Virtual Fekete point configurations: a case study in perturbing complex systems

Abstract

Virtual environments have shown great promise as a research tool in science and engineering. In this paper, we study a classical problem in mathematics: that of approximating globally optimal Fekete point configurations. We found that a highly interactive virtual environment, combined with a time-critical computation, can provide valuable insight into the symmetry and stability of Fekete point configurations. We believe that virtual environments provide more natural interfaces to complex systems, allowing users to perceive, interpret and interact with the problem more rapidly.