(a) Standard deviation of grid field distances for all grid fields from all rats. Left: Before wall removal. Each dot represents one grid field and is color coded according to the standard deviation of distances to all neighboring fields within 130% of the cell’s average grid spacing in A, B, and AB (blue = minimum standard deviation in A|B and AB; red = maximum standard deviation in A|B and AB; n =128 cells, 1576 fields, 10 rats). Right: After wall removal (n =128 cells, 1447 fields, 10 rats). To compute average local standard deviations, standard deviations were sorted into square windows of side length 16 cm and averaged (see Fig. 3b, c). Scale bar, 50cm.(b) Local grid field offset as a function of distance from partition wall. Average field offset between A|B or AB and a template grid pattern determined from A (A|B vs. template in black; AB vs. template in red; offsets are binned into 10th percentile bands of 200 x 20 cm each, mean ± s.e.m., n = 128 cells). Grey stippled line indicates location of the former partition wall. (c) As in a but for a template pattern determined from B. Note, before wall removal phase offsets change abruptly in the center percentiles and approximate a step function. After wall removal, phase offsets change more linearly between A and B, indicating translocation of single grid fields into a pattern that is locally continuous throughout the environment. To quantify this transition, a linear regression was fit to the data from 10% bands spanning from the distal north wall in A to the distal south wall in B, as well as a step function with the step at the position of the partition wall. The residual mean square root (r.m.s.) for differences between data and step function increased when the wall was removed (r.m.s. expressed as percentage grid spacing for A|B vs. AB: 2.0% vs. 4.0%, square residuals A|B vs. AB: t(38) = 2.1, P = 0.04, two-sided Student’s t-test). The residual mean square root for differences between data and linear regression decreased (r.m.s. A|B vs. AB: 4.3% vs. 2.2%, square residuals A|B vs. AB: t(38) = 3.9, P = 3.3 x 10−4, two-sided Student’s t-test), suggesting that translocation of firing locations decreased gradually with distance from the partition wall. This trend was generally upheld when we analyzed data from subsets of grid cells with either small or large grid scales (small: 44 cm to 61 cm, n = 38 cells, r.m.s. step function A|B vs AB: 2.4 % vs. 3.6 %, r.m.s. linear regression A|B vs AB: 3.6% vs. 2.0%; large-scale grid cells range: 84 cm to 136 cm, n = 38 cells, r.m.s. step function A|B vs AB: 2.9% vs. 4.9%, r.m.s. linear regression A|B vs AB: 3.5% vs. 2.1%). The progression towards a linear change in offsets from the template indicates that local grid coherence increased throughout the environment.