  We propose a mechanism enabling the appearance of border cells -- neurons
firing at the boundaries of the navigated enclosures. The approach is based on
the recent discovery of discrete complex analysis on a triangular lattice,
which allows constructing discrete epitomes of complex-analytic functions and
making use of their inherent ability to attain maximal values at the boundaries
of generic lattice domains. As it turns out, certain elements of the
discrete-complex framework readily appear in the oscillatory models of grid
cells. We demonstrate that these models can extend further, producing cells
that increase their activity towards the frontiers of the navigated
environments. We also construct a network model of neurons with border-bound
firing that conforms with the oscillatory models.
