# Pillars

This page was automatically generated by NetLogo 3.1.4. Questions, problems? Contact feedback@ccl.northwestern.edu.

The applet requires Java 1.4.1 or higher. It will not run on Windows 95 or Mac OS 8 or 9. Mac users must have OS X 10.2.6 or higher and use a browser that supports Java 1.4. (Safari works, IE does not. Mac OS X comes with Safari. Open Safari and set it as your default web browser under Safari/Preferences/General.) On other operating systems, you may obtain the latest Java plugin from Sun’s Java site.  General information on the models, including instructions for running them on your own computer, is available from the NetLogo Simulation Information Page.  To download this page, do not use "Save As," but right-click (or on Macs control-click) on this link.  You also need to download the NetLogo program, which you can do by right-clicking or control-clicking this link.

There is also a 3D version of this program, Pillars3D.  You cannot run it as an applet, but you can download it with this link, and run it on NetLogo 3D Preview 4, available at http://ccl.northwestern.edu/netlogo.

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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 (P, H, C, or cement).

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.

## CREDITS AND REFERENCES

Implemented 2007-10-01 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.