turtles-own
[
  temp               ;; specific turtle's temperature
  turtle-neighbors   ;; set of sourrounding turtles
]

globals
[
  ave-metal-temp   ;; shows average temperature of all metal
  num-frozen       ;; keeps track of how many atoms are frozen
  time             ;; keeps track of time passing in system
  temp-range       ;; for histogram
  colors           ;; used both to color turtles, and for histogra
  pens             ;; keeps track of all the histogram's pen names
]

to setup
  ca 
  set colors sentence (white - 1) [cyan sky blue violet magenta pink red]
  set pens []
  set temp-range (init-metal-temp - melting-temp) / (length colors - 1)

  ask patches with [(abs pycor >= box-width / 2) or  
                    (abs pxcor >= box-width / 2)]
  [ set pcolor white ] 

  ;; fill room to desired percentage
  ask patches
  [
    if ((fill-percentage > random-float 100) and (pcolor != white))
    [
      sprout 1
      [
        set shape "T"
        set temp init-metal-temp
        set turtle-neighbors (turtles at-points [[1 0] [0 1] [-1 0] [0 -1]])
        set-color
      ]
    ]
  ]
  set ave-metal-temp init-metal-temp
  set time 0
  if (count turtles > 0)
  [ 
    setup-plots
    do-plots 
  ]
end


to go 
  ;; stop if all turtles are below melting temp
  if (max (values-from turtles [temp]) < melting-temp)[ stop ] 
  ;; otherwise... 
  set time (time + 1)
  set num-frozen 0
  ask turtles [ move ]
  ask turtles [ rotate ]
  ask turtles [ cool-turtles ]
  ask turtles [ set-color ]
  set ave-metal-temp (mean values-from turtles [temp])
  if (count turtles > 0)
  [ do-plots ]
end


;; turtles procedure -- if metal is liquid, move to a randomly
;; selected neighboring patch that is not already occupied
to move  
  locals [move-choices]
  if (temp > melting-temp)   
  [
    set move-choices neighbors4 with [(pcolor != white) and (not any?
turtles-here)]
    if (random-one-of move-choices != nobody)
    [ 
      set move-choices random-one-of move-choices 
      setxy pxcor-of move-choices pycor-of move-choices
    ]
  ]
end


;; turtle procedure -- if metal is liquid and it is next to a solid,
;; change its heading to that of the solid; otherwise, just rotate
;; randomly
to rotate 
  locals [frozen-neighbors]
  set turtle-neighbors turtles at-points [[1 0] [0 1] [-1 0] [0 -1]] 
  if (temp > melting-temp) 
  [
    set frozen-neighbors (turtle-neighbors with [temp <= melting-temp])
    ifelse (any? frozen-neighbors)
      [ set heading (heading-of (random-one-of frozen-neighbors)) ]
      [ rt random-float 360 ]
  ]
end


;; turtle procedure -- sets turtle's temp to ave temp of all
;; neighboring turtles and patches added turtle's own temp in twice so
;; it changes more slowly
to cool-turtles
  locals [total-temp total-num walled-sides]
  set walled-sides neighbors4 with [pcolor = white]
  set total-temp ((sum values-from turtle-neighbors [temp]) + 
                  (room-temp * (count walled-sides) + temp))
  set total-num ((count turtle-neighbors) + (count walled-sides) + 1)
  set temp (total-temp / total-num)
end


;; turtle procedure
to set-color  
  locals [index]
  ; create index ranging from 1 to 8 for all melting colors
  set index (floor ((temp - melting-temp) / temp-range)) + 1
  ifelse (index < 0 ) 
  [
    set color white - 1
    set num-frozen (num-frozen + 1)
  ]
  [
    if index >= length colors
    [ set index (length colors) - 1 ]
    set color item index colors
  ]
end


to setup-plots
  set-current-plot "Average Metal Temperature"
  set-plot-y-range room-temp init-metal-temp

  set-current-plot "Number Solidified"
  set-plot-y-range 0 count turtles

  set-current-plot "Temperatures"
  set-plot-y-range 0 count turtles
  set-histogram-num-bars 1 + (length colors)
  make-histogram-pens
end

to make-histogram-pens
  locals [index top bottom]
  set bottom (round room-temp)
  set top (round melting-temp)
  set index 0
  repeat (length colors) 
  [
    create-temporary-plot-pen bottom + " - " + top
    set-plot-pen-mode 1
    set-plot-pen-color (item index colors)
    set pens lput (bottom + " - " + top) pens

    set index index + 1
    set bottom top
    set top (round ((index * temp-range) + melting-temp))
  ]
end

to do-plots
  set-current-plot "Average Metal Temperature"
  plot ave-metal-temp
  set-current-plot "Number Solidified"
  plot num-frozen
  if histogram? [ do-histogram ]
end

to do-histogram
  locals [index temp-color]
  set-current-plot "Temperatures"
  set index 0
  repeat (length colors)
  [
    set temp-color (item index colors)
    set-current-plot-pen (item index pens)
    plot-pen-reset
    if any? turtles with [color = temp-color]
    [ plotxy index count turtles with [color = temp-color] ]
    set index index + 1
  ]
end


; *** NetLogo Model Copyright Notice ***
;
; This model was created 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.
;
; Copyright 2002 by Uri Wilensky.  Updated 2002.  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.
;
; To refer to this model in academic publications, please use:
; Wilensky, U. (2002).  NetLogo Crystallization Moving model.
; http://ccl.northwestern.edu/netlogo/models/CrystallizationMoving.
; 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/CrystallizationMoving
; for terms of use.
;
; *** End of NetLogo Model Copyright Notice ***
@#$#@#$#@
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@#$#@#$#@
WHAT IS IT?
-----------
This model simulates the movement of metal atoms as a system crystallizes.  It is very similar to the Crystallization Basic model, except here the atoms are free to move about.  They randomly move in any direction that is not already occupied by something else, such as another atom or a wall.  Therefore, in order to allow movement, there must be empty spaces between atoms.  Initially these empty spaces, or voids, are randomly distributed, as they would be in a liquid metal.

