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4 Simulation Results
In this section, we comment on some simulations. We shall first compare the
formation of a unique cluster for a single type of corpses, in the cases of proba-
bilistic and deterministic pick-up. We then observe how our CA, in the presence
of several types of corpses, sorts them into distinct clusters. Finally, we study
the number of clusters and the density of the largest cluster as a function of
time. This provides a measurement of the e
A
ciency of the clustering process.
We consider a 290
×
200 lattice, with periodic boundary conditions, containing
N
0
= 1500 corpses. This is fixed for all simulations. During a given run,
N
0
and the number of ants remain constant (no birth or death). Throughout the
dynamics, clusters of corpses appear, gathered as a result of the pick-up and
deposition activity of the moving ants. The mean-free path of an ant is set to 50
via the probability
r
0
=0
.
98 of not being deflected at a site.
Simulations were run on a farm of PCs using eight 1 GHz Pentium nodes
under Linux. As our code is not optimized, we only give an idea of the simulation
time. Typically, 10
000 iterations with a 1000 ants took 320[s] on 8 nodes and
1600[s] on a single one. Note that these timings depends little on the number of
ants.
4.1 Clustering
In figure 1, we show three stages of the clustering process with a 1000 ants in a
space without obstacles. Ants and corpses are initially randomly distributed. The
pick-up probability parameters are
α
p
=10
,β
p
=0
.
35. Deterministic pick-up
(
α
p
=
∞,β
p
>
1) means a corpse is loaded with probability 1. For probabilistic
pick-up, after about 3
.
6
×
10
5
iterations (approximately 190 minutes), a single
compact cluster emerges. At the same stage, in the deterministic case, there
are two loosely bound clusters scattered with empty sites. This results from the
ants being allowed to pick-up indiscriminately from any cluster. Similar sparse
clusters were already observed in [4]. In both cases, the final cluster is not static,
since the ants can still withdraw corpses from it and re-deposit them elsewhere
about its perimeter. However, in the deterministic case, the final cluster keeps
on assembling and disassembling, while in the probabilistic case, it is almost
inactive. The bias between pick-up and deposition, related to the probability
given by (2), is responsible for cluster compactness. In Deneubourg's model, this
bias results from the intelligence of the ants (their memory) which locally favors
the growth of large clusters at the expense of smaller ones.
Let us now define what we mean by cluster. This definition depends on
the local topology. A cluster is a set of corpses. Two corpses with overlapping
neighborhoods belong to the same cluster. The area covered by a cluster is
defined as the number of sites occupied by its corpses and their neighborhoods.
The density of a cluster is then the number of corpses in it divided by its area.
From our simulations, we observe that
ρ ≈
0
.
88. Note that the density of corpses
in clusters is mainly constant after the start-up stage. The area covered by a
cluster always includes sites without corpses on its border. Hence, our density
