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Contact: Morgan Kelly
Princeton University

Exclusion Regions

Caption: The simulation revealed the underlying pattern of the chicken's cones. While the arrangement is a type of packing problem, it has the addition of an "exclusion region" around each type of cone that other cones cannot enter. Cones of the same type shut out each other more than they do unlike cones, and this variant exclusion causes distinctive cone patterns. Each type of cone's pattern overlays the pattern of another cone. So, while it appeared that the cones were irregularly placed, their distribution was actually uniform over large distances. In the diagram above, two cells (left) appear randomly placed. However, the exclusion regions for both the black (center) and red cells (right) push against nearby cells and give the cell arrangements structure. The black cells fall into a triangle-like pattern in the absence of other cell types.

Credit: Image courtesy of Salvatore Torquato, Princeton University

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