a, Grid orientations (φ) can only be compared across contexts relative to some common reference frame. Here, we used the Squircle as the common reference frame; however, this reference frame choice may have been arbitrary, particularly because participants were not exposed to the Squircle until after having already learned the location-context associations in the Square and Circle. To provide further evidence for grid realignment, we therefore tested whether φs were differentially aligned to local orientational cues in the Square and Circle. In square environments, φ has been found to be offset 7.5° from the boundaries26,27. Since φ ranges between 0°–60°, we tested whether Sq φ clustered around four possible angles, each 7.5° from one of the two cardinal axes of the square boundaries. To do so, we folded the grid orientations of all participants by φ mod 15°, which would align all hypothesis-consistent alignments to 7.5° in a circular 0° to 15° space. b, We also tested whether φ was reliably aligned to the Sq or Ci distal cues, either directly (0° offset from a distal cue) or maximally offset between distal cues (45° offset from a distal cue, since distal cues were offset from each other by 90° in each context). In addition to 0° offset, a 45° offset was tested because a prior report suggests that in sparse circular VR-environments with only distal orienting cues, φ is maximally offset from the cues (rather than aligned) (Schroeder, T. N. et al. (2018) Entorhinal cortex minimises uncertainty for optimal behaviour. BioRxiv 166306). Since φ ranges between 0°–60°, we thus tested whether φ clustered around four possible angles in each context. To do so, we folded the grid orientations of all participants by φ mod 15°, which would align all hypothesis-consistent alignments to 12° in the Sq and 3° in the Circle, in a circular 0° to 15° space. c, Boundary and distal cue φ alignment. Middle: average φ in each participant (n = 24) in the Sq (red squares, top) and Ci (blue circles, bottom). Left and right: histograms of average φ across participants, modulo 15°. In the Sq (left), φ clustered around 7.5° (V-test, V = 5.96, p = 0.043), consistent with alignment to the square boundaries, but not around 12° (V = −4.077, p = 0.880) which would have been consistent with alignment to the distal cues. In the Ci (right), φ clustered around 3° (V = 8.63, p = 0.006), consistent with reliable distal cue alignment. Since grid orientations aligned to different local cues in each context, this provides further support for the existence of grid-like realignment between the two training contexts.