Everybody as a child would have played with Spirograph for drawing. This geometric drawing toy can create intricate patterns by combining two circular motions. These patterns fall into the class of mathematical curves known as trochoids. This trochoidal motion has been observed in planetary movements, biological spiral waves, electron behaviors, and many more naturally occurring phenomena. Engineers have leveraged such patterns for applications like atomic force microscopy, rotary pumps, cam gears, etc. One of the main characteristics of this pattern is that it is contained in a limited area, which is finely swept through by the curves in the pattern. Suppose, if a team of mobile robots wants to trace these patterns, e.g. for surveying an area, what kind of control laws will ensure that the robots trace trochoidal patterns? My doctoral dissertation explores the problem of geometric pattern formation by a group of autonomous agents. The patterns are formed by the trajectories of the agents, which are modelled either as single integrator kinematics or double integrator dynamics. The patterns are annular, which can either be closed or can cover the entire space. The proposed control laws are distributed, which is an extension of the consensus protocol. The class of patterns generated by these control laws falls within trochoidal curves. There is no restriction on the underlying graph topology. The proposed control laws are based on distributed linear consensus protocol. The necessary and sufficiency conditions for pattern formation for a more general graph topology, given that the agents are modelled as single integrators or double integrators are derived. Computer simulations and multi-robot experiments are presented to validate the theoretical findings.