Research Letter

Kleinberg Navigation on Anisotropic Lattices

Figure 2

Extrapolation results for (a) lattice and (b) angular anisotropies. Extrapolating to 1 / I n 2 𝐿 0 with a linear least-squares fit to the curves in Figure 1 shows excellent convergence of 𝛼 ( ) to the expected value of 𝑑 = 2 . Good values should occur when the curves are flattest, which happens roughly around 0.25. A more robust fitting procedure could be used, but the accuracy of these results implies that it is unnecessary. The horizontal lines at 𝛼 = 2 provide a guide for the eye.
346543.fig.002a
(a) Lattice
346543.fig.002b
(b) Angle