pendown (pd).  This may help to show the relationship between the circles of individual turtles and the circle you see as they all move together.


EXTENDING THE MODEL
-------------------
What tools can you build to help visualize what is going on?


NETLOGO FEATURES
----------------
Notice the behavior of the NetLogo function ATAN. It gives positive values for x positive, so it is necessary to multiply x by -1 in order to get the tangent angles for the circle.


CREDITS AND REFERENCES
----------------------
To refer to this model in academic publications, please use: Wilensky, U. (1997).  NetLogo Turtles Circling model. http://ccl.northwestern.edu/netlogo/models/TurtlesCircling. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

In other publications, please use: Copyright 1997 by Uri Wilensky.  All rights reserved.  See http://ccl.northwestern.edu/netlogo/models/TurtlesCircling for terms of use.
@#$#@#$#@
default
true
0
Polygon -7566196 true true 150 5 40 250 150 205 260 250

turtle
true
0
Circle -7566196 true true 60 59 181
Circle -7566196 true true 124 1 57
Circle -7566196 true true 98 80 8
Circle -7566196 true true 89 55 31
Circle -7566196 true true 179 56 30
Circle -7566196 true true 92 214 32
Circle -7566196 true true 172 216 33

@#$#@#$#@
NetLogo 2.0beta4
@#$#@#$#@
setup
set radius 40
repeat 210 [ all-circle ]
@#$#@#$#@
@#$#@#$#@