Abstract We describe our conversion of a simulation of the seed foraging behavior of the ant species P. barbatus to a generative art technique for creating ant paintings. We also show how the key parameters involved influence the results

Gary R Greenfield

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Ant Paintings Based on the Seed Foraging Behavior of P. barbatus
Gary R. Greenfield
Department of Mathematics & Computer Science
University of Richmond
Richmond, VA 23173, USA
ggreenfi@richmond.edu
Abstract
We describe our conversion of a simulation of the seed foraging behavior of the ant species P. barbatus to a generative
art technique for creating ant paintings. We also show how the key parameters involved influence the results.
1 Introduction
Ant paintings trace their origins to the ant colony simulation experiments of Ramos [18, 19]. These exper-
iments led directly to the physically embodied collective robotics paintings of Moura [15, 16]. Monmarché
et al. [2] appear to be the first to have actually used the term “ant painting” to describe abstract images made
by virtual ants that roam over a toroidal grid. In their model, 4 to 6 virtual ants paint by depositing “scent”
in the form of one color while searching for scent in the form of a different color. Greenfield [7] evolved ant
paintings using a very similar model but with 8 to 12 ants. Urbano [21] considered an ant painting model
where individual cells in the environment exuded virtual scent to attract ants. Because cells ceased to exude
scent after they were first visited by an ant, once all cells are visited and painted according to the colors
assigned to the ants, the painting was finished. Greenfield [6][7] further developed this model by having
the ants also exude virtual scents which acted as ant attractants or repellants. A gray scale version of an
ant painting model from Greenfield [10] was also used by Greenfield and Machado as part of an artists and
critics simulation [13].
The first ant paintings faithful to a biological model were executed by Urbano. He appealed to a model
for nest construction by the ant species T. albipennis [22]. Here, virtual ants use a stochastic virtual sand
grain foraging, collecting, and depositing algorithm in order to construct circular walls defining their nest’s
outermost boundary. By carefully specifying radii, centers, and sand grain color preferences, Greenfield used
this same technique to develop ant paintings composed of symmetric patterns of circles [11, 12]. Greenfield
[5] has also modified an ant colony model proposed by Jones [14] for visualizing evolution and formation of
plasma transport networks of the slime mold Physarum to develop ant paintings which he called called “net-
work transport overlays”. For both of these these physically motivated ant painting models the environment
is toroidal.
In this paper we develop an ant painting technique based on the seed foraging behavior of the ant species
P. barbatus. It does not use a toroidal environment.
2 P. barbatus Seed Foraging Behavior
The guiding theme of a recent book on ant behavior by biologist D. Gordon [4] is that many ant behaviors are
governed by the rate of interaction with other ants. In particular, for the species of harvester ant P. barbatus,
seed forager recruitment is controlled by the rate of return of seed bearers. Although, certain specifics and
technical details are scattered in the literature [1, 3, 17, 20], the general nature of the seed foraging behavior
is summarized in [4] as follows:
Proceedings of Bridges 2013: Mathematics, Music, Art, Architecture, Culture
43
To initiate foraging patroller ants leave the nest to determine the days foraging trails. The patrollers
meander around the foraging area, and eventually return to the nest. The patrollers put down a short chemical
on the nest mound only about 20 centimeters long that shows the foragers which direction to take when they
leave the nest. Foraging begins when patrollers return at a rate of about 6 per minute. When a forager follows
a patroller marked direction, it may travel another 20 meters in that general direction. Once a forager goes
out, it searches until it finds and brings back a seed. The forager then waits inside the nest entrance until it
meets enough foragers returning with food to be stimulated to go out again. Interestingly, for all subsequent
trips after the first one, “a forager proceeds directly to the site where it first found food that morning, and
then searches around for another seed. Once it finds food it goes directly back to the nest” [4, p. 60].
A visualization of the foraging pattern that occurs from simulating the search phase in shown in Figure 1
which is reproduced from Greenfield [9]. It simulates one hours’ worth of foraging by 3780 foragers on a
2000×2000 grid of cells. Only about half the foragers are actively foraging outside the nest at any one time.
It is important here that the environment is not toroidal.
