Dynamics and thermodynamics of a gas of automata

We consider a system of point charges interacting within a cone of vision and confined by an external potential, as a simple model of individuals provided with vision. The non Newtonian nature of the interaction introduces dissipative effects which are balanced by a memory mechanism. The two-body system is amenable to quadrature, whereas the N ≫ 1 body system exhibits crystal-like and disordered states with a non-trivial phase diagram if the interaction range and memory persistence are chosen as control parameters.