Short range and long range coupling in stochastic functional self organization

A new stochastic model for the stochastic functional self-organization is proposed. Our model does not require any hierarchical decision maker or direct communication between the individuals in order to organize the environment. The environment is a two-dimensional rectangular lattice with a number of initially random distributed physical objects which have to be sorted by some individuals – random-walk like robots. The goal of the system's dynamics is to organize, i.e. to sort, the physical objects in order to form some well defined lattice structures (clusters or even more general texture).

We present some theoretical arguments and numerical simulations to support the idea that our new algorithm represents a powerful tool in studying collective sorting.