  Grid cells in the medial entorhinal cortex (MEC) respond when an animal
occupies a periodic lattice of "grid fields" in the environment. The grids are
organized in modules with spatial periods, or scales, clustered around discrete
values separated by ratios in the range 1.2--2.0. We propose a mechanism that
produces this modular structure through dynamical self-organization in the MEC.
In attractor network models of grid formation, the grid scale of a single
module is set by the distance of recurrent inhibition between neurons. We show
that the MEC forms a hierarchy of discrete modules if a smooth increase in
inhibition distance along its dorso-ventral axis is accompanied by excitatory
interactions along this axis. Moreover, constant scale ratios between
successive modules arise through geometric relationships between triangular
grids and have values that fall within the observed range. We discuss how
interactions required by our model might be tested experimentally.
