This paper presents a framework for decentralized control of self-organizing swarm systems based on the artificial potential functions (APFs). The framework explores the benefits by associating agents based on position information to realize complex swarming behaviors. A key development is the introduction of a set of association rules by APFs that effectively deal with a host of swarming issues such as flexible and agile formation. In this scheme, multiple agents in a swarm self-organize to flock and achieve formation control through attractive and repulsive forces among themselves using APFs. In particular, this paper presents an association rule for swarming that requires less movement for each agent and compact formation among agents. Extensive simulations are presented to illustrate the viability of the proposed framework.