patches-own [
  P new_P      ; cement with active pheromone
  C new_C      ; density of laden termites
  H new_H      ; pheromone in the air
  M new_M      ; cumulative cment
  ]
  
to setup
  cp
  ask patches with [pzcor = 0] [  ; initialize fields to small random values
    set P random 10
    set H random 10
    set C random 10
    set M C
  ]
end

to go
  ask patches with [pzcor = 0] [ ; update variables according to Deneubourg equations (except diffusion terms)
    set new_P P + C_transfer_rate * C - P_transfer_rate * P
    set new_H H + P_transfer_rate * P - H_decay_rate * H
    set new_C C + Phi - C_transfer_rate * C - C_mobility * div-grad-CH
    set new_M M + C_transfer_rate * C
    
    set P max list 0 (min list 100 new_P)  ; keep all variables within bounds
    set C max list 0 (min list 100 new_C)
    set H max list 0 (min list 100 new_H)
    set M max list 0 (min list 500 new_M)
  ]
  
  diffuse H H_diff_rate  ; pheromone diffuses in air
  diffuse C C_diff_rate  ; termite random walk is equivalent to diffusion
  show-fields            ; display requested fields
end

to show-fields           ; display requested fields
  ask patches with [pzcor = 0] [ ; ground-level patches display fields
      ifelse show_field = "cement" [ set pcolor scale-color white M 0 100]
    [ ifelse show_field = "P" [ set pcolor scale-color red P 0 10 ]
    [ ifelse show_field = "H" [ set pcolor scale-color green H 0 10 ]
    [ if show_field = "C" [ set pcolor scale-color yellow C 0 10 ]
    ]]]
  ]
  
  ask patches with [pzcor > 0] [
    ifelse show_field = "cement" and pzcor < ([M] of patch pxcor pycor 0) / 30
      [ set pcolor brown ]  ; if displaying cement, show the amount accumulated
      [ set pcolor black ]  ; otherwise clear patches above ground level
  ]
end

to-report div-grad-CH       ; approximate divergence of gradient of CH
  let Cu0 [C] of patch-at 1 0 0
  let Cd0 [C] of patch-at -1 0 0
  let C0u [C] of patch-at 0 1 0
  let C0d [C] of patch-at 0 -1 0
  report (Cu0 * [H] of patch-at 2 0 0)
   + (Cd0 * [H] of patch-at -2 0 0)
   + (C0u * [H] of patch-at 0 2 0)
   + (C0d * [H] of patch-at 0 -2 0)
   - (Cu0 + Cd0 + C0u + C0d) * H 
end
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TEXTBOX
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cement = cumulative deposited cement\nP = cement with active pheromone\nH = pheromone in environment\nC = termites carrying active cement
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0

BUTTON
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WHAT IS IT?
-----------
This program simulates the Deneubourg model of how termites coordinate their behavior to construct pillars in their nests.


HOW IT WORKS
------------
The Deneubourg model is a system of three differential equations relating the following quantities, which are two-dimensional fields.

P = amount of deposited cement with still active pheromone,
H = concentration of cement pheromone in air,
C = density of termites laden with cement.

In addition, a parameter Phi defines the rate at which laden termites arrive throughout the space. The system is dfined by the following partial differential equations:

dP / dt = C_transfer_rate C - P_transfer_rate P,
dH / dt = P_transfer_rate P - H_decay_rate H + H_diff_rate div H,
dC / dt = Phi - C_transfer_rate C + C_diff_rate div C - C_mobility div (C grad H).

Furthermore, this simulation tracks the cumulative cement (with or without pheromone) deposited in a location. This is defined by the equation:

d cement / dt = C_transfer_rate C.

HOW TO USE IT
-------------
SETUP initializes the P, H, and C fields to small random values.
RUN runs the simulator.

The parameters of the simulation are defined by the sliders P_TRANSFER_RATE, H_DECAY_RATE, H_DIFF_RATE, C_DEPOSITION_RATE, C_TRANSFER_RATE, C_MOBILITY, and PHI.

SHOW_FIELD allows the user to choose which field to display.  The P, H, and C fields are displayed on the groundplane where diffusion takes place.  If "cement" is selected, then the cumulative cement is shown by the height of the brown pillars in the Z direction. This will be more apparent if you rotate the view to an oblique perspective.

If the simulation is running, the displayed field will change as soon as SHOW_FIELD is changed. If the simulation is not running, then the displayed field can be changed by clicking UPDATE (after SHOW_FIELD has been changed).

THINGS TO NOTICE
----------------
The simulation quickly converges to a state in which the P, H, and C fields are approximately the same (subject to differing diffusion rates, etc.).

With certain parameter settings (such as the defaults), a small number of well-spaces pillars forms. With ther settings you get no pillars or a very dense forrest of pillars.

A certain amount of cement accumulates between the pillars. Why is this?


THINGS TO TRY
-------------
Explore the parameters that lead to the formation of (more or less) equally spaced pillars, as found in wasp nests? Which controls the number of pillars? Which their spacing? Begin by varying a single parameter; then try varying them in various combinations.


EXTENDING THE MODEL
-------------------
The model does not account for the depletion of material from which the termites make cement with active pheromone. How would you add this?


NETLOGO FEATURES
----------------
The diffusion of H and C (which models the wandering of the termites) are implemented with the "diffuse" command. The other derivatives (div and grad) are approximated by subtracting the values on neighboring patches.


RELATED MODELS
--------------
This section could give the names of models in the NetLogo Models Library or elsewhere which are of related interest.


CREDITS AND REFERENCES
----------------------
Implemented 2007-09-27 by B.J. MacLennan.

To refer to the original model in academic publications, please use: MacLennan, B.J. (2007).  Pillars 3D model.  http://www.cs.utk.edu/~mclennan/Classes/420/NetLogo3D/Pillars3D.html.  Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville.

In other publications, please use:  Copyright 2007 Bruce MacLennan.  All rights reserved.  See http://www.cs.utk.edu/~mclennan/Classes/420/Copyright.html for terms of use.

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NetLogo 3D Preview 5
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