We study an Eulerian walker on a square lattice, starting from an initial randomly oriented background using Monte Carlo simulations. We present evidence that, for a large number of steps N , the asymptotic shape of the set of sites visited by the walker is a perfect circle. The radius of the circle increases as N1/3, for large N , and the width of the… (More)

@article{Kapri2009AsymptoticSO,
title={Asymptotic shape of the region visited by an Eulerian walker.},
author={Rajeev Kapri and Deepak Dhar},
journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
year={2009},
volume={80 5 Pt 1},
pages={051118}
}