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Abstract and Applied Analysis
Volume 2014, Article ID 241684, 11 pages
Research Article

Identification of V-Formations and Circular and Doughnut Formations in a Set of Moving Entities with Outliers

Universidad Nacional de Colombia, Sede Medellín, Bloque M8A, Medellín, Colombia

Received 1 November 2013; Revised 8 February 2014; Accepted 24 February 2014; Published 10 April 2014

Academic Editor: J.-C. Cortés

Copyright © 2014 Francisco Javier Moreno Arboleda et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Diverse movement patterns may be identified when we study a set of moving entities. One of these patterns is known as a V-formation for it is shaped like the letter V. Informally, a set of entities shows a V-formation if the entities are located on one of their two characteristic lines. These lines meet in a position where there is just one entity considered the leader of the formation. Another movement pattern is known as a circular formation for it is shaped like a circle. Informally, circular formations present a set of entities grouped around a center in which the distance from these entities to the center is less than a given threshold. In this paper we present a model to identify V-formations and circular formations with outliers. An outlier is an entity which is part of a formation but is away from it. We also present a model to identify doughnut formations, which are an extension of circular formations. We present formal rules for our models and an algorithm for detecting outliers. The model was validated with NetLogo, a programming and modeling environment for the simulation of natural and social phenomena.