Figure 1: Left: The grid cells visited during the search phase of one hours’ worth of foraging. Right:
Those same grid cells weighted by visitation frequency in order to reveal the areas where seed foraging is
concentrated.
3 Stylization of the Foraging Pattern
Our goal is to visualize in a more aesthetic way the underlying complexity of the pattern that occurs when
the initial wave of foraging ants streams out of the nest, finds their first seed of the day, and then returns to
the nest.
In order to do so, we simulate the release of 1000 ants over the course of 500 time steps. Each ant follows
one of n patroller trails. Since it tends to look “wrong” from a compositional standpoint if the patroller trails
are simply arbitrary as in Figure 1, we “symmetrize” the pattern of patroller trails by spacing them uniformly
so they are separated by 360◦/n. Ants streaming out along the same trail do so in a tight beam that is only
1.5◦ degrees wide. The ants “break off” from the patroller trail in such a way that the distribution of their
distances from the nest entrance located in the center of the canvas are approximately normally distributed.
Greenfield
44
Once they break off from the trail, the ants then initiate a quasi-random walk — they meander — in
search of seeds. Seeds are uniformly distributed in the 1000×1000 cell environment in such a way that the
number of seeds per cell (the seed density) is 0.02. At this density, in order for the simulation to remain
faithful to empirical results obtained from field studies regarding the length of time it should take to find a
seed, the decision as to whether or not to award the seed to the ant when it is encountered must be stochastic.
A seed is collected from a found seed dispenser with probability 0.4.
It is not known if ants sense seeds in some way or just stumble upon them, hence it is clear that some
version of a random walk is called for. From observation, it is obvious that an ant’s random walk is not
“truly” random in the sense of changing direction at each time step, thus we call the algorithm we use a
“quasi random walk” to indicate that ants actually travel a few cells before changing direction. Moreover,
change in direction is restricted so that an ant veers up to at most 60 degrees off its current heading.
Figure 2: Clockwise, seed foraging patterns using 4, 6, 8, and 10 patroller trails.
Ant Paintings Based on the Seed Foraging Behavior of P. barbatus
45
The precise mechanism that ants use to return directly to the nest after they have found the first seed is
also not known. It has been suggested that they are able to navigate by the angle of the sun. We use two
different colors to distinguish between the search phase and the direct return phase to the nest. Further, we
modulate the color for better definition of the trail. Figure 2 shows foraging patterns using 4, 6, 8, and 10
patroller trails.
To return to the key parameter that governs the quasi-random walk search phase — the number of cells
an ant is expected to traverse before it veers — using a slightly thicker line, Figure 3 shows how the foraging
pattern is affected as this parameter takes on the values 2, 4, 6, and 8. Note that the default is 6.
Figure 3: Clockwise, seed foraging patterns using six patroller trails resulting from setting the meander
parameter set to 2, 4, 6, and 8.
Greenfield
46
4 Summary and Future Work
We have described how we converted the P. barbatus seed foraging model implemented in [9] to a generative
technique for ant paintings on a nontoroidal grid. One shortcoming is that although the virtual ants mark their
outward journey from the nest using narrow pre-assigned trails, those outward bound paths get obliterated
by ants who quickly find seeds and returm to the nests using essentailly the same paths. Another drawback
is that the paintings to not convey a strong sense of the outbound-search-inbound flow patterns that actually
place. Timing, and the fact that paths may span several pixels, complicate addressing these shortcomings.
Perhaps better use of color or modulating color shades and path widths could help.
It would also be interesting to extend the techniques here so that the paintings could also visualize the
autonomous nature of the foraging ants whereby after the first foraging excursion ants return to a dedicated
location, and to convey the return-rate induced nature of their repeated forays from the nest.
References
[1] Adler, F.R., Gordon, D.M., Optimization, conflict and non-overlapping foraging ranges in ants. Ameri-
can Naturalist, vol. 162, 2003, 529–543.
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Greenfield
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Ant Paintings Based on the Seed Foraging Behavior of P. barbatus

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Ant Paintings Based on the Seed Foraging Behavior of P. barbatus

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