Figure 1.

The grid cell spatial pattern. Different descriptions of the grid suggest different underlying mechanisms. The simplest descriptions as (A) an equilateral triangular tessellation or (B) a hexagonal grid suggest no obvious mechanism. (C) The pattern can be thought of as inactivity-surrounded place fields packed as closely as possible, which leads to Kropff and Treves (2008). Alternatively, the regularity of the pattern suggests that perhaps only a small segment, e.g., (D) a rhombus (skewed rectangle) or a rectangle large enough for (E) only one or (F) two or more appropriately spaced fields, is represented and when the animal walks off the segment it re-enters from the other side. If a rectangle containing only one field is used, it must be twisted so that walking off the bottom on the left brings the animal to the top on the right (the top edge is shifted by half its width, see dashed rectangle), while walking off the left or right sides wraps around normally. The grid can also be thought of as the overlap or interference between other spatial patterns, such as (G) smaller scale grids or (H) sinusoid-like gratings, not unlike a Fourier decomposition of the grid, and this produces the temporal interference models when generalized to the temporal domain. Note that in all figures spatial plots are shown in perspective to distinguish them from 2D plots of neural activities or synaptic weights.