The patterns created by antlion groups are emergent: they don't exhibit top-down structure like a highly regular tiled or even consistent polymorphism across trials.
However, the antlions did cluster somewhat (remaining close to eachother despite available space, in some cases) but regardless maintained sufficient area to capture food, either of the cannibalistic or regular sort.
These patterns likely developed, at least in the short terms these antlions were studied, by slow movement of the pits across the trial area, either by live migration or abandonment of old pits (which often occurred).
The Voronoi diagrams are the primary source which exhibits these traits: scaled down to the window of the trial area which antlions populated, the area claimed by each individual antlion is somewhat consistent, explicable by a selfish algorithm: each antlion wants to optimize its area of ant capture (represented by ``claimed'' regions on the Voronoi diagrams), so the area was shared about equally by the group.
Also, average distance to nearest neighbor decreased with lesser trial area: from 5--6cm on average in the 33x32cm trial down to 3--3.5cm in tho 8x7cm trial, the graph in Figure 3 demonstrates a clear correlation, with a notable (but inconclusive) p-value of about 8\%, between territorial area and total area.
Additionally, compensatory behaviors were exhibited which further managed the population: cannibalism and reclusion both prevented surface overpopulation (because when two antlions were too close, one or the other usually occurred)

On the scale of individual pits, antlions optimize for energy. Unrelated to their partners' pits size, antlions typically size their pits to capture ants.
Weekly feedings helped maintain the natural analogue to scarce ant feedings, so the antlions had to create their pits as determined by the density of the environment (simulated by a small area, which antlions readily detected despite their blindness by extensive trails created in the container).
This caused them to create significantly smaller pits (so much so that at about .8cm deep and .8cm wide, measurement errors became excessively significant) in smaller containers (in terms of depth and width) because the antlions were aware that ants would, regardless, fall in rather than survive throughout the antlion colony.
This is in contrast to the 33x32 where none of the antlions formed pits shallower than 1.1cm and one pit was 4.2cm wide.
Furthermore, large pits may have become an unnecessary aggression or warning mechanism because, in order to preserve the larvae, the species would require sufficiently clear land that a group could populate the surface fully without unintentionally increasing cannibalism rates.

Throughout the study a clear increase in extreme behaviors was noted, which is shown by Table 1 (Appendix B, Figure 4), which shows that the initial 33x32 trial size had a 19.35\%  fatality rate among the 31 antlions involved in the trial, compared the last 8x7 trial size which had a 33.33\% fatality rate.
This resulted in a 13.9785\% increase in deaths throughout the study, which falls within a p value of below 0.05, making the results statistically significant.
The increase in deaths point towards increased cannibalism within the competing antlion population, as all deceased bodies were found with no head or appendages, but rather just a hard exoskeleton, leading to the conclusion that the antlions were cannibalized.
The observed cannibalism of antlions supported the hypothesis that extreme behaviors would increase as trial size decreased, as antlions are known to resort to cannibalism in times of environmental and biological stress.
Furthermore, the increased cannibalism was most likely a result of increased one one interactions between antlions within a smaller trial groups, as the antlions in smaller trial groups have less space to settle in, increasing the chances that they will come into contact with another antlion.
Increased cannibalism could also have been a result of increased competition at lower trial sizes, as in lower trial sizes food was not as spread out as much as it was in larger trial sizes, which could result in increased competition, leading to aggressive behavior such as cannibalism.
Furthermore, extreme behavior such as reclusivity, measured in the total antlions without pits, barely changed in relation to the total antlions introduced in the trial, as a reclusivity percentage of 29.03\% was noted in the 33x32 trial, and a reclusivity percentage of 25\% was noted in the 8x7 trial (Appendix B, Figure 4), which is not statistically significant change.
This led to the conclusion that as trial size decreases aggressive behavior such as cannibalism increases, however, pacifistic behaviors such as reclusiveness are not affected.
However, because the total amount of pits observed in each trial decrease as trial size decreases, it is possible that antlions keep a ration between the total amount of available territory and the number of active pits to avoid competition, as mentioned above in the territory calculation.

Both sets of behavior---extreme interactions like high levels of reclusivity or cannibalism and the spatial patterning of antlions under space constraints---are useful in models of the natural environments and behavior of antlion larvae.
Reclusivity, for example, is an evolved behavior intended to allow as many larvae as possible to become adults as quickly as possible: rather than spread the wealth of ant food across a very large population, a partial proportion surface and would become adults within a matter of weeks.
This is a protection mechanism against predators, and makes sense for the individual: reclusive behavior underground usually doesn't lead to death and below a certain threshold of energy intake, a pit on the surface doesn't make sense---especially considering the cannibalism risk.
Cannibalism is partially an accidental behavior, but could certainly have some evolutionary implications: if the food supply runs low, antlions will move more and more antlions will be consumed by their peers to make up for the food supply.
Furthermore, the increased surface density under more dense conditions, simulated by a small trial area, (rather than constant density with increasing reclusivity) means that antlions use population density as a proxy for food density because in nature, it would mean the area can support sufficient surface-dwellers.
Antlions' behavior in the artifically constrained trial areas models closely their behavior in densely populated, constantly recycling nurseries, which explains the lack of highly regular structure.