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% Images of Voronoi Diagrams with side captions
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\fourpic{imgs/2019-10-30.png}{imgs/trails-24x24.png}{imgs/obstacles-24x24.png}{imgs/pits-24x24.png}{2.5in}{2in}
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\noindent{\bf Individual Trial Voronoi Diagrams}
These Voronoi diagrams, which label the territories of each ant\-lion (an ant\-lion ``possesses'' a part of the map within its segmented portion if its pit---the blue dot---is closest to that point).
By examination of the Voronoi diagrams in conjunction with measurement of the closest neighboring pit, it was determined that ant\-lions reclude and cannibalize sufficiently to ensure roughly constant habitation density
The Voronoi diagrams show how the distribution patterns of the ant\-lions changed with respect to the type of obstacle introduced in the trial, as the differences in distribution are clearly shown by the respective Voronoi diagrams. Based on the Voronoi diagrams depicted it can be concluded that the introduction of fake pits altered the distribution patterns of the ant\-lions the most, as the Voronoi diagram shows the least number of pits for this trial.
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%%Images
\fourpic{imgs/2019-12-3.png}{imgs/trails-12x12.png}{imgs/pits-12x12.png}{imgs/obstacles-12x12.png}{2.5in}{2in}
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\vbox{\hsize=5.5in%
\noindent{\bf Trial and subtrial Voronoi Diagrams}
In order to determine the true correlation between environmental factors and spacial distribution of the ant\-lions four sub trial were conducted after the initial $24\times24$ trial, where the enclosure size was reduced to $12\times12$. The Voronoi diagrams for this subtrial for each of environmental conditions and a $12\times12$ control are shown to the left.
Given the fact that the Voronoi area (the area of land that is closest to a given pit) remaIns relatively constant across all trials and sub\-trials it can effectively be concluded that the antlions have a non-random distribution pattern. Furthermore, since the mode of communication of the antlions seems to be undisturbed by both the introduction of fake pits, obstacles and the removal of trails, it can be concluded that the non-random distribution observed is not due to communication, but rather canabalsim, which is the regulating factor in the antlions distribution pattern.
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