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view/download model file: Pillars.nlogo
This program simulates the Deneubourg model of how termites coordinate their behavior to construct pillars in their nests.
There is a 3D version of Pillars, Pillars3D.nlogo, which you can download and run on your copy of NetLogo 3D Preview 5 (available from http://ccl.northwestern.edu/netlogo/). Unfortunately, it is not available as an Applet.
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.
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 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?
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.
The model does not account for the depletion of material from which the termites make cement with active pheromone. How would you add this?
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.
This section will give the names of models in the NetLogo Models Library or elsewhere which are of related interest.
Implemented 2007-09-27 by B.J. MacLennan.
To refer to this
model in academic publications, please use: MacLennan, B.J.
(2008). NetLogo Pillars model.
http://www.cs.utk.edu/~mclennan. Dept. of Electrical Engineering
& Computer Science, Univ. of Tennessee, Knoxville.