Controlling a group of unmanned autonomous vehicles (agent) to reach a given point is an active area in control theory. Gradient-based extremum seeking control as an non-model based optimization algorithm provides a good tool for solving this problem. Localization of an unknown source is one of gradient-based extremum seeking control algorithms. In source localization problem, the agent must find the unknown location of a source by upgrading an static map. The intensity of the signal emitted from the source is assumed to have a maximum vale at the source position and decreases as the distance drops. In this thesis, by using extremum seeking control and diffusion heat equation, the problem of formation of groups of holonomic agents as an multi-agent system is investigated. For the mathematical description of multi-agent systems , it is typically distinguished between the discrete and the continuous approach. The latter is particularly suited for systems involving a large number of agents and a multi-agent system is presented using a partial differential equation. By controlling a partial differential equation in order to converge to the equilibrium solution, a desired formation could be achieved. In this thesis, the diffusion heat equation with its boundary control is proposed to achieve the desired formation of a continuum of holonomic agents. Controlling boundary conditions which are an extremum seeking control, causes two ends of a continuum which are named as an anchor to be in a desired position near an unknown source and at two ends of the optimal formation. The diffusion heat equation causes interior agents which are named followers to deploy on an equilibrium profile of the equation and form an optimal formation around an unknown source. By using two similar diffusion heat equation, planar multi-agent line formation was obtained. With the aim of deploying holonomic agents into palnar curves, the general form of the diffusion heat equation and the complex diffusion heat equation were used. The general form of the diffusion heat equation does not give a complete formation and the extremum seeking control could not be used. Different geometric planar curves are formed by using a complex diffusion heat equation. In particular, by using a complex diffusion heat equation and extremum seeking control of boundary conditions, it is possible to obtain a circle with a desired radius around an unknown source. In each case, the diffusion heat equation will be spatialy discretized by central three-point differencing approximation. By spatialy discretizing the heat equation, decentralized control laws are obtained for agents that are in a chain-like communication topology. Analysis of the stability of the provided dynamics in each case has been made and numerous simulation s of the theoretical arguments have been presented. Key Words : Averaging , Extremum seeking , Diffusion heat equation , Multi-agent formation