A swarm model that induces emergent collective behaviors from the individuals in the swarm is proposed for the planar formations of multiple autonomous unmanned aerial vehicles (UAVs). The stability of the formations, or cohesiveness of the swarm, is guaranteed via the the Direct Method of Lyapunov which is used to construct the instantaneous velocity of each individual. A Lyapunov-like function, from which the velocity controllers are constructed, expresses the three well-known Reynolds' flocking rules as artificial potential fields for inter-individual attraction and avoidance. Basic patterns of planar formation which are similar to emergent behaviors distinctive of swarming in nature are demonstrated via computer simulations. Different emergent patterns are obtained with variations in the system parameters.