Q2R+Q2R AS A UNIVERSAL BILLIARD

In this work we study the computing capabilities as well as some dynamical properties of an automaton called M4R. This automaton corresponds to the mixing of the energy profiles of two independent copies of the Q2R automaton with frustrations. We associate to each copy of a Q2R an equivalent automaton M2R, which, with the Margoluos neighborhood, exhibits the local changes of the Q2R energy.1 By doing so we generalize the dynamics by upgrading M2R according to four partitions of the lattice. This new dynamics — called M4R — is based on a local rule which corresponds to the local energy change of two independent copies of Q2R. The M4R model is reversible and conservative (magnetization is constant in time) and it has properties of a discrete billiard (as some of the hydrodynamics discrete versions of Navier-Stokes models). Moreover, this automaton has powerful computing capabilities. In fact, by using some special configurations of M4R, we exhibit universal gates and register that allow us to code any algorithm.