(A) Individual examples of rate maps for three units in the STD and ROT20 sessions. Top, rate maps calculated in the room reference frame. Bottom, autocorrelograms, from which the orientations of the three canonical grid axes (dashed black: STD, solid white: ROT20) were extracted and the grid rotation (mean angular difference between the two sets of axes, noted to the right of the autocorrelograms) was calculated. Right, rotation-adjusted crosscorrelogram between the two rate maps, computed after the STD rate map was rotated to equalize the orientation of its grid with that in ROT20. Center (0,0) of the crosscorrelogram is marked with cross-hair. Phase shift (noted above the crosscorrelogram in x,y cm) is the vector between the center of the crosscorrelogram and that of its closest correlation field. Each example shows that the grid did not rotate as much as the box, under-rotating by 4°, 8°, and 3°. In contrast, there was little phase offset between the two grid patterns. Unit ID is at the left of the figure (r: rat number; d: day of recording; t: tetrode number; c: cell number on that tetrode). (B) All grid rotations in ROT20. Dashed lines indicate the expected grid rotation for ideally room-controlled (R) or platform-controlled (P) grids. The grids on average rotated in the CW direction, with an undershoot of ~6°. Note that because of the 60° rotational symmetry of the grids, the abscissa represents a circular coordinate system, with the −30° value equal to the +30° value. Grids of different scale (ordinate) responded equivalently (see Figure 8). (C) Phase shifts for the grids in B, calculated on rotation-adjusted crosscorrelograms as in A. Top: Absolute phase shift magnitude. The amount of phase shift was very small compared to the size of the platform (superimposed shape of the platform is to scale). Bottom: Phase shift magnitude as a proportion of grid period. When the phase shift for each cell was plotted as a fraction of the grid period for that cell, the average shift is much smaller than the size of an individual grid vertex (superimposed grid is in an arbitrary orientation).