The first atoms to crystallize have a random orientation.  However, when a liquid atom about to crystallize is next to an already crystallized atom, the liquid atom orients itself with the solid atom, thus creating a crystal.  As more and more atoms solidify, the crystals grow.  Within each crystal, all the atoms are oriented with one another, but within the entire metal, all the crystals have random orientations.  Each individual crystal is called a grain.   When two crystals grow up next to each other, they form what is called a grain boundary.

When a metal is stressed, such as when it is pulled from both ends, deformations occur in the crystal structure.  As more stress is applied, these deformations pass through the crystal structure, allowing the metal to bend.  Grain boundaries prevent deformations from flowing through the metal.  Therefore, pieces of metal with fewer grain boundaries tend to be ductile, while pieces of metal with more grain boundaries tend to be brittle.

(Note that the actual number of atoms is small compared to a real metal sample and the metal is only two-dimensional.  In addition, the movement of the atoms is limited to discrete patch sizes.)


HOW TO USE IT
-------------
Buttons:
SETUP: Resets the simulation, and sets the metal to the correct size.
GO-ONCE: Runs the simulation for one time step.
GO: Runs the simulation continuously until either the GO button is pressed again, or all of the atoms are frozen.

Sliders:
BOX-WIDTH: How many atoms wide the metal is.
FILL-PERCENTAGE: What percentage of the box contains atoms.  Smaller values allow for more movement.
ROOM-TEMP: Varies the temperature of the room.
INIT-METAL-TEMP: Varies the initial temperature of the metal.
MELTING-TEMP: Varies the temperature at which the metal solidifies.

Monitors:
AVE-METAL-TEMP: Monitors the average temperature of all the atoms.
TIME: Keeps track of the time that has elapsed during each run.

Switches:
HISTOGRAM?: Turns the histogram plotting on and off.  Turning off the histogram speeds up the model.

Graphs:
AVERAGE METAL TEMPERATURE: Plots the average temperature of all the metal over time.
NUMBER SOLIDIFIED: Plots how many metal atoms are below the melting temperature over time.
TEMPERATURES:  Histograms how many atoms are in each temperature range.  (Note that the colors of the histogram match the actual colors of the atoms.)


THINGS TO TRY
---------------
Set BOX-WIDTH to 15, FILL-PERCENTAGE to 85, and leave the rest of the sliders at their initial values (ROOM-TEMP at 20, INIT-METAL-TEMP at 1550, and MELTING-TEMP at 500).  Run the entire simulation by clicking on SETUP and GO, and then waiting for the metal to completely crystallize.  Repeat this several times.  What happens to the empty spaces between the atoms?  How do you think this would affect the properties of the overall metal?

Now set BOX-WIDTH to 29 and leave the rest of the settings how they were in the previous paragraph.  As before, run the entire simulation by clicking on SETUP and GO, and then waiting for the metal to completely crystallize.  What are some things that are different this time?  What stayed the same?

Set ROOM-TEMP to -20, INIT-METAL-TEMP to 1550, and MELTING-TEMP to 1500.  Leave BOX-WIDTH at 29 and FILL-PERCENTAGE at 85.  Now run the entire simulation.  What happens to the empty spaces between the atoms?  Why is this different from the previous simulations?  How do you think this would affect the properties of the overall metal?


EXTENDING THE MODEL
-------------------
This model prevents more than one atom from occupying the same space.  However, in three dimensions, atoms are able to move over one another.  Change the code so turtles can move to any space inside the boundaries.  What does the resulting crystal look like?  Can you imagine what this would look like in three dimensions?

Some metal applications require that the metal's grains form long strips across the metal.  To achieve this, only one side of the metal is cooled.  This causes all of the crystals to begin on one side of the metal, and consequently grow across its length.  This is called directional solidification.  In the Procedures window, change the code so one side of the room is much cooler than the rest.


NETLOGO FEATURES
------------------
In NetLogo, a turtle's heading specifies which direction the turtle's shape appears.  However, in this model, turtles must move in a direction unrelated to their shape direction.  To circumvent this, SETXY was used to move the turtles instead of FD.

Note how we can draw a multi-colored histogram.  The HISTOGRAM primitive can only draw in one color at a time, but we work around this by calling it over and over again, plotting only one bar each time, and changing the pen color each time.

With every time step, each atom's temperature changes to the average of everything around it.  To do this, each turtle has an agent set of all of its neighboring turtles that is updated each time the turtles move.  In addition, each turtle has an agent set of all the patches surrounding it that is also updated.  Any white patches in the set are on the outside wall.  Therefore, the new temperature is taken as the average of the temperatures of the neighbor list, plus the room temperature multiplied by the number of white patches in the set.  Therefore, turtles on the edge of the metal will average in the room temperature to their temperature, but other turtles will not.


RELATED MODELS
--------------
Crystallization Basic
Crystallization Directed
Crystallization Bending


CREDITS AND REFERENCES
----------------------
Original implementation: Carrie Hobbs, for the Center for Connected Learning and Computer-Based Modeling.

To refer to this model in academic publications, please use: Wilensky, U. (2002).  NetLogo Crystallization Moving model. http://ccl.northwestern.edu/netlogo/models/CrystallizationMoving. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

In other publications, please use: Copyright 2002 by Uri Wilensky.  All rights reserved.  See http://ccl.northwestern.edu/netlogo/models/CrystallizationMoving for terms of use.
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@#$#@#$#@
NetLogo 2.0beta5
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