Eulerian Walker On A Square Lattice

Abstract

In this thesis, we study the asymptotic shape of the region visited by Eulerian walkers in a square lattice using monte carlo simulations. For a single walker, this region was found to be a perfect circle. We extended the study for two Eulerian walkers that start their walks from two different origins on the lattice. Our preliminary study suggests that the shape of the region is likely to be circular if both walkers rotate the direction of arrows on the lattice in the same sense. The shape of the region changes to elliptical if the two walkers rotate the direction of arrows on the lattice in the opposite sense.