Emergent behavior in systems of confined growth

Abstract

Nature abounds with elegant structures, like the spirals of galaxies and the bilateral symmetry of the human form. It is believed that the forms of these structures are natural results of the interactions between their numerous constituents. These interactions are believed to be simple, but from the study of complex systems, it is known that as the number of constituents in a system increases, it may approach a state of order. This natural emergence of order is called emergent behavior, which is believed to be responsible for the existence of the order that we see in nature.
In this paper we study the behavior of structures that undergo confined growth. These structures are grown using simple rules and we try to look for signatures of spontaneous ordering or emergent behavior. The system considered consists of two-dimensional structures made up of identical circular cells confined in a square field of a particular size. Every cell in the structure is in contact with at least one other cell and none of the cells' interior must overlap with another cells' interior.