Figure 2. Identical grid field translation.

Stepwise horizontal linear translation of identical, overlapping grid fields ($N=3$, $\sigma =1$) moving from the top left corner to the right and/or downwards on a rate map $(N=17)$ (A, C). EMD score is shown on the left while Pearson’s r is shown on the right. 12 steps are shown and scores are rounded for display (top panel - EMD vs Pearson). Grid maps were sliced from a larger map with sufficient fields and bins to support N*N steps. Initial grid maps were chosen by taking a slice from the wider map. Scores from remapping tested across N*N different shifts from the initial grid map (0 to N combinations) (bottom panel). EMD and Pearson’s r scores tested at N*N different centroid positions on the wider grid (B, D). Scores for horizontal and diagonal translations along the rate map are shown for all rows $(N=17)$ (top panel). Heatmap showing the gradient of scores for both raw and inverted EMD (left and center) and for Pearson’s r (right) (bottom panel).