globals [ time ]

turtles-own [ x-cor y-cor z-cor ]

to setup
  ca
  set time 0
  set-default-shape turtles "circle"
  cct number [
    ;; randomly distribute the turtles over the xy plane
    set x-cor random-float 40 - 20 
    set z-cor random-float 40 - 20
    set y-cor 0
    move
    render
  ]
end

to go
  set time time + 1
  ask turtles [
    move
    render
  ]
end

to move ; turtle procedure
  set y-cor ( 5 * cos ( 5 * ( time + x-cor ) ) )
            + ( 5 * cos ( 5 * ( time + z-cor ) ) )
end

to render ; turtle procedure
  ; convert 3-space coordinates to screen coordinates
  setxy (x-cor + ( z-cor / 2 ))   (y-cor + ( z-cor / 2 ))
  ; make lightness/darkness proportional to height, for added 3D effect
  set color scale-color blue y-cor -12 10
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 3D Surface model.
; http://ccl.northwestern.edu/netlogo/models/3DSurface.
; 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/3DSurface
; for terms of use.
;
; *** End of NetLogo Model Copyright Notice ***
@#$#@#$#@
GRAPHICS-WINDOW
278
23
612
378
40
40
4.0
1
10
1
1
1

CC-WINDOW
11
170
265
365
Command Center

BUTTON
63
47
130
80
NIL
setup
NIL
1
T
OBSERVER

BUTTON
142
47
209
80
NIL
go
T
1
T
OBSERVER

SLIDER
11
104
264
137
number
number
10
1500
120
10
1
NIL

@#$#@#$#@
WHAT IS IT?
-----------
This model maps turtles between Cartesian and spherical 3-dimensional coordinates.  To create the appearance of a curved 3D surface, the program generates turtles with random x- and z-coordinates, then computes each turtle's y-coordinate based on x and z, and time.  The cosine function is used in the formula to produce a curved surface.  Varying the y coordinate based on time produces motion.

To render the surface in the NetLogo graphics window, it maps from 3D to 2D coordinates as follows:

  screen x = turtle x + (turtle z) / 2
  screen y = turtle y + (turtle z) / 2

In other words, increasing z causes the turtle's apparent position to move both up and to the right.

HOW TO USE IT
------------- 
Click the SETUP button to generate the turtles and place them on the surface.  Click the GO (forever) button to run the model, which continuously varies the turtles' y-coordinates to generate a wavelike motion.

The NUM-TURTLES slider determines the number of turtles that make up the surface.

THINGS TO NOTICE
----------------
Notice that as the turtles move down (y-coordinate decreases) they become darker in color, and when they move up (y-coordinate increases) they become lighter.

THINGS TO TRY
-------------
Experiment with the NUM-TURTLES slider.  How many turtles are needed to produce a realistic effect?  Why doesn't it keep getting better-looking indefinitely as you add more turtles?

In the "move" procedure, try other numbers besides 5 in front of and inside the cosine function.  Explain the new behavior!

to move ; turtle procedure
  set y-cor ( 5 * cos ( 5 * ( time + x-cor ) ) )
            + ( 5 * cos ( 5 * ( time + z-cor ) ) )
end

EXTENDING THE MODEL
-------------------
Try changing the formula used to compute the y-coordinate to produce differently shaped surfaces.

See if you can draw not just a surface, but a three dimensional shape such as a cone or a sphere.

LANGUAGE FEATURES
-----------------
Notice the use of SCALE-COLOR to change a turtle's color based on its y-coordinate. Also see the model "Wave Machine" for a version that uses patches rather than turtles to make a 3-D membrane.


CREDITS AND REFERENCES
----------------------
To refer to this model in academic publications, please use: Wilensky, U. (2001).  NetLogo 3D Surface model. http://ccl.northwestern.edu/netlogo/models/3DSurface. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

In other publications, please use: Copyright 2001 by Uri Wilensky.  All rights reserved.  See http://ccl.northwestern.edu/netlogo/models/3DSurface for terms of use.
@#$#@#$#@
default
true
0
Polygon -7566196 true true 150 5 40 250 150 205 260 250

circle
false
0
Circle -7566196 true true 35 35 230